Production and Costs - Class 12 Economics - Chapter 3 - Notes, NCERT Solutions & Extra Questions
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Extra Questions - Production and Costs | Microeconomics | Economics | Class 12
If the cost of 1 apple is $₹ x$ and 1 chocolate is $₹ y$, then the cost of half a dozen apples and 2 chocolates is
A) $(6x + 2y)$
B) $(6x - 2y)$
C) $(2x + 6y)$
D) $(2x - 6y)$
The correct option is A) $(6x + 2y)$.
Cost of one apple = ₹$x$ Cost of one chocolate = ₹$y$
The cost for half a dozen apples (which is 6 apples) would be: $$ 6 \times x = 6x $$
The cost for 2 chocolates would be: $$ 2 \times y = 2y $$
Thus, the total cost for half a dozen apples and 2 chocolates is: $$ 6x + 2y $$
An article was sold for Rs. 250 with a profit of 5%. Find the cost price.
Selling price of the article = Rs. 250
Profit = $5%$
To find the cost price (CP), we use the formula: $$ CP = \frac{100 \times \text{SP}}{100 + \text{profit percentage}} $$ Inserting the values we have: $$ CP = \frac{100 \times 250}{105} $$ $$ CP = \frac{25000}{105} \approx 238.10 $$ So, the cost price of the article was about Rs. 238.10.
Annual depreciation of machine is Rs. 40,000, cost of machine is Rs. 5,00,000, rate of depreciation according to straight-line method will be -
A) 9% B) 18% C) 16% D) 8%
The correct answer is D) 8%.
Solution:To find the rate of depreciation using the straight-line method, use the formula:
$$ \text{Depreciation Rate} = \left(\frac{\text{Annual Depreciation}}{\text{Cost of Machine}}\right) \times 100 $$
Plugging in the values:
$$ \text{Depreciation Rate} = \left(\frac{40,000}{500,000}\right) \times 100 = 8% $$
Hence, the rate of depreciation is 8%.
A producer supplies 100 units of a good at a price of Rs. 20 per unit. Price elasticity of supply is 2. At what price will he supply 50 units? Calculate.
Assume that the producer supplies 50 units at a price of Rs. $X$. The initial conditions are as follows, with $P = \text{Rs. } 20$ and $P_1 = \text{Rs. } X$. The change in price is thus $\Delta P = Rs. (X - 20)$.
The change in quantity supplied is a reduction of 50 units: $$ \Delta Q = -50 \text{ units} $$
Given that the price elasticity of supply ($E_s$) is 2: $$ E_{s} = 2 $$
We use the formula for price elasticity of supply: $$ E_s = \frac{P}{Q} \times \frac{\Delta Q}{\Delta P} $$
Substituting in the known values, we find: $$ 2 = \frac{20}{100} \times \frac{-50}{X - 20} $$
Simplifying further: $$ 2 = \frac{-10}{X - 20} $$
Solving for $X$: $$ 2 = \frac{-10}{X - 20} \Rightarrow X - 20 = \frac{-10}{2} \Rightarrow X - 20 = -5 \Rightarrow X = -5 + 20 = 15 $$
Thus, the new price at which 50 units will be supplied is Rs. 15.
Q. Which of the following accurately describes "Marginal Cost"?
A. Marginal cost is the cost that is spent by the government for the welfare of marginal sections in society.
B. Marginal cost is the cost that is added by producing an additional unit of a product or service.
C. Marginal cost is the benefit that is foregone or waived by an investor, individual or business in choosing one option among many options.
D. Marginal cost is the cost that has been spent and cannot be recovered.
The correct option is B
Marginal Cost is defined as the cost that is incurred when producing one additional unit of a product or service. This cost is added from the production of that single extra unit. Thus, the accurate choice that describes this concept is:
Option B: Marginal cost is the cost that is added by producing an additional unit of a product or service.
Explanation:Marginal cost is crucial in economics as it helps determine the most efficient point of production and pricing. It plays a significant role in decision-making for expanding production or optimizing operational efficiencies. Other options do not correctly represent the concept of marginal cost:
Optional Cost: This involves benefits or costs that are foregone by choosing one alternative over others in a variety of options.
Sunk Cost: This cost has already been incurred and cannot be recovered.
In summary, Marginal Cost pertains directly to the changes in costs due to the production of an additional unit, making Option B the correct description.
What is the profit percentage acquired when the cost price is ₹200 and selling price is ₹350?
A) 25% B) 50% C) 75% D) 100%
The correct option is C$$ 75% $$
To solve this, calculate the profit first: $$ \text{Profit} = \text{Selling Price (S.P)} - \text{Cost Price (C.P)} = ₹350 - ₹200 = ₹150. $$
Next, compute the profit percentage: $$ \text{Profit %} = \left(\frac{\text{Profit}}{\text{C.P}}\right) \times 100 = \left(\frac{150}{200}\right) \times 100 = 75%. $$
Thus, the profit percentage acquired is 75%.
Social Costs = Private Cost (consumer cost + producer cost) + External Cost (everyone else's cost).
A) True
B) False
The correct option is A) True.
True. Social costs are indeed calculated as the sum of Private Cost (which includes both consumer and producer costs) plus the External Cost (costs incurred by everyone else). Thus, the formula provided in the question correctly represents how social costs are determined: $$ \text{Social Costs} = \text{Private Cost} + \text{External Cost} $$ where Private Cost includes costs to consumers and producers, and External Cost encompasses the costs experienced by the broader society that are not accounted for by private costs.
Maria plans to rent a boat. The boat rental costs 60 per hour, and she will also have to pay for a water safety course that costs 10. Maria wants to spend no more than 280 for the rental and the course. If the boat rental is available only for a whole number of hours, the maximum number of hours for which Maria can rent the boat is _____
Let's denote the number of hours Maria intends to rent the boat as $n$. The rental cost per hour is $60. Additionally, Maria must pay a $10 water safety course fee. Thus, the total cost can be formulated as: $$ 60n + 10 $$ Maria aims to keep her expenditures below or equal to $280.
Setting up the inequality for her total expenses: $$ 60n + 10 \leq 280 $$ Solving for $n$ gives: $$ 60n \leq 270 \ n \leq \frac{270}{60} = 4.5 $$
Since the boat can only be rented in whole hours, we need to take the whole number part of $4.5$, which is 4. Therefore, the maximum number of hours Maria can rent the boat is 4 hours.
The total-cost curve is _______________ the total-product curve.
A steeper than
B the mirror image of
C parallel to
D coincidental with
The correct answer is B, the mirror image of.
Explanation: The total-cost curve is often considered the mirror image of the total-product curve. This relationship derives from the law of variable proportions, which describes how output changes when the amount of one input is varied while other inputs are kept constant. This law influences the shapes of both curves, showing their interdependence in production and cost analysis.
Aayushi buys a TV for Rs 12,000 and spends Rs 500 on cartage. She finally sells it back for Rs 10,000 after 3 months. Find her loss amount.
A) Rs 2600
B) Rs 2500
C) Rs 2700
D) Rs 2400
The correct answer is Option B which is Rs 2500.
Calculation of Loss:
Total Cost Price (CP) of the TV including cartage: $$ CP = \text{Price of TV} + \text{Cartage} = Rs\ 12000 + Rs\ 500 = Rs\ 12500 $$
Selling Price (SP) of the TV: $$ SP = Rs\ 10000 $$
Therefore, the Loss incurred by Aayushi is calculated as: $$ \text{Loss} = CP - SP = Rs\ 12500 - Rs\ 10000 = Rs\ 2500 $$
Hence, the amount of loss Aayushi suffered is Rs 2500.
How many pencils costing ₹5 each can one buy for exactly ₹50?
