The Theory of the Firm under Perfect Competition - Class 12 Economics - Chapter 4 - Notes, NCERT Solutions & Extra Questions
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Extra Questions - The Theory of the Firm under Perfect Competition | Microeconomics | Economics | Class 12
Explain the relation between marginal revenue and average revenue when a firm is able to sell more quantity of output: (i) at the same price. (ii) only by lowering the price.
Relation between Marginal Revenue (MR) and Average Revenue (AR) in different scenarios:
(i) Selling at the same price:
When a firm sells more products at a constant price, both the Average Revenue (AR) and Marginal Revenue (MR) remain constant. In this scenario, when the selling price per unit remains the same regardless of the quantity sold, it implies that:
$$ \text{MR} = \text{AR} $$
This equation holds because no change in selling price (which is essentially the AR) means every additional unit sold yields the same revenue as the previous ones, maintaining MR equal to AR.
(ii) Selling only by lowering the price:
If a firm can sell more products only by reducing the price, the Average Revenue decreases as the sales volume increases. Here, the Marginal Revenue is less than the Average Revenue. This relates as:
$$ \text{MR} < \text{AR} $$
Such a situation indicates that to increase sales, the price per unit must drop, hence decreasing AR, and since each additional unit sells at a lower price than the previous, MR falls below AR.
When the government enforces a price ceiling on a good, which is lower than the current market price, $\qquad$ .
A) a perfectly competitive firm produces more.
B) a perfectly competitive firm produces less.
C) a monopoly firm produces more.
D) a monopoly firm produces less.
The correct answers are:
B) a perfectly competitive firm produces less
C) a monopoly firm produces more
When the government imposes a price ceiling below the existing market price, the impacts differ based on the market structure:
For a perfectly competitive firm, production decreases. This is due to the lower price making it less profitable to produce at previous levels. Hence, the profit-maximizing quantity for these firms is less than it was at the higher price.
For a monopoly firm, contrary to intuitive expectations, production increases. This occurs because, under a monopoly where the firm sets prices above marginal cost to maximize profit, a lower price might still cover the marginal cost but less than the monopoly price, pushing the firm to increase output to maintain profitability. Therefore, the profit-maximizing quantity at the reduced price turns out to be greater than it was at a higher price.
Explain the effect of the following on the supply of a commodity: (a) Fall in the prices of factor inputs. (b) Rise in the prices of other commodities.
Effects on commodity supply due to economic changes:
(a) Fall in the prices of factor inputs:
A decrease in the costs of factor inputs leads to a reduction in production costs. This situation makes production more profitable, encouraging producers to increase supply. Therefore, we expect:
$$ \text{Decrease in factor input prices} \rightarrow \text{Increase in supply} $$
(b) Rise in the prices of other commodities:
When the prices of alternate goods rise, producing these other goods becomes more lucrative compared to the original commodity. This reallocation of resources to more profitable products results in a decrease in the supply of the original commodity:
$$ \text{Increase in prices of other commodities} \rightarrow \text{Decrease in supply of the original commodity} $$
Each of these scenarios reveals the dynamic relationship between production costs and market conditions, and their direct effects on market supply.
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Ask Chatterbot AINCERT Solutions - The Theory of the Firm under Perfect Competition | Microeconomics | Economics | Class 12
What are the characteristics of a perfectly competitive market?
A perfectly competitive market is characterized by the following elements:
Large Number of Buyers and Sellers: This ensures that no single buyer or seller has the power to influence market prices.
Homogenous Product: Each firm produces a product that is identical to that of other firms, making it impossible for any firm to differentiate its product.
Free Entry and Exit: Firms can enter or exit the market without significant barriers, allowing the number of firms to adjust to changes in market conditions.
Perfect Information: All buyers and sellers have complete knowledge about the price, quality, and availability of products, allowing them to make informed decisions.
These characteristics lead to a market where each firm is a "price taker"—unable to influence the price of its products, and thus, must accept the market price determined by the overall supply and demand.
How are the total revenue of a firm, market price, and the quantity sold by the firm related to each other?
The total revenue (TR) of a firm in a perfectly competitive market is calculated by multiplying the market price of the good ($p$) by the quantity of the good produced and sold by the firm ($q$). This relationship is mathematically represented as:
$$ TR = p \times q $$
In other words, total revenue is directly proportional to both the market price and the quantity sold. Thus, if the price or the quantity sold increases, the total revenue also increases, assuming the other factor remains constant. Likewise, a decrease in either the price or the quantity sold would result in a decrease in total revenue, assuming the other factor remains constant. This relationship shows that the total revenue depends linearly on the quantity when the price is constant, forming a straight line equation where the slope of the line is equal to the price.