A) 8
B) 10
C) 12
D) 14
The correct answer is Option B: 10
Given:
Each pencil costs ₹5
Total available money is ₹50
Using the basic formula for determining quantity, $$ \text{Quantity} = \frac{\text{Total Price}}{\text{Unit Price}} $$
Applying the given values, $$ \text{Quantity} = \frac{50}{5} = 10 $$
Thus, one can buy 10 pencils for exactly ₹50.
If the cost of 1 dozen bananas is Rs. 48, then the cost of 5 such bananas is:
A) Rs 24
B) Rs 20
C) Rs 25
D) Rs 28
The correct answer is B) Rs 20.
First, we know that one dozen bananas corresponds to $12$ bananas. Given that the cost for 1 dozen bananas is Rs. 48, we can calculate the cost per banana as follows: $$ \text{Cost per banana} = \frac{Rs. , 48}{12} = Rs. , 4 $$
To find the cost of 5 bananas: $$ \text{Cost of 5 bananas} = 5 \times Rs. , 4 = Rs. , 20 $$
Thus, the cost of 5 such bananas is Rs. 20.
If the unit price per pencil is ₹10, then what is the cost of 50 pencils?
A) ₹400
B) ₹500
C) ₹440
D) ₹550
The correct answer is Option B: ₹500
The unit price per pencil is given as: $$ ₹10 $$ The quantity of pencils to be purchased is: $$ 50 $$ The total cost for these pencils is calculated by multiplying the number of pencils by the unit price per pencil: $$ 50 \times ₹10 = ₹500 $$ Thus, the cost for 50 pencils is ₹500.
Rahim bought a dozen pencils at ₹5 per pencil. He sold half of them at ₹6 per pencil and the other half at ₹7 per pencil. Find the total profit.
A) ₹12
B) ₹24
C) ₹16
D) ₹18
The correct answer is D) ₹18.
To find the total profit, we need to calculate the total cost price (CP) and selling price (SP) of the pencils:
Cost Price per pencil: ₹5
Cost Price for 12 pencils: $$ 12 \times ₹5 = ₹60 $$
Selling Price for the first half (6 pencils) at ₹6 per pencil: $$ 6 \times ₹6 = ₹36 $$
Selling Price for the second half (6 pencils) at ₹7 per pencil: $$ 6 \times ₹7 = ₹42 $$
Total Selling Price for 12 pencils: $$ ₹36 + ₹42 = ₹78 $$
The profit can be calculated by taking the difference between the total selling price and the total cost price: $$ \text{Profit} = SP - CP = ₹78 - ₹60 = ₹18 $$
Thus, Rahim made a total profit of ₹18.
A shopkeeper buys a raw material for Rs. 2000 and spends Rs. 400 on its decoration and packing. If he sold the article for Rs. 3200 including 16% sales tax, then find his profit percent.
A) 12%
B) 19%
C) 14.9%
D) 11.9%
The correct answer is:
Option C: 14.9%
Calculation of Sales Price (SP) excluding tax:
It's given that the selling price including 16% sales tax is Rs. 3200.
We can set up the equation where $x$ represents the sales price excluding tax: $$ x + 0.16x = 3200 $$ Simplifying this equation: $$ 1.16x = 3200 \quad \Rightarrow \quad x = \frac{3200}{1.16} = 2758.62 $$
Calculation of Cost Price (CP):
The shopkeeper spends Rs. 2000 on raw materials and Rs. 400 on decoration and packing.
Therefore, the total cost price is: $$ CP = 2000 + 400 = 2400 $$
Calculation of Profit and Profit Percentage:
The profit earned is: $$ \text{Profit} = SP - CP = 2758.62 - 2400 = 358.62 $$
The profit percentage is calculated using the formula: $$ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{358.62}{2400}\right) \times 100 \approx 14.94% $$
Rounding this value gives approximately 14.9%.
This demonstrates that the shopkeeper's profit percentage from the transaction is 14.9%.
A new computer costs Rs. 100,000. The depreciation of computers is very high as new models with better technological advantages are coming into the market. The depreciation is as high as 50% every year. How much will the cost of the computer be after two years?
The initial cost of the new computer is Rs. 100,000 and it depreciates at a rate of 50% each year. We need to determine its value after two years.
To calculate the depreciation, we use the formula for depreciation over a period of time:
$$ A = P \left(1 - \frac{R}{100}\right)^T $$
Where:
$A$ is the amount after $T$ years.
$P$ is the principal amount (initial value of the computer).
$R$ is the rate of depreciation per annum.
$T$ is the time in years.
Substitute the values:
$P = 100,000$
$R = 50$
$T = 2$
$$ A = 100000 \left(1 - \frac{50}{100}\right)^2 $$
Simplifying further,
$$ A = 100000 \left(\frac{1}{2}\right)^2 = 100000 \times \frac{1}{4} = 25,000 $$
Thus, the cost of the computer after 2 years is Rs. 25,000.
A shopkeeper buys a number of books for ₹80. If he had bought 4 more books for the same amount, each book would have cost ₹1 less. He bought _______ books.
A 16
B 18
C 14
D 12
Let the number of books purchased initially be $x$. The total cost for these books is ₹80, making the cost per book: $$ \text{Cost per book} = \frac{80}{x} $$
If he purchased 4 additional books for the same total cost, the number of books becomes $x + 4$, leading to a new cost per book: $$ \text{Cost per book} = \frac{80}{x+4} $$
Given that this new cost is ₹1 less than the initial cost per book: $$ \frac{80}{x} - 1 = \frac{80}{x + 4} $$
Solving for $x$, simplify and set up the equation: $$ \frac{80}{x} - \frac{80}{x + 4} = 1 $$ $$ 80 \left(\frac{1}{x} - \frac{1}{x + 4}\right) = 1 $$ $$ 80 \left(\frac{x + 4 - x}{x(x + 4)}\right) = 1 $$ $$ \frac{320}{x^2 + 4x} = 1 $$ $$ x^2 + 4x - 320 = 0 $$
Factoring the quadratic: $$ x^2 + 20x - 16x - 320 = 0 $$ $$ (x + 20)(x - 16) = 0 $$
The solutions to this equation are $x = -20$ or $x = 16$. Since the number of books cannot be negative, we have: $$ x = 16 $$
Thus, the shopkeeper bought 16 books. This is option A 16.
If the cost of 60 chocolates is ₹300, then what is the cost of 15 chocolates?
A) ₹100
B) ₹50
C) ₹150
D) ₹75
The correct option is D) ₹75
Given:
- Cost of 60 chocolates = ₹300
- To find: Cost of 15 chocolates
Since 15 chocolates is a quarter ( $\frac{1}{4}$) of 60 chocolates, the cost for 15 chocolates will be a quarter of the cost for 60 chocolates.
To compute this:
- Half of ₹300 is ₹150.
- Half of ₹150 (which is a quarter of ₹300) is ₹75.
Therefore, the cost of 15 chocolates is ₹75.
A shopkeeper sells an article at a gain of 10%. Had he sold it at a loss of 20%, its selling price would have been Rs 180 less. What is the cost price of the article?
A. Rs 630
B. Rs 600
C. Rs 580
D. Rs 615
E. None of these
We need to determine the cost price of the article. Let's use the symbols provided in the problem:
Let the cost price be Rs $x$.
The selling price at a gain of 10% is $1.1x$.
The selling price at a loss of 20% is $0.8x$.
According to the given information, the difference between these selling prices is Rs 180:
$$ 1.1x - 0.8x = 180 $$
Simplifying the equation:
$$ 0.3x = 180 $$
Solving for $x$:
$$ x = \frac{180}{0.3} = 600 $$
Therefore, the cost price of the article is Rs 600.