What is the ‘price line’?
In the context of a perfectly competitive market, the 'price line' refers to a graphical representation of the price at which a firm sells its product, which is also equal to the average revenue (AR) and marginal revenue (MR) of the firm. The price line is a horizontal straight line on a graph where the market price is constant and independent of the quantity of goods produced or sold by the firm. This line demonstrates that in a perfectly competitive market, the price set by the market is accepted by individual firms (as they are price-takers), and it intersects the y-axis at the height equal to the market price, $p$.
This price line represents the demand curve facing the individual firm in a perfectly competitive market. It is perfectly elastic, indicating that the firm can sell any amount of its product at the market price but cannot influence the price by altering its output level.
Why is the total revenue curve of a price-taking firm an upward-sloping straight line? Why does the curve pass through the origin?
The total revenue (TR) curve of a price-taking firm is an upward-sloping straight line because of the nature of the revenue calculation and the constant market price in perfect competition. Total revenue for a firm is calculated as: $$ TR = p \times q $$ where ( p ) is the market price, which stays constant under perfect competition, and ( q ) is the quantity of goods sold.
Upward Sloping: Since ( p ) is constant, the total revenue ( TR ) increases linearly with an increase in ( q ). This direct relationship between quantity sold and total revenue (without changes in price) makes the TR Curve a straight line with a positive slope equal to the price ( p ).
Passes Through the Origin: When ( q = 0 ), ( TR = p \times 0 = 0 ). This means that if no goods are sold, the firm's total revenue is zero. Hence, the TR curve starts at the origin (0,0), indicating that zero quantity results in zero revenue.
The linearity and intercept at the origin demonstrate the straightforward relationship between sales volume and revenue generation for a firm in a perfectly competitive market, where price remains unchanged regardless of the quantity sold.
What is the relation between market price and average revenue of a pricetaking firm?
For a price-taking firm in a perfectly competitive market, the average revenue (AR) equals the market price (p). This relationship exists because the firm can sell as many units of the good as it wants at the market price. Therefore, the firm's average revenue per unit—the total revenue divided by the quantity sold—is exactly the market price.
In mathematical terms: $$ AR = \frac{TR}{q} = \frac{p \times q}{q} = p $$
Here, ( TR ) is the total revenue and ( q ) is the quantity of goods sold, making the average revenue equal to the market price for every unit sold.
What is the relation between market price and marginal revenue of a pricetaking firm?
In a perfectly competitive market, a price-taking firm's marginal revenue (MR) is equal to the market price (p) of the good it sells. This means that when a firm increases its output by one unit, the additional revenue generated from selling that unit will be precisely the market price, establishing that MR = p.
What conditions must hold if a profit-maximising firm produces positive output in a competitive market?
In a competitive market where a firm aims to maximize its profit while producing a positive output, the following conditions must hold:
The price ($p$) must be equal to the marginal cost ($MC$). This condition ensures that the profit margin on the last unit produced is neither positive nor negative.
The marginal cost curve must be non-decreasing at the level of output where profit is maximized. This condition ensures that increasing output further would not increase profit.
For the firm to continue operating, particularly:
In the short run, price ($p$) must be greater than or equal to the average variable cost ($AVC$). This ensures the firm covers its variable costs.
In the long run, price must be greater than or equal to the average cost ($AC$), ensuring all costs, including fixed costs, are covered and the firm can justify remaining in the market.
These conditions help determine the optimal production level at which the firm maximizes its profits while being viable in the market conditions dictated by perfect competition.
Can there be a positive level of output that a profit-maximising firm produces in a competitive market at which market price is not equal to marginal cost? Give an explanation.
In a perfectly competitive market, for a firm to be profit-maximizing, there cannot be a positive level of output at which the market price is not equal to the marginal cost. Here's why:
Price Equals Marginal Cost: In perfect competition, one of the key conditions for profit maximization is that the price ($p$) should equal the marginal cost ($MC$) of production at the optimal output level. This is because the marginal cost curve represents the cost of producing one additional unit. At any output level where price exceeds marginal cost, the firm can increase its profit by producing more; if price is below marginal cost, the firm can reduce its loss by producing less.
Profit Maximization and Market Equilibrium: When $p = MC$, the firm is maximizing profit because it is neither beneficial to produce more nor less. Producing more would increase cost more than revenue, and producing less would decrease revenue more than cost.
Price-Taking Behavior: In perfect competition, firms are price takers, meaning they have no influence over the market price. They can sell as much as they can produce at the prevailing market price. If a firm set a price above the market level, it would sell nothing because buyers have perfect information and can purchase from other firms at the lower price.