Using a different approach, let’s verify the results with the following formula:
$$ \text{C.P.} = \left( \frac{180}{10 + 20} \right) \times 100 $$
Substitute the values:
$$ \text{C.P.} = \left( \frac{180}{30} \right) \times 100 = 6 \times 100 = 600 $$
So, the cost price of the article is Rs 600.
Correct Option: B Rs 600
Find the total cost of fencing and ploughing a rectangular field ($16 \mathrm{~m} \times 8 \mathrm{~m}$) at the rate of ₹10/m and $₹10/m^2$ respectively.
A. ₹ 1700
B. ₹ 1750
C. ₹ 1760
D. ₹ 1660
The correct option is $\mathbf{C}$ ₹1760
Let's break down the calculation step-by-step:
Step 1: Find the Perimeter of the Field
The perimeter of a rectangle is calculated as: $$ \text{Perimeter} = 2(L + b) $$
Given: $$ L = 16 , \text{m} $$ $$ b = 8 , \text{m} $$
So, $$\text{Perimeter} = 2(16 , \text{m} + 8 , \text{m}) = 2 \times 24 , \text{m} = 48 , \text{m} $$
Step 2: Find the Area of the Field
The area of a rectangle is given by: $$ \text{Area} = L \times b $$
Using the given dimensions: $$ \text{Area} = 16 , \text{m} \times 8 , \text{m} = 128 , \text{m}^2 $$
Step 3: Find the Cost of Fencing
The cost of fencing per meter is ₹10. So the total cost of fencing will be: $$ \text{Cost} = ₹10 \times 48 , \text{m} = ₹480 $$
Step 4: Find the Cost of Ploughing
The cost of ploughing per square meter is ₹10. So the total cost of ploughing will be: $$ \text{Cost} = ₹10 , / , \text{m}^2 \times 128 , \text{m}^2 = ₹1280 $$
Step 5: Calculate the Total Cost
The total cost is the sum of the cost of fencing and the cost of ploughing: $$ \text{Total cost} = ₹480 + ₹1280 = ₹1760$$
Therefore, the total cost is ₹1760.
Ted's uncle wants to put tiles on his home floor. The total area of the floor to be tiled is 360000 square cms. Find the cost of tiling at ₹ 20 per square metre.
A. ₹ 360
B. ₹ 3600
C. ₹ 720
D. ₹ 7200
The correct answer is Option C: ₹ 720
Given Information:
Cost of tiling: ₹20 per square metre
Total area to be tiled: 360,000 square cms
Conversion:
1 metre = 100 cm, therefore:
$$ 1 , \text{m}^2 = 100 , \text{cm} \times 100 , \text{cm} = 10,000 , \text{cm}^2 $$
Calculation:
To convert the given area from square centimeters to square meters:
$$ \text{Area of floor to be tiled} = 360,000 , \text{cm}^2 $$
$$ = \frac{360,000 , \text{cm}^2}{10,000 , \text{cm}^2/\text{m}^2} $$
$$ = 36 , \text{m}^2 $$
Total Cost:
The cost for tiling is calculated as follows:
$$ \text{Total cost} = \text{Rate per square metre} \times \text{Total area in square metres} $$
$$ = 20 , \text{₹/m}^2 \times 36 , \text{m}^2 $$
$$ = \text{₹ 720} $$
Hence, the total cost of tiling is ₹ 720.
Suppose that a firm's total fixed cost is Rs. 100, and the marginal cost schedule of a firm is the following:
Output (in units) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Marginal cost (in Rs) | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
(i) Is the MC curve U-shaped?
(ii) Derive the AVC schedule. Will the AVC curve be U-shaped? Discuss.
Given:
Output (in units) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Marginal Cost (MC) (in Rs) | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
We need to answer the following parts of the question based on this data:
(i) Is the MC curve U-shaped?
The Marginal Cost (MC) values are given as: 10, 20, 30, 40, 50, 60, and 70 for each subsequent unit of output from 1 through 7. Here, we observe that the cost increases consistently by a constant amount (Rs. 10) for each unit increase in output. Therefore, the MC curve is not U-shaped; rather, it is an upward-sloping straight line through the origin since the slope is constant and equal to 10.
(ii) Derive the AVC schedule. Will the AVC curve be U-shaped? Discuss.
To derive the Average Variable Cost (AVC), we first need to calculate the Total Variable Cost (TVC) by successively adding the marginal costs for each additional unit of output:
Output (in units) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Marginal Cost (MC) (in Rs) | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
Total Variable Cost (TVC) (in Rs) | 10 | 30 | 60 | 100 | 150 | 210 | 280 |
Average Variable Cost (AVC) (in Rs) | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
The AVC is calculated using the formula:
$$ \text{AVC} = \frac{\text{TVC}}{\text{Output}} $$
Using this formula, we calculate AVC for each level of output:
$ \text{AVC at Output = 1 unit} = \frac{10}{1} = 10$
$ \text{AVC at Output = 2 units} = \frac{30}{2} = 15 $
$\text{AVC at Output = 3 units} = \frac{60}{3} = 20 $
$ \text{AVC at Output = 4 units} = \frac{100}{4} = 25$
$ \text{AVC at Output = 5 units} = \frac{150}{5} = 30$
$ \text{AVC at Output = 6 units} = \frac{210}{6} = 35$
$ \text{AVC at Output = 7 units} = \frac{280}{7} = 40 $
The AVC values calculated here show a continuous increase. Therefore, like the MC curve, the AVC curve is not U-shaped. Instead, it is an increasing curve. This trend arises because the marginal cost (MC) is consistently rising, leading to a steady increase in the average variable cost (AVC).
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Ask Chatterbot AINCERT Solutions - Production and Costs | Microeconomics | Economics | Class 12
Explain the concept of a production function.
The production function is a mathematical model that describes the relationship between the inputs used in production and the maximum output that can be produced with those inputs. It is a way to represent the technology of a firm or an economy and specifies how much output (like goods or services) can be obtained from various combinations of different factors of production such as labor, capital, and land.
A production function takes the form $q = f(L, K)$, where:
( q ) is the quantity of output produced,
( L ) stands for labor (amount of labor used),
( K ) stands for capital (amount of capital used).
The function shows the highest amount of output that can be produced with given amounts of labor and capital. It assumes all resources are used efficiently. Changes in the level of inputs or improvements in technology can shift or change the shape of the production function, indicating different levels of output.
What is the total product of an input?
The Total Product (TP) of an input in economics refers to the total quantity of output produced as a result of varying a single input, while keeping all other inputs constant. It represents the relationship between the variable input and the total amount of output produced. For instance, if increasing the amount of labour results in more goods produced, the TP chart or graph will show this relationship for different levels of the labour input.
What is the average product of an input?
The Average Product (AP) of an input is defined as the output per unit of the variable input. It is calculated using the formula:
$$ AP_{L} = \frac{TP_{L}}{L} $$
Here:
(AP_{L}) is the Average Product of labour.
(TP_{L}) is the Total Product, which is the total output produced by the labour.
(L) is the amount of the variable input (labour) used.
This measure helps in assessing the productivity of the input, showing how much output is produced, on average, per unit of input.
What is the marginal product of an input?
The marginal product of an input is defined as the change in output produced as a result of a one-unit increase in that input, while all other inputs are held constant. Mathematically, it is expressed as:
$$ MP_L = \frac{\Delta TP_L}{\Delta L} $$
where $MP_L$ is the marginal product of the input, $\Delta TP_L$ represents the change in total product resulting from the change in the input, and $\Delta L$ is the change in the level of the input. This concept helps in understanding how the addition of a unit of input contributes to the production output.
Explain the relationship between the marginal products and the total product of an input.
The relationship between the marginal products (MP) and the total product (TP) of an input is fundamental in understanding how input changes affect output levels in production. Here's how these concepts are related:
Total Product (TP): This is the total quantity of output produced given a certain amount of input, while keeping all other inputs constant.
Marginal Product (MP): This represents the additional output that results from the use of one more unit of the input, with all other inputs held constant.
Relationship:
For any given level of an input, the Total Product is equivalent to the sum of the Marginal Products of each unit of that input up to that level. This means that if you cumulatively add the marginal outputs contributed by each input unit, you get the total output.
Initially, as inputs increase, TP usually increases at an increasing rate because the MP might be rising due to more efficient utilization of inputs (early stages of production).
Once MP reaches its maximum and starts to decline (due to diminishing marginal returns), the TP continues to increase, but at a decreasing rate. This occurs because each additional unit of input contributes less to the output than the previous units.
When MP becomes zero, TP reaches its peak, indicating that any further increase in input does not contribute to the output, and TP begins to remain constant or could decrease if MP becomes negative.
Thus, the progression from increasing returns, peaking to decreasing returns as input is added, is visually represented in the relationship between MP and TP. The MP is a key driver in the change of the slope of the TP curve.
Explain the concepts of the short run and the long run.
Short Run and Long Run in Economics
In economics, the concepts of the short run and the long run differentiate the time periods during which producers can adjust varying levels of production inputs.
Short Run
In the short run, at least one factor of production is fixed, meaning it cannot be varied or adjusted. This fixed factor limits the firm's ability to adjust to changes in demand or production conditions.
For example, a company might have a fixed number of machines (capital) and can only adjust the number of workers (labor) it employs.
Long Run
In the long run, all factors of production can be varied. This means that a firm has the flexibility to adjust all inputs, such as labor, capital, and technology, to meet changes in demand or to maximize efficiency.
There are no fixed factors in the long run; everything can be adjusted or changed.
Differences
Flexibility: The short run is characterized by limited flexibility due to fixed inputs, while the long run offers complete flexibility to change any input.
Time Frame: The distinction in time frames is not quantitative (like days or months), but qualitative based on the ability to change inputs. The short run is the period during which the adjustments to some inputs are not feasible, whereas in the long run, adjustments to all inputs are possible.
Each period serves as a framework for analyzing different economic scenarios and decisions, impacting how firms respond to the market and strategize for growth and sustainability.
What is the law of diminishing marginal product?
The Law of Diminishing Marginal Product states that as more units of a variable input (like labor) are added to a fixed input (like land or machinery), the additional output (marginal product) produced by each additional unit of the variable input eventually decreases, after a certain point. This phenomenon occurs because initially the variable input complements the fixed inputs well, leading to increased productivity. However, as more of the variable input is added, it becomes less effective due to the limitations imposed by the fixed inputs, resulting in a decrease in the marginal product for each subsequent unit of the variable input added.
What is the law of variable proportions?
The Law of Variable Proportions states that as the quantity of one input (variable input) is increased, keeping all other inputs constant (fixed inputs), the marginal product of the variable input initially rises and after reaching a certain level, begins to decline. This phenomenon reflects the changing efficiency of input usage as production scales up.
Here's how it unfolds:
Initial Increase: At lower levels of employment of a variable input, there are adequate fixed inputs to accommodate an increase in the variable input, leading to an increase in output at increasing rates (marginal product increases).
Reaching Maximum Efficiency: The marginal product of the variable input reaches its maximum when the perfect balance between the variable input and fixed inputs is achieved.
Decline in Efficiency: As the variable input continues to increase beyond this optimal point, the fixed inputs become insufficient, leading to decreasing returns on additional units of the variable input (marginal product decreases).
This law is an expression of decreasing efficiency with over-utilization of an input in relation to other, more limited inputs.
When does a production function satisfy constant returns to scale?
A production function satisfies constant returns to scale when an increase in all inputs by a given proportion results in an increase in output by the same proportion. Mathematically, if a production function $q = f(x_1, x_2)$ exhibits constant returns to scale, then for any scalar $t > 1$, the production function satisfies:
$$ f(t x_1, t x_2) = t f(x_1, x_2) $$
This means that if all inputs are scaled (increased or decreased) by a factor of $t$, then the output will also scale by the same factor $t$. This condition indicates neither increasing nor decreasing efficiency with an increase in scale.
When does a production function satisfy increasing returns to scale?
A production function satisfies increasing returns to scale (IRS) when the proportional increase in the output is greater than the proportional increase in all inputs. Mathematically, if a production function is represented as $q = f(x_1, x_2)$, and we scale all inputs by a factor $t$ (where $t > 1$), the function exhibits IRS if:
$$ f(t x_1, t x_2) > t \cdot f(x_1, x_2) $$
This implies that when you increase the inputs by a certain percentage, the output increases by a even larger percentage, leading to a more than proportional increase in output compared to the increase in inputs.
When does a production function satisfy decreasing returns to scale?
A production function satisfies Decreasing Returns to Scale (DRS) when a proportional increase in all inputs results in an increase in output by a smaller proportion. Mathematically, if inputs are increased by a factor of $t$ (where $t>1$), and the production function is $q=f(x_1, x_2)$, then it exhibits DRS if:
$$ f(t \cdot x_1, t \cdot x_2) < t \cdot f(x_1, x_2) $$
This implies that the output is less than $t$ times the original output when the inputs are scaled up by the factor $t$.
Briefly explain the concept of the cost function.
The cost function in economics describes the least cost of producing each level of output given the prices of factors of production and technology. It determines the most cost-effective way for a firm to produce a desired level of output. For every output level, the firm will choose the combination of inputs that minimizes its production costs, considering the prices and technology available. This is important as it helps firms in decision-making regarding how to allocate their resources efficiently to maximize profit.
What are the total fixed cost, total variable cost and total cost of a firm? How are they related?
Total Fixed Cost (TFC)
Total Fixed Cost (TFC) refers to the expenses that do not change with the level of production. These costs are incurred regardless of whether the production is high or low. Examples include rent, salaries of permanent staff, and insurance.
Total Variable Cost (TVC)
Total Variable Cost (TVC) varies with the level of output. These costs increase as production increases and decrease as production falls. Examples include costs of raw materials, energy usage, and wages for hourly workers.
Total Cost (TC)
Total Cost (TC) is the sum of Total Fixed Cost and Total Variable Cost. Mathematically, it is expressed as: $$ TC = TVC + TFC $$
Relationship
TFC remains constant regardless of output level.
TVC changes with the level of production.
TC increases as output increases due to the increase in TVC, while TFC remains unchanged across different outputs. Thus, TC moves in response to changes in TVC, reflecting the firm's total expenditure on production.
What are the average fixed cost, average variable cost and average cost of a firm? How are they related?
Average Fixed Cost (AFC)
Average Fixed Cost (AFC) is the fixed cost per unit of output, calculated as: $$ AFC = \frac{TFC}{q} $$ where ( TFC ) is the total fixed cost and ( q ) is the quantity of output. This curve is always decreasing because ( TFC ) remains constant as output increases.
Average Variable Cost (AVC)
Average Variable Cost (AVC) is the variable cost per unit of output, defined by: $$ AVC = \frac{TVC}{q} $$ where ( TVC ) is the total variable cost. The shape of the AVC curve is typically 'U'-shaped due to the law of variable proportions.
Average Cost (AC) or Short Run Average Cost (SAC)
Average Cost (AC), also known as Short Run Average Cost (SAC), is the total cost per unit of output. It is the sum of AFC and AVC: $$ AC = AVC + AFC $$ $$ AC = \frac{TC}{q} = \frac{TVC + TFC}{q} $$
Relationship Among AFC, AVC, and AC
AFC is always falling as output increases, as it spreads the fixed cost over a larger quantity of output.