In conclusion, at a positive level of output for a profit-maximizing firm in a competitive market, the market price must equal the marginal cost. If this condition is not met, the output level cannot be optimal, indicating either an opportunity to increase profit by adjusting output or that the firm is not in equilibrium.
Will a profit-maximising firm in a competitive market ever produce a positive level of output in the range where the marginal cost is falling? Give an explanation.
In a perfectly competitive market, a profit-maximizing firm will not produce a positive level of output in the range where the marginal cost (MC) is falling. This conclusion is based on the important concept of equilibrium where the price equals the marginal cost (P=MC), and the MC curve must be non-decreasing at the output level that maximizes profit.
Here’s why a profit-maximizing firm avoids producing in the range where MC is decreasing:
Profit Maximization Condition: For a firm to maximize its profit, the marginal revenue (MR) must equal the marginal cost (MC). In a perfectly competitive market, the MR equals the market price (P). Thus, profit maximization occurs where P = MC.
Nature of the Marginal Cost Curve: In the short run, the marginal cost curve typically has a U-shape due to the law of variable proportions. Initially, MC falls as outputs increase due to better utilization of fixed resources (increasing returns to factor). However, after a certain point, MC starts to rise due to diminishing returns.
Decision Point for Profit Maximization: The critical point for setting the output level is where the MC curve begins to rise after reaching its minimum point. If a firm were to produce where MC is still falling, it implies that there exists a higher output level where MC=MR, meaning more profit can still be made. Hence, producing where MC is decreasing would not maximize profits.
Stability and Equilibrium: At any quantity where MC is falling, a small increase in output will lead to lower MC and higher MR, suggesting that the firm can increase profits by expanding output. Therefore, it isn’t optimal or stable for a firm to produce in this range if maximizing profit is the goal.
In summary, for optimal and stable production that ensures maximum profitability in a perfectly competitive market, a firm would operate where the MC curve is non-decreasing and intersects with the market price. This ensures no further reduction in MC can occur without increasing costs, hence safeguarding maximum profit levels.
Will a profit-maximising firm in a competitive market produce a positive level of output in the short run if the market price is less than the minimum of AVC? Give an explanation.
No, a profit-maximizing firm in a competitive market will not produce a positive level of output in the short run if the market price is less than the minimum of the Average Variable Cost (AVC). Here’s why:
In the short run, a firm's total variable costs increase with output, and if the price per unit of the good is less than the AVC, the firm would lose money on each unit it produces. Since each additional unit sold increases the firm's losses, the firm would minimize its losses by not producing any output at all.
The decision rule for a firm in the short run is to produce a positive output only if the market price is at least equal to the AVC. This is because:
If $p \geq AVC$, covering the AVC means the firm can contribute to covering fixed costs and possibly make a loss smaller than the total fixed costs (since fixed costs are incurred even if output is zero).
If $p < AVC$, then producing any output would increase the firm's losses beyond just its fixed costs. Therefore, the rational decision is to halt production to minimize losses.
This scenario reflects the short-run shutdown condition in economics, where a firm decides to temporarily cease production to avoid augmenting its losses when market conditions are unfavorable.
Will a profit-maximising firm in a competitive market produce a positive level of output in the long run if the market price is less than the minimum of AC? Give an explanation.
No, a profit-maximising firm in a competitive market will not produce a positive level of output in the long run if the market price is less than the minimum of average cost (AC). Here’s why:
Cost and Revenue Analysis: In the long run, all costs are variable, and a firm's long run average cost (LRAC) curve reflects the lowest possible cost at which any output level can be produced when the scale of production is variable. The minimum point on the LRAC curve represents the least cost per unit at which the firm can produce. This cost includes a normal profit, which is the minimum profit necessary to keep the firm in the industry.
Market Price Below AC: When the market price is below the minimum of the LRAC, selling the product at this price means the revenue generated per unit is less than the cost per unit. This condition leads to losses because the total revenue is insufficient to cover the total costs.
Long-Term Decision: In such a scenario, continuing production would lead to continuous losses. In the long run, a firm aims for at least a normal profit. Operating under conditions where the price is less than the AC would mean the firm cannot even achieve normal profit, resulting in a rational decision to cease production. Therefore, in the long run, if the market price is below the minimum AC, the firm will produce zero output to minimize losses, leading to a shutdown decision.
Economic Rationality: The decision to produce no output under these prices is economically rational as it minimizes the firm's losses. The losses in such a case would only be equal to the fixed costs, which, in the long run, are considered variable and can be avoided if the firm decides not to produce.