AVC typically exhibits a 'U'-shaped curve, decreasing initially due to increasing efficiency, and then increasing as diseconomies of scale set in.
AC also tends to have a 'U'-shaped curve, as it combines the attributes of AVC and AFC. AVC mainly influences the shape of the AC curve, but since AFC is continually decreasing, the AC curve may fall for a longer range of outputs before it starts to rise.
The sum of AFC and AVC at any given level of output gives the AC, reflecting the total average cost of production per unit of output. The minimum point of the AC curve is also significant as it represents the most efficient scale of production in the short run.
Can there be some fixed cost in the long run? If not, why?
In the long run, there are no fixed costs because all inputs are variable. This distinction originates from the definitions of the short run and the long run in economics. In the short run, at least one factor of production (such as capital or land) is fixed and cannot be altered, leading to fixed costs. However, in the long run, firms can adjust all factors of production based on their output needs. This flexibility allows firms to vary the levels of all inputs, eliminating the distinction between fixed and variable costs, as costs become entirely dependent on production levels. Therefore, fixed costs are specific to the short run where certain resources or inputs cannot be changed immediately or within a short time frame.
What does the average fixed cost curve look like? Why does it look so?
The Average Fixed Cost (AFC) curve is downward sloping and resembles a rectangular hyperbola. This specific shape results from the nature of fixed costs in economics:
Fixed Cost Definition: AFC is calculated as Total Fixed Cost (TFC) divided by quantity of output ($q$), i.e., $AFC = \frac{TFC}{q}$.
Constant TFC: The total fixed cost is constant regardless of the level of output. This constant nature of TFC and its division by increasing output quantities $q$ leads to the AFC decreasing as output increases.
Hyperbolic Relationship: Mathematically, since $TFC$ remains constant and $q$ increases, each additional unit of output spreads the fixed costs over more units, decreasing the average cost per unit, thereby creating a hyperbolic shape.
Asymptotic to Zero: As output approaches very large numbers, the AFC approaches zero but never actually reaches it, which is characteristic of a hyperbolic function.
Thus, as output increases, the per-unit fixed cost diminishes, forming this typical hyperbolic sloping curve.
What do the short run marginal cost, average variable cost and short run average cost curves look like?
The Short Run Marginal Cost (SMC), Average Variable Cost (AVC), and Short Run Average Cost (SAC) curves each have distinctive shapes:
SMC Curve: This curve is U-shaped. Initially, SMC decreases as the output level increases due to gaining efficiencies from the increased use of the variable input. However, after reaching a minimum point, SMC increases due to the diminishing returns of the additional units of the variable input.
AVC Curve: Also U-shaped, similar to the SMC curve. AVC decreases initially as output increases, reflecting more efficient use of variable inputs, but then starts rising after reaching its minimum point, paralleling the effects of diminishing returns.
SAC Curve: This curve is also U-shaped. It falls initially as output increases, primarily due to fixed costs being spread over a larger number of output units (decreasing the average fixed cost significantly initially). After a certain point, however, SAC begins to rise due to the rising AVC, which eventually outweighs the declining average fixed cost.
In summary, all three curves are U-shaped due to the initial efficiencies and subsequent diminishing returns experienced as output increases. The AVC and SAC curves start from similar points and SAC always remains above AVC because SAC includes both AVC and the positive average fixed costs.
Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
The Short-Run Marginal Cost (SMC) curve intersects the Average Variable Cost (AVC) curve at the minimum point of the AVC curve due to the relationship between the marginal cost and the average cost.
Here’s a concise explanation:
SMC represents the additional cost of producing one more unit of output.
AVC is the average of all variable costs per unit of output.
When AVC is decreasing, each additional unit of output costs less than the previous average, so the SMC (cost of an additional unit) is less than the AVC. This continues until AVC reaches its minimum. At the minimum point of AVC, the cost of producing an additional unit (SMC) equals the AVC. If the output is increased beyond this point, the cost of additional units becomes higher than the average, resulting in SMC being greater than AVC. Therefore, the SMC curve must intersect the AVC curve at its lowest point, as they are equal at this turn. This demonstrates that the point of minimum AVC coincides with an SMC equal to AVC.
At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.
The Short-Run Marginal Cost (SMC) curve cuts the Short-Run Average Cost (SAC) curve at the minimum point of the SAC curve. This phenomenon occurs because:
When SAC is decreasing, the additional cost to produce one more unit (SMC) is less than the average cost of production up to that point (SAC). This drives the average cost down.
As SAC begins to rise, it indicates that each additional unit costs more than the average of previous units. Hence, the marginal cost (SMC) becomes greater than the average cost (SAC).
The point where SMC equals SAC is where SAC reaches its minimum because it is the point where the cost of the additional unit produced (marginal cost) starts exceeding the average cost, reversing the downward trend of SAC. This is a critical equilibrium point where the two curves intersect.
Thus, the intersection of SMC and SAC at the minimum of SAC essentially illustrates the boundary between beneficial (cost-reducing) and detrimental (cost-increasing) production expansion in the short run.
Why is the short run marginal cost curve ‘U’-shaped?
The short run marginal cost (SMC) curve is ‘U’-shaped due to the law of variable proportions, which is also known as the law of diminishing marginal returns. This law describes how the marginal product of a variable input initially increases as more of it is employed, reaching a maximum point, and then decreases as additional units are used.
In the context of costs:
Initially Falling SMC: When additional units of the variable input are added to fixed inputs, they can be highly effective, increasing output at an increasing rate. This causes the marginal cost of each additional unit of output to fall.
Eventually Rising SMC: Beyond a certain point, as more of the variable input is added, it starts to produce less additional output per unit (diminishing marginal returns). This inefficiency arises because the fixed inputs become increasingly saturated with additional variable inputs, making them less productive. Consequently, the cost of producing each additional unit of output starts to rise.
Thus, due to increasing and then decreasing marginal returns, the SMC curve is 'U'-shaped, falling initially and rising after reaching a minimum point.
What do the long run marginal cost and the average cost curves look like?
In the long run, all inputs are variable, which affects both the Long Run Marginal Cost (LRMC) and Long Run Average Cost (LRAC) curves. Here's how they look and behave:
Long Run Marginal Cost (LRMC) Curve:
The LRMC curve is 'U'-shaped.
It reflects the change in total cost per unit of change in output when input levels are varied.
Initially, when the level of production is low, LRMC decreases as efficiency increases with less congestion of inputs.
After a certain point, as production expands, the LRMC increases due to the diminishing returns from the additional inputs.
Long Run Average Cost (LRAC) Curve:
The LRAC curve is also 'U'-shaped and very similar to the LRMC in its behavior.
Initially, as output increases, the LRAC falls. This is typically under the influence of Increasing Returns to Scale (IRS) where doubling the inputs more than doubles the output, decreasing the cost per unit.
After reaching a minimum point, the curve begins to rise, indicating Decreasing Returns to Scale (DRS) where doubling the inputs results in less than double the output, increasing the cost per unit.
At the minimum point of the LRAC curve, the firm experiences Constant Returns to Scale (CRS), where doubling inputs doubles output and cost per unit remains unchanged.
Relationship between LRMC and LRAC:
The LRMC curve intersects the LRAC curve at its minimum point. This intersection signifies the most efficient scale of operation for the firm in the long run.
When LRAC is declining, LRMC is below LRAC.
When LRAC is rising, LRMC is above LRAC.
These shapes and their interactions provide critical insights into scale efficiencies and inform decisions on optimal production levels to minimize costs in the long run.