Thus, in the long run, a profit-maximizing firm will not operate if the market price does not cover the minimum average cost, including the normal profit. This ensures the firm avoids incurring additional losses beyond recoverable fixed costs.
What is the supply curve of a firm in the short run?
In the short run, a firm's supply curve is represented by the rising part of the Short-Run Marginal Cost (SMC) curve that lies above the minimum Average Variable Cost (AVC). Additionally, for all prices that are strictly less than the minimum AVC, the firm produces zero output.
Hence, the short-run supply curve effectively begins at the minimum AVC point where the SMC curve intersects the AVC curve and continues upward along the SMC curve. This arrangement ensures that the firm only produces when it can at least cover its variable costs. Below this price, the firm is better off not producing anything, which is depicted on the supply curve as zero output for prices below the minimum AVR.
What is the supply curve of a firm in the long run?
In the context of a perfectly competitive market, the long run supply curve of a firm is represented by the rising part of the long run marginal cost curve (LRMC) from and above the minimum point of the long run average cost (LRAC). This curve also includes zero output for all prices that are less than the minimum LRAC. This supply behavior is a result of the firm's profit maximization strategy, where it seeks to equate the market price with its marginal cost while ensuring that the price also covers the average cost in the long run, ensuring the firm's survival and normal profit attainment.
How does technological progress affect the supply curve of a firm?
Technological progress typically has the effect of shifting a firm's supply curve to the right. This shift happens because technological improvements often lead to increased productivity, which allows a firm to produce more units of output with the same levels of input, or the same output with fewer inputs. Lower marginal costs at any level of production result from these efficiencies, meaning the firm can offer more goods at the same price or the same quantity of goods at lower prices, effectively shifting the supply curve outward.
How does the imposition of a unit tax affect the supply curve of a firm?
The imposition of a unit tax on a firm results in an upward shift of both the firm's long-run marginal cost (LRMC) and long-run average cost (LRAC) curves by the amount of the tax. This occurs because the firm must pay an additional fixed amount per unit of output produced, effectively increasing its cost of production.
In graphical terms, before the imposition of a unit tax, the LRMC and LRAC are at positions LRMC0 and LRAC0, respectively. After the unit tax is implemented, these curves shift to LRMC1 and LRAC1. Each level of output now costs more to produce by exactly the amount of the tax.
Consequently, the long-run supply curve of the firm, which is the portion of the LRMC above the minimum LRAC, also shifts to the left. This leftward shift of the supply curve means that at any given market price, the quantity of goods that the firm is willing and able to supply decreases. In other words, the supply curve becomes steeper, reflecting the higher cost of production due to the tax.
How does an increase in the price of an input affect the supply curve of a firm?
When the price of an input increases, it leads to an increase in the cost of production for a firm. This usually causes an increase in the firm's marginal cost (MC) at any given level of output, because the firm now pays more for its inputs.
Since the supply curve of a firm is essentially a segment of its marginal cost curve that is above the average variable cost, an increase in input prices shifts the marginal cost curve leftward or upward. This shift means that for any given level of output, the minimum price at which the firm is willing to supply that output is now higher.
Consequently, the supply curve shifts to the left: at any given market price, the firm will now supply fewer units of output than before. This reflects a reduction in the quantity supplied at the same price due to higher production costs.
How does an increase in the number of firms in a market affect the market supply curve?
An increase in the number of firms in a market causes the market supply curve to shift to the right. This shift occurs because more firms lead to higher total market output at each price level, assuming other conditions remain unchanged. This is due to the aggregation of a greater number of individual firm supply curves, each contributing additional quantities of the product at any given price. Thus, the overall market becomes more capable of supplying goods, reducing prices and making the product more available to consumers.
What does the price elasticity of supply mean? How do we measure it?
Price Elasticity of Supply Meaning
The price elasticity of supply measures the responsiveness of the quantity supplied of a good to a change in its price. It is a key concept in economic theory reflecting how much quantity supplied changes in response to a price change.
Measurement of Price Elasticity of Supply
The price elasticity of supply ($e_S$) can be calculated using the formula:
$$ e_S = \frac{\Delta Q/Q}{\Delta P/P} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} $$
Where:
$\Delta Q$ is the change in quantity supplied.
$Q$ is the original quantity supplied.
$\Delta P$ is the change in price.
$P$ is the original price.
This ratio thus captures the percentage change in quantity supplied divided by the percentage change in price. A higher elasticity indicates that the quantity supplied is highly responsive to price changes, while a lower elasticity suggests it is less responsive.
Examples of Computing:
If a price increase from Rs 10 to Rs 30 leads to an increase in supply from 200 units to 1000 units, you would calculate it as follows:
Percentage change in quantity supplied: $$\frac{1000 - 200}{200} \times 100 = 400%$$
Percentage change in price: $$\frac{30 - 10}{10} \times 100 = 200%$$
Price elasticity of supply: $$\frac{400%}{200%} = 2$$
A price elasticity of 2 indicates that for every 1% increase in price, the quantity supplied increases by 2%.
Compute the total revenue, marginal revenue and average revenue schedules in the following table. Market price of each unit of the good is Rs 10.
Quantity Sold | TR | MR | AR |
---|---|---|---|
0 | |||
1 | |||
2 | |||
3 | |||
4 | |||
5 | |||
6 |
To compute the Total Revenue (TR), Marginal Revenue (MR), and Average Revenue (AR) for each quantity sold, we use the following formulas given the market price per unit (P) is Rs 10:
Total Revenue (TR): It is calculated as the product of the quantity sold and the market price, $$ TR = P \times Q $$
Marginal Revenue (MR): For a perfectly competitive firm, MR equals the price per unit, $$ MR = P $$
Average Revenue (AR): This is calculated by dividing the total revenue by the quantity sold, $$ AR = \frac{TR}{Q} $$
Since the price (P) is Rs 10 for all units, let's compute TR, MR, and AR for each quantity sold:
Quantity (Q) | TR ( (P \times Q) ) | MR ( (P) ) | AR ( (\frac{TR}{Q}) ) |
---|---|---|---|
0 | 0 | Not applicable | Not applicable |
1 | (10 \times 1 = 10) | 10 | (10/1 = 10) |
2 | (10 \times 2 = 20) | 10 | (20/2 = 10) |
3 | (10 \times 3 = 30) | 10 | (30/3 = 10) |
4 | (10 \times 4 = 40) | 10 | (40/4 = 10) |
5 | (10 \times 5 = 50) | 10 | (50/5 = 10) |
6 | (10 \times 6 = 60) | 10 | (60/6 = 10) |
Here:
Total Revenue (TR) increases by Rs 10 as each additional unit is sold.
Margyinal Revenue (MR) remains constant at Rs 10, because each additional unit sold at the fixed price adds another Rs 10 in revenue.
Average Revenue (AR) is equal to the price for all quantities, Rs 10, since each unit is sold at the same price.
Thus, for a firm under perfect competition with a constant market price:
TR is a linear increase as Q increases.
MR is constant and equal to the market price.
AR is constant and equals the market price.
The following table shows the total revenue and total cost schedules of a competitive firm. Calculate the profit at each output level. Determine also the market price of the good.
Quantity Sold | TR (Rs) | TC (Rs) | Profit |
---|---|---|---|
0 | 0 | 5 | |
1 | 5 | 7 | |
2 | 10 | 10 | |
3 | 15 | 12 | |
4 | 20 | 15 | |
5 | 25 | 23 | |
6 | 30 | 33 | |
7 | 35 | 40 |
To calculate the profit at each level of output, we use the formula:
$$ \text{Profit} = TR - TC $$
where ( TR ) is the total revenue and ( TC ) is the total cost. Let's calculate the profit for each quantity sold:
Quantity = 0: ( TR = 0 ), ( TC = 5 ) [ \text{Profit} = 0 - 5 = -5 ]
Quantity = 1: ( TR = 5 ), ( TC = 7 ) [ \text{Profit} = 5 - 7 = -2 ]
Quantity = 2: ( TR = 10 ), ( TC = 10 ) [ \text{Profit} = 10 - 10 = 0 ]
Quantity = 3: ( TR = 15 ), ( TC = 12 ) [ \text{Profit} = 15 - 12 = 3 ]
Quantity = 4: ( TR = 20 ), ( TC = 15 ) [ \text{Profit} = 20 - 15 = 5 ]
Quantity = 5: ( TR = 25 ), ( TC = 23 ) [ \text{Profit} = 25 - 23 = 2 ]
Quantity = 6: ( TR = 30 ), ( TC = 33 ) [ \text{Profit} = 30 - 33 = -3 ]
Quantity = 7: ( TR = 35 ), ( TC = 40 ) [ \text{Profit} = 35 - 40 = -5 ]
Given that this is a competitive market and the firm is a price taker, we can determine the market price per unit of good by observing the consistent pattern of total revenue increase as quantity increases. From the data:
Increase in TR from quantity 0 to quantity 1 is ( \Delta TR = 5 ), and quantity change is 1.
The market price ( p ) can be determined as: [ p = \frac{\Delta TR}{\Delta q} = \frac{5}{1} = 5 , \text{Rs per unit} ]
Thus, the market price of the good is Rs 5 per unit.