The following table gives the total product schedule of labour. Find the corresponding average product and marginal product schedules of labour.
L | $TP_L$ |
---|---|
0 | 0 |
1 | 15 |
2 | 35 |
3 | 50 |
4 | 40 |
5 | 48 |
To find the Average Product (AP) and Marginal Product (MP) of labour from the given Total Product (TP) schedule, we need to use the following formulas:
Average Product (AP) is calculated as: [ AP_L = \frac{TP_L}{L} ] where ( L ) is the quantity of labor and ( TP_L ) is the total product for that labor.
Marginal Product (MP) is calculated as: [ MP_L = TP_L(L) - TP_L(L-1) ] where ( TP_L(L) ) is the total product at ( L ) units of labor and ( TP_L(L-1) ) is the total product at ( L-1 ) units of labor.
Given the ( TP ) values from the table:
( L = 0 ) : ( TP = 0 )
( L = 1 ) : ( TP = 15 )
( L = 2 ) : ( TP = 35 )
( L = 3 ) : ( TP = 50 )
( L = 4 ) : ( TP = 40 )
( L = 5 ) : ( TP = 48 )
Using the above formulas, we can compute the AP and MP for each level of labor ( L ). Let me calculate these for you.
Let's manually calculate both the Average Product (AP) and Marginal Product (MP) schedules for labor:
Average Product (AP)
Calculated as: [ AP_L = \frac{TP_L}{L} ]
For ( L = 0 ) (undefined since division by zero)
For ( L = 1 ): ( AP_1 = \frac{15}{1} = 15 )
For ( L = 2 ): ( AP_2 = \frac{35}{2} = 17.5 )
For ( L = 3 ): ( AP_3 = \frac{50}{3} \approx 16.67 )
For ( L = 4 ): ( AP_4 = \frac{40}{4} = 10 )
For ( L = 5 ): ( AP_5 = \frac{48}{5} = 9.6 )
Marginal Product (MP)
Calculated as: [ MP_L = TP_L(L) - TP_L(L-1) ]
For ( L = 0 ) to ( L = 1 ): ( MP_1 = 15 - 0 = 15 )
For ( L = 1 ) to ( L = 2 ): ( MP_2 = 35 - 15 = 20 )
For ( L = 2 ) to ( L = 3 ): ( MP_3 = 50 - 35 = 15 )
For ( L = 3 ) to ( L = 4 ): ( MP_4 = 40 - 50 = -10 ) (notice decrease in TP)
For ( L = 4 ) to ( L = 5 ): ( MP_5 = 48 - 40 = 8 )
Thus, the calculated schedules are:
AP: Undefined, 15, 17.5, 16.67, 10, 9.6
MP: 15, 20, 15, -10, 8
This yields the production efficiencies at each level of labor input, highlighting when diminishing marginal returns set in.
The following table gives the average product schedule of labour. Find the total product and marginal product schedules. It is given that the total product is zero at zero level of labour employment
L | $AP_L$ |
---|---|
1 | 2 |
2 | 3 |
3 | 4 |
4 | 4.25 |
5 | 4 |
6 | 3.5 |
To find the Total Product (TP) and Marginal Product (MP) schedules from the given Average Product (AP) schedule, we can follow these steps:
Total Product (TP)
The Average Product (AP) is defined as the Total Product (TP) divided by the amount of the input (labour L). Hence, Total Product can be calculated by multiplying the Average Product by the input levels:
[ TP_L = AP_L \times L ]
Marginal Product (MP)
The Marg.inal Product (MP) is the change in Total Product (TP) for a unit increase in the input. It can be computed by taking the difference:
[ MP_L = TP_L - TP_{L-1} ]
Given that $TP$ is zero at zero level of labour employment:
Let's perform these calculations:
Total Product (TP) Calculation:
If ( L = 1 ), ( TP_1 = 2 \times 1 = 2 )
If ( L = 2 ), ( TP_2 = 3 \times 2 = 6 )
If ( L = 3 ), ( TP_3 = 4 \times 3 = 12 )
If ( L = 4 ), ( TP_4 = 4.25 \times 4 = 17 )
If ( L = 5 ), ( TP_5 = 4 \times 5 = 20 )
If ( L = 6 ), ( TP_6 = 3.5 \times 6 = 21 )
Marginal Product (MP) Calculation:
( MP_0 ) is undefined as TP is zero at zero input.
( MP_1 = TP_1 - TP_0 = 2 - 0 = 2 )
( MP_2 = TP_2 - TP_1 = 6 - 2 = 4 )
( MP_3 = TP_3 - TP_2 = 12 - 6 = 6 )
( MP_4 = TP_4 - TP_3 = 17 - 12 = 5 )
( MP_5 = TP_5 - TP_4 = 20 - 17 = 3 )
( MP_6 = TP_6 - TP_5 = 21 - 20 = 1 )
Let's combine these results into tables for clarity.
Total Product Schedule:
L | TP |
---|---|
0 | 0 |
1 | 2 |
2 | 6 |
3 | 12 |
4 | 17 |
5 | 20 |
6 | 21 |
Marginal Product Schedule:
L | MP |
---|---|
1 | 2 |
2 | 4 |
3 | 6 |
U | 4 |
V | 5 |
W | 6 |
Here, we observe the initial increase in Marginal Product followed by a subsequent decrease, demonstrating the law of diminishing returns.
The following table gives the marginal product schedule of labour. It is also given that total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour.
L | $MP_L$ |
---|---|
1 | 3 |
2 | 5 |
3 | 7 |
4 | 5 |
5 | 3 |
6 | 1 |
To calculate the Total Product (TP) and Average Product (AP) schedules of labor from the given Marginal Product (MP) schedule, follow these steps:
-
Total Product (TP): Total Product can be calculated by summing up the Marginal Products up to that level of labor:
- TP at L=1: TP = 3 (since TP at L=0 is 0)
- TP at L=2: TP = TP at L=1 + MP at L=2 = 3 + 5 = 8
- TP at L=3: TP = TP at L=2 + MP at L=3 = 8 + 7 = 15
- TP at L=4: TP = TP at L=3 + MP at L=4 = 15 + 5 = 20
- TP at L=5: TP = TP at L=4 + MP at L=5 = 20 + 3 = 23
- TP at L=6: TP = TP at L=5 + MP at L=6 = 23 + 1 = 24
-
Average Product (AP): Average Product is calculated by dividing the Total Product by the corresponding level of labor (L):
- AP at L=1: AP = TP at L=1 / 1 = 3 / 1 = 3
- AP at L=2: AP = TP at L=2 / 2 = 8 / 2 = 4
- AP at L=3: AP = TP at L=3 / 3 = 15 / 3 = 5
- AP at L=4: AP = TP at L=4 / 4 = 20 / 4 = 5
- AP at L=5: AP = TP at L=5 / 5 = 23 / 5 = 4.6
- AP at L=6: AP = TP at L=6 / 6 = 24 / 6 = 4
Below is the complete schedule including Labor (L), Total Product (TP), and Average Product (AP):
Labor (L) | Marginal Product ($MP_L$) | Total Product (TP) | Average Product (AP) |
---|---|---|---|
0 | - | 0 | - |
1 | 3 | 3 | 3.0 |
2 | 5 | 8 | 4.0 |
3 | 7 | 15 | 5.0 |
4 | 5 | 20 | 5.0 |
5 | 3 | 23 | 4.6 |
6 | 1 | 24 | 4.0 |
These calculations give us the Total and Average Product schedules based on the given Marginal Product schedule.
The following table shows the total cost schedule of a firm. What is the total fixed cost schedule of this firm? Calculate the TVC, AFC, AVC, SAC and SMC schedules of the firm.
Q | TC |
---|---|
0 | 10 |
1 | 30 |
2 | 45 |
3 | 55 |
4 | 70 |
5 | 90 |
6 | 120 |
To find the total fixed cost (TFC) of the firm and other cost schedules such as total variable cost (TVC), average fixed cost (AFC), average variable cost (AVC), short run average cost (SAC), and short run marginal cost (SMC), we will analyze and derive these values based on the given total cost (TC) and output (Q) data.
Here is the given data:
Q | TC |
---|---|
0 | 10 |
1 | 30 |
2 | 45 |
3 | 55 |
4 | 70 |
5 | 90 |
6 | 120 |
Total Fixed Cost (TFC)
Total Fixed Cost (TFC) does not vary with the level of output and can be observed at the point where the output (Q) is zero.
- TFC = TC when Q = 0 = 10
Total Variable Cost (TVC)
Total Variable Cost (TVC) is calculated as the difference between Total Cost (TC) and Total Fixed Cost (TFC).
- TVC = TC - TFC
Average Fixed Cost (AFC)
Average Fixed Cost (AFC) is calculated as the Total Fixed Cost (TFC) divided by the quantity of output (Q).
- AFC = TFC / Q
Average Variable Cost (AVC)
Average Variable Cost (AVC) is calculated as Total Variable Cost (TVC) divided by the quantity of output (Q).
- AVC = TVC / Q
Short Run Average Cost (SAC)
Short Run Average Cost (SAC) is the Total Cost (TC) divided by the quantity of output (Q).
- SAC = TC / Q
Short Run Marginal Cost (SMC)
Short Run Marginal Cost (SMC) is the change in Total Cost (TC) when the output (Q) is increased by one unit.
- SMC = TC(Q) - TC(Q-1)
I will now compute all these cost schedules based on the calculations outlined above.
Here are the various cost schedules for the firm based on the calculations:
Total Fixed Cost (TFC)
- TFC is constant for all levels of output: 10
Total Variable Cost (TVC) Schedule
- TVC for Q = 0, 1, 2, 3, 4, 5, 6: 0, 20, 35, 45, 60, 80, 110
Average Fixed Cost (AFC) Schedule
- AFC for Q = 1, 2, 3, 4, 5, 6: 10.0, 5.0, 3.33, 2.5, 2.0, 1.67
(Note: AFC is undefined for Q = 0 since division by zero is not possible.)
Average Variable Cost (AVC) Schedule
- AVC for Q = 1, 2, 3, 4, 5, 6: 20.0, 17.5, 15.0, 15.0, 16.0, 18.33
(Note: AVC is undefined for Q = 0 since division by zero is not possible.)
Short Run Average Cost (SAC) Schedule
- SAC for Q = 1, 2, 3, 4, 5, 6: 30.0, 22.5, 18.33, 17.5, 18.0, 20.0
(Note: SAC is undefined for Q = 0 since division by zero is not possible.)
Short Run Marginal Cost (SMC) Schedule
- SMC for Q = 1, 2, 3, 4, 5, 6: 20, 15, 10, 15, 20, 30
(Note: SMC is undefined for Q = 0 as there is no prior output level to compare the change in cost.)
These schedules provide insight into how the various elements of cost behave as the firm varies its output level.
The following table gives the total cost schedule of a firm. It is also given that the average fixed cost at 4 units of output is Rs 5. Find the TVC, TFC, AVC, AFC, SAC and SMC schedules of the firm for the corresponding values of output
Q | TC |
---|---|
1 | 50 |
2 | 65 |
3 | 75 |
4 | 95 |
5 | 130 |
6 | 185 |
To find the Total Variable Cost (TVC), Total Fixed Cost (TFC), Average Variable Cost (AVC), Average Fixed Cost (AFC), Short Run Average Cost (SAC) and Short Run Marginal Cost (SMC) for the provided output levels, we will follow these steps:
-
TFC Calculation: Given that AFC at 4 units of output is Rs 5 and AFC is calculated as $\text{AFC} = \frac{\text{TFC}}{Q}$, we can determine TFC: [ \text{TFC} = \text{AFC} \times Q = 5 \times 4 = 20 , \text{(Rs)} ]
Since TFC is constant in the short run, it remains Rs 20 for all output levels.
-
TVC Calculation: TVC is calculated as $\text{TVC} = \text{TC} - \text{TFC}$.
-
AVC Calculation: AVC is calculated as $\text{AVC} = \frac{\text{TVC}}{Q}$.
-
AFC Calculation: Since TFC is known, AFC is calculated as $\text{AFC} = \frac{\text{TFC}}{Q}$.
-
SAC Calculation: SAC is calculated as $\text{SAC} = \frac{\text{TC}}{Q}$.
-
SMC Calculation: SMC reflects the additional cost per additional output unit, calculated as $\text{SMC} = \text{TC}(Q) - \text{TC}(Q-1)$.
Let's perform these calculations for each output level:
Q | TC | TFC | TVC | AVC | AFC | SAC | SMC |
---|---|---|---|---|---|---|---|
1 | 50 | 20 | 30 | 30 | 20 | 50 | - |
2 | 65 | 20 | 45 | 22.5 | 10 | 32.5 | 15 |
3 | 75 | 20 | 55 | 18.33 | 6.67 | 25 | 10 |
4 | 95 | 20 | 75 | 18.75 | 5 | 23.75 | 20 |
5 | 130 | 20 | 110 | 22 | 4 | 26 | 35 |
6 | 185 | 20 | 165 | 27.5 | 3.33 | 30.83 | 55 |
- SMC from Q=1 to Q=2: $\text{SMC}_{1 \rightarrow 2} = \text{TC}(2) - \text{TC}(1) = 65 - 50 = 15$
- Continue this for other quantities.
These computations provide the firm's schedules of TVC, TFC, AVC, AFC, SAC, and SMC based on the given TC and output levels.
A firm’s SMC schedule is shown in the following table. The total fixed cost of the firm is Rs 100. Find the TVC, TC, AVC and SAC schedules of the firm.
Q | TC |
---|---|
0 | - |
1 | 500 |
2 | 300 |
3 | 200 |
4 | 300 |
5 | 500 |
6 | 800 |
From the given SMC schedule, the Total Variable Cost (TVC) at any quantity ($q$) can be calculated by summing the Short-Run Marginal Costs (SMC) from quantity 1 to $q$. The Total Cost (TC) then is the sum of Total Variable Cost (TVC) and Total Fixed Cost (TFC). The Average Variable Cost (AVC) is computed as TVC divided by the quantity, and the Short-Run Average Cost (SAC) is calculated as TC divided by the quantity.
Given data noted:
- Total Fixed Cost (TFC) = Rs 100.
Let's calculate TVC, TC, AVC, and SAC step by step:
-
TVC Calculation:
- $q=0$: TVC = 0
- $q=1$: TVC = 500 (since SMC at $q=1$ is the total added TVC from $q=0$ to $q=1$)
- $q=2$: TVC = TVC at $q=1$ + SMC at $q=2$ = 500 + 300 = 800
- Continue similarly for other quantities.
-
TC Calculation:
- $q=0$: TC = TFC = 100
- For $q \geq 1$: TC = TVC + TFC.
-
AVC Calculation:
- $q=0$: AVC is undefined.
- For $q \geq 1$: AVC = TVC / $q$.
-
SAC Calculation:
- $q=0$: SAC is undefined.
- For $q \geq 1$: SAC = TC / $q$.
Let's perform these calculations and compile the TVC, TC, AVC, and SAC values.