Here are the profits and the market price summarized:
Quantity Sold | TR (Rs) | TC (Rs) | Profit (Rs) |
---|---|---|---|
0 | 0 | 5 | -5 |
1 | 5 | 7 | -2 |
2 | 10 | 10 | 0 |
3 | 15 | 12 | 3 |
4 | 20 | 15 | 5 |
5 | 25 | 23 | 2 |
6 | 30 | 33 | -3 |
7 | 35 | 40 | -5 |
Market Price: Rs 5 per unit
The following table shows the total cost schedule of a competitive firm. It is given that the price of the good is Rs 10. Calculate the profit at each output level. Find the profit-maximising level of output.
Output | TC (Rs) |
---|---|
0 | 5 |
1 | 15 |
2 | 22 |
3 | 27 |
4 | 31 |
5 | 38 |
6 | 49 |
7 | 63 |
8 | 81 |
9 | 101 |
10 | 123 |
To calculate the profit at each output level for the competitive firm, we can use the formula:
[ \text{Profit} (\pi) = \text{Total Revenue} (TR) - \text{Total Cost} (TC) ]
Given that the price of the good is Rs 10, the total revenue for any output level ( q ) is:
[ TR = p \times q ]
where ( p = 10 ) Rs.
Now, let's calculate the Total Revenue (TR) and Profit ((\pi)) for each level of output and determine the profit-maximizing level of output:
We already have the Total Cost (TC) for each output level from the given table:
Output (q) | TC (Rs) |
---|---|
0 | 5 |
1 | 15 |
2 | 22 |
3 | 27 |
4 | 31 |
5 | 38 |
6 | 49 |
7 | 63 |
8 | 81 |
9 | 101 |
10 | 123 |
Now, let's perform the calculations for TR and (\pi).
Here are the profits calculated at each output level:
Output (q) | TR (Rs) | TC (Rs) | Profit (π = TR - TC) |
---|---|---|---|
0 | 0 | 5 | -5 |
1 | 10 | 15 | -5 |
2 | 20 | 22 | -2 |
3 | 30 | 27 | 3 |
4 | 40 | 31 | 9 |
5 | 50 | 38 | 12 |
6 | 60 | 49 | 11 |
7 | 70 | 63 | 7 |
8 | 80 | 81 | -1 |
9 | 90 | 101 | -11 |
10 | 100 | 123 | -23 |
The maximum profit of Rs 12 occurs at an output level of 5. Therefore, the profit-maximizing output level for this firm is 5 units.
Consider a market with two firms. The following table shows the supply schedules of the two firms: the SS1 column gives the supply schedule of firm 1 and the SS2 column gives the supply schedule of firm 2. Compute the market supply schedule.
Price (Rs) | SS1 (units) | SS2 (units) |
---|---|---|
0 | 0 | 0 |
1 | 0 | 0 |
2 | 0 | 0 |
3 | 1 | 1 |
4 | 2 | 2 |
5 | 3 | 3 |
6 | 4 | 4 |
To compute the market supply schedule for the market with two firms given the supply schedules SS1 and SS2, we need to add the supply quantities of both firm 1 and firm 2 at each price level.
Here are the steps to find the market supply schedule:
List each price level.
For each price, add the supply quantities from firm 1 (SS1) and firm 2 (SS2).
Record the combined supply, which will form the market supply schedule.
From your provided data:
Price: 0, SS1 (units): 0, SS2 (units): 0 → Market Supply = 0 + 0 = 0
Price: 1, SS1 (units): 0, SS2 (units): 0 → Market Supply = 0 + 0 = 0
Price: 2, SS1 (units): 0, SS2 (units): 0 → Market Supply = 0 + 0 = 0
Price: 3, SS1 (units): 1, SS2 (units): 1 → Market Supply = 1 + 1 = 2
Price: 4, SS1 (units): 2, SS2 (units): 2 → Market Supply = 2 + 2 = 4
Price: 5, SS1 (units): 3, SS2 (units): 3 → Market Supply = 3 + 3 = 6
Price: 6, SS1 (units): 4, SS2 (units): 4 → Market Supply = 4 + 4 = 8
Thus, the market supply schedule is:
Price (Rs) | Market Supply (units) |
---|---|
0 | 0 |
1 | 0 |
2 | 0 |
3 | 2 |
4 | 4 |
5 | 6 |
6 | 8 |
This schedule indicates how many total units will be supplied to the market at various prices by the two firms combined.
Consider a market with two firms. In the following table, columns labelled as SS1 and SS2 give the supply schedules of firm 1 and firm 2 respectively. Compute the market supply schedule.