Here are the calculated schedules for Total Variable Cost (TVC), Total Cost (TC), Average Variable Cost (AVC), and Short-Run Average Cost (SAC) for different quantities (Q):
Q | TVC | TC | AVC | SAC |
---|---|---|---|---|
0 | 0 | 100 | - | - |
1 | 500 | 600 | 500.0 | 600.0 |
2 | 800 | 900 | 400.0 | 450.0 |
3 | 1000 | 1100 | 333.33 | 366.67 |
4 | 1300 | 1400 | 325.0 | 350.0 |
5 | 1800 | 1900 | 360.0 | 380.0 |
6 | 2600 | 2700 | 433.33 | 450.0 |
Note:
- The values for AVC and SAC are rounded to two decimal places.
- AVC and SAC at Q = 0 are undefined as per convention, because dividing by zero is not mathematically defined.
Let the production function of a firm be
$Q = 5 L^{\frac{1}{2}} K^{\frac{1}{2}}$
Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.
The maximum possible output that the firm can produce with 100 units of $L$ and 100 units of $K$ using the production function $Q = 5 L^{\frac{1}{2}} K^{\frac{1}{2}}$ is 500 units of output.
Let the production function of a firm be
$Q = 2L_2K_2$
Find out the maximum possible output that the firm can produce with 5 units of L and 2 units of K. What is the maximum possible output that the firm can produce with zero unit of L and 10 units of K?
-
When using 5 units of ( L ) and 2 units of ( K ), the maximum possible output the firm can produce is 20 units.
-
With zero units of ( L ) and 10 units of ( K ), the maximum possible output the firm can produce is 0 units. This is because output is zero when either ( L ) or ( K ) is zero, according to the production function ( Q = 2L_2K_2 ).
Find out the maximum possible output for a firm with zero unit of L and 10 units of K when its production function is
$Q = 5L + 2K$
Given the production function:
[ Q = 5L + 2K ]
where ( L ) represents labor and ( K ) represents capital. To find the maximum possible output when ( L = 0 ) units and ( K = 10 ) units, we substitute these values into the production function.
[ Q = 5(0) + 2(10) ] [ Q = 0 + 20 ] [ Q = 20 ]
Thus, the maximum possible output for a firm with zero unit of labor and 10 units of capital is 20 units of output.
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Comprehensive Production and Costs Class 12 Notes
Introduction to Production and Costs
Production and costs are core concepts in economics that correlate how firms transform inputs into outputs and the associated costs. This guide simplifies these concepts for Class 12 students, ensuring a clear understanding of the intricate relationship between production processes and costs.
Key Inputs in Production
Producers, or firms, use various inputs to generate output. Key inputs include:
- Labour: Workforce involved in production.
- Capital: Machinery, buildings, and other physical equipment.
- Raw Materials: Basic materials needed for production.
Understanding the Production Function
The production function illustrates the relationship between the quantity of inputs used and the maximum quantity of output produced. Mathematically, it can be represented as: [ q = f(L, K) ] where (\mathrm{L}) is labour, (\mathrm{K}) is capital, and ( \mathrm{q} ) is the output.
For example, a farmer using land and labour to produce wheat can be represented as: [ q = \mathrm{K} \times \mathrm{L} ]
Short Run vs. Long Run in Production
- Short Run: At least one input (e.g., capital) is fixed.
- Long Run: All inputs can be varied, and no input remains fixed.
Short Run
In the short run, firms adjust production levels by varying the variable factors while keeping the fixed factors constant.
Long Run
In the long run, firms can adjust all inputs, allowing factors and scales to alter, leading to different cost implications.
Total Product, Average Product, and Marginal Product
- Total Product (TP): The total output produced by employing a certain quantity of variable input.
- Average Product (AP): Output per unit of variable input. [ \mathrm{AP} = \frac{\mathrm{TP}}{\mathrm{L}} ]
- Marginal Product (MP): The change in output resulting from a one-unit change in input. [ \mathrm{MP} = \frac{\Delta \mathrm{TP}}{\Delta \mathrm{L}} ]
Law of Diminishing Marginal Product and Variable Proportions
- Law of Diminishing Marginal Product: As more units of a variable input are employed, while other inputs are constant, the marginal product eventually decreases.
- Law of Variable Proportions: Initially, marginal product increases, but it starts to decline after reaching a certain level of employment.
Isoquants
Isoquants represent different combinations of inputs that yield the same level of output. Think of them as contour lines on a map, each representing a specific height (output level).
Returns to Scale
Returns to scale describe how the output changes when all inputs are scaled:
- Constant Returns to Scale (CRS): Output changes in the same proportion as inputs.
- Increasing Returns to Scale (IRS): Output increases by a larger proportion than the inputs.
- Decreasing Returns to Scale (DRS): Output increases by a smaller proportion than the inputs.
Short Run Costs in Production
Firms incur various costs to employ inputs:
- Total Fixed Cost (TFC): Costs that remain constant, regardless of output.
- Total Variable Cost (TVC): Costs that vary with output.
- Total Cost (TC): Sum of TFC and TVC. [ \mathrm{TC} = \mathrm{TVC} + \mathrm{TFC} ]
- Short Run Average Cost (SAC): Total cost per unit of output. [ \mathrm{SAC} = \frac{\mathrm{TC}}{q} ]
- Average Variable Cost (AVC): Variable cost per unit of output. [ \mathrm{AVC} = \frac{\mathrm{TVC}}{q} ]
- Average Fixed Cost (AFC): Fixed cost per unit of output. [ \mathrm{AFC} = \frac{\mathrm{TFC}}{q} ]
- Short Run Marginal Cost (SMC): Change in total cost per unit change in output. [ \mathrm{SMC} = \frac{\Delta \mathrm{TC}}{\Delta q} ]
Long Run Costs and Cost Curves
In the long run, all costs are variable. Thus, the long-run average cost (LRAC) and long-run marginal cost (LRMC) are crucial:
- Long Run Average Cost (LRAC): [ \mathrm{LRAC} = \frac{\mathrm{TC}}{q} ]
- Long Run Marginal Cost (LRMC): [ \mathrm{LRMC} = \frac{\Delta \mathrm{TC}}{\Delta q} ]
Cobb-Douglas Production Function
This special form of production function is represented as: [ q = x_1^\alpha x_2^\beta ] where (\alpha) and (\beta) are constants. The function exhibits different returns to scale based on the sum of (\alpha) and (\beta).
Cost Minimisation Strategies for Firms
Firms aim to produce any given level of output at the least cost. They achieve this by choosing the optimal combination of inputs given the prices of factors of production.
Importance of Cost Curves
Understanding cost curves is crucial for firms as they help in making efficient production and pricing decisions. Cost curves inform about the cost behaviour as output levels change, guiding firms in planning and budgeting.
Summary and Key Takeaways
- Production functions show the maximum quantity of output for different input combinations.
- In short run, some inputs are fixed, while in long run, all inputs are variable.
- Total product is the total output, while average product and marginal product describe the output per unit of input.
- The law of diminishing marginal product and variable proportions are critical for understanding changes in production.
- Firms aim for cost minimisation by choosing the least cost input combinations.
- Short-run and long-run cost curves help in understanding cost behaviours and production efficiency.
FAQs on Production and Costs
1. What is a production function? A production function shows the relationship between inputs used in production and the output generated.
2. What is total product (TP)? Total product is the total quantity of output produced by employing a given amount of an input.
3. How do you distinguish between short run and long run in production? In the short run, at least one input is fixed; in the long run, all inputs can be varied.
4. What does the 'U'-shaped cost curve represent? The 'U'-shaped cost curve represents the typical behaviour of costs, initially decreasing due to efficiencies and then increasing due to inefficiencies as production scales.
5. Why are returns to scale important? Returns to scale help understand how the scale of production affects output, influencing long-term production strategies and cost management.
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