Price (Rs) | SS1 (kg) | SS2 (kg) |
---|---|---|
0 | 0 | 0 |
1 | 0 | 0 |
2 | 0 | 0 |
3 | 1 | 0 |
4 | 2 | 0.5 |
5 | 3 | 1 |
6 | 4 | 1.5 |
7 | 5 | 2 |
8 | 6 | 2.5 |
To compute the market supply schedule, add the individual supply quantities of firm 1 and firm 2 at each price level.
The market supply schedule calculation:
Price (Rs) | SS1 (kg) | SS2 (kg) | Market Supply (kg) |
---|---|---|---|
0 | 0 | 0 | 0 + 0 = 0 |
1 | 0 | 0 | 0 + 0 = 0 |
2 | 0 | 0 | 0 + 0 = 0 |
3 | 1 | 0 | 1 + 0 = 1 |
4 | 2 | 0.5 | 2 + 0.5 = 2.5 |
5 | 3 | 1 | 3 + 1 = 4 |
6 | 4 | 1.5 | 4 + 1.5 = 5.5 |
7 | 5 | 2 | 5 + 2 = 7 |
8 | 6 | 2.5 | 6 + 2.5 = 8.5 |
Thus, the market supply at each price level is calculated as the sum of the supplies from both firms.
There are three identical firms in a market. The following table shows the supply schedule of firm 1. Compute the market supply schedule.
Price (Rs) | SS1 (units) |
---|---|
0 | 0 |
1 | 0 |
2 | 2 |
3 | 4 |
4 | 6 |
5 | 8 |
6 | 10 |
7 | 12 |
8 | 14 |
Since the firms are identical and there are three firms in the market, the market supply schedule can be computed by multiplying the supply of each individual firm (Firm 1) by three for each price level.
The calculation for the market supply schedule based on the individual supply schedule of Firm 1:
Price (Rs) | SS1 (units per firm) | Market Supply (3 firms) |
---|---|---|
0 | 0 | 0 * 3 = 0 |
1 | 0 | 0 * 3 = 0 |
2 | 2 | 2 * 3 = 6 |
3 | 4 | 4 * 3 = 12 |
4 | 6 | 6 * 3 = 18 |
5 | 8 | 8 * 3 = 24 |
6 | 10 | 10 * 3 = 30 |
7 | 12 | 12 * 3 = 36 |
8 | 14 | 14 * 3 = 42 |
Thus, the market supply for this group of three identical firms increases in proportion to three times the supply of each individual firm at every specific price level.
A firm earns a revenue of Rs 50 when the market price of a good is Rs 10. The market price increases to Rs 15 and the firm now earns a revenue of Rs 150.What is the price elasticity of the firm’s supply curve?
To calculate the price elasticity of the firm's supply curve, we use the formula:
[ e_{S} = \frac{\Delta Q / Q}{\Delta P / P} = \frac{\Delta Q}{Q} \times \frac{P}{\Delta P} ]
Where:
$ \Delta Q $ is the change in quantity supplied
$ Q $ is the initial quantity supplied
$ \Delta P $is the change in price
$ P $ is the initial price
First, let's calculate $\Delta Q $, $ Q $, $ \Delta P $, and $ P $ based on the information provided:
Initial revenue $ R_1 = \text{Rs } 50 $, price $ P_1 = \text{Rs } 10 $
New revenue $ R_2 = \text{Rs } 150 $, new price $ P_2 = \text{Rs } 15 $
Calculating initial and new quantity supplied:
$ Q_1 = \frac{R_1}{P_1} = \frac{50}{10}$
$Q_2 = \frac{R_2}{P_2} = \frac{150}{15} $
Now, calculate ( \Delta Q ), ( \Delta P ):
$ \Delta Q = Q_2 - Q_1 $
$ \Delta P = P_2 - P_1 $
Finally, use these to calculate $ e_S $:
$ e_{S} = \frac{\Delta Q}{Q_1} \times \frac{P_1}{\Delta P}$
Let's perform these calculations to find the price elasticity of supply ( e_S ).
Based on the calculations:
Initial quantity supplied, $ Q_1 = 5 $
New quantity supplied, $ Q_2 = 10 $
Change in quantity supplied, $ \Delta Q = Q_2 - Q_1 = 10 - 5 = 5 $
Initial price, $ P_1 = 10 $
Change in price,$\Delta P = 15 - 10 = 5$
Now, substituting these values into the formula for price elasticity of supply,
[ e_S = \frac{\Delta Q}{Q_1} \times \frac{P_1}{\Delta P} = \frac{5}{5} \times \frac{10}{5} ]
Calculating this value:
The price elasticity of the firm's supply curve is $ e_S = 2 $.
This indicates that the quantity supplied is relatively responsive to price changes, as the percentage change in quantity supplied is twice the percentage change in price.
The market price of a good changes from Rs 5 to Rs 20. As a result, the quantity supplied by a firm increases by 15 units. The price elasticity of the firm’s supply curve is 0.5. Find the initial and final output levels of the firm.
To find the initial and final output levels of the firm, we can start by using the formula for the price elasticity of supply:
$$ e_S = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} $$
Where:
$e_S$ is the price elasticity of supply,
$\Delta Q$ is the change in quantity supplied,
$\Delta P$ is the change in price,
$P$ is the average price,
$Q$ is the average quantity supplied.
Given:
$e_S = 0.5$,
$\Delta Q = 15$ units,
$P_1 = 5$,
$P_2 = 20$.
First, calculate $\Delta P$ and the average price (P):
[ \Delta P = P_2 - P_1 = 20 - 5 = 15 ]
[ P = \frac{P_1 + P_2}{2} = \frac{5 + 20}{2} = 12.5 ]
Next, rearrange the elasticity formula to solve for (Q), the average quantity supplied:
[ e_S = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} \Rightarrow Q = \frac{\Delta Q}{\Delta P} \times \frac{P}{e_S} ]
Substitute the known values:
[ Q = \frac{15}{15} \times \frac{12.5}{0.5} = 1 \times 25 = 25 ]
Thus, the average quantity supplied is 25 units. We can now calculate the initial quantity $Q_1$ and final quantity $Q_2$:
[ Q_2 = Q_1 + \Delta Q ]
[ Q = \frac{Q_1 + Q_2}{2} = \frac{Q_1 + (Q_1 + 15)}{2} = \frac{2Q_1 + 15}{2} = 25 ]
[ 2Q_1 + 15 = 50 \Rightarrow 2Q_1 = 50 - 15 = 35 \Rightarrow Q_1 = \frac{35}{2} = 17.5 ]
[ Q_2 = Q_1 + 15 = 17.5 + 15 = 32.5 ]
Therefore, the initial output level of the firm is 17.5 units, and the final output level is 32.5 units.
At the market price of Rs 10, a firm supplies 4 units of output. The market price increases to Rs 30. The price elasticity of the firm’s supply is 1.25. What quantity ? will the firm supply at the new price?
The firm will supply approximately 14 units of output at the new price of Rs 30.
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Ask Chatterbot AINotes - The Theory of the Firm under Perfect Competition | Class 12 Microeconomics | Economics
The Theory of the Firm Under Perfect Competition: Class 12 Notes
Introduction
Understanding how firms operate under perfect competition is essential for students of economics. This guide delves into key concepts, assumptions, and determinants affecting firms in perfectly competitive markets, providing thorough insights suitable for Class 12 students.
Key Assumptions and Features
Firm Behaviour Assumptions
In perfect competition, firms are considered ruthless profit maximisers. This theoretical assumption simplifies the complex decision-making process firms undergo to maximise their profits.
Defining Features of Perfect Competition
A perfectly competitive market possesses several key features:
- Large number of buyers and sellers: No single entity can influence market prices.
- Homogeneous products: Products are identical, making it impossible to differentiate between firms.
- Free entry and exit: Firms can freely enter or exit the market without barriers.
- Perfect information: Buyers and sellers have complete knowledge about prices and products.
Price-Taking Behaviour
Price-Taking for Firms
Firms in a perfectly competitive market accept the prevailing market price. If a firm sets prices higher, it risks losing customers to competitors.
Price-Taking for Buyers
Buyers also practice price-taking behaviour, where they purchase goods at the market price. Any attempt to negotiate a price lower than the market price would result in no sellers willing to sell.
Revenue and Profit in Perfect Competition
Total Revenue
Total revenue (TR) is calculated by multiplying the market price (p) by the quantity of goods sold (q). For example, if the market price of a box of candles is ₹10 and two boxes are sold, TR = ₹10 * 2 = ₹20.
Average Revenue
Average revenue (AR) is the total revenue per unit of output. It equals the market price in perfect competition since AR = TR / q = p.
Marginal Revenue
Marginal revenue (MR) is the increase in total revenue from selling one more unit of output. In perfect competition, MR equals the market price (p).
graph TD;
A[Market Price] --> B[Total Revenue] --> C[Average Revenue] --> D[Marginal Revenue]
A --> D
Profit Maximisation
Conditions for Profit Maximisation
For a firm to maximise profits, three conditions must hold:
- MR = MC: Marginal revenue must equal marginal cost.
- Non-decreasing MC: Marginal cost must not be decreasing.
- Price conditions: In the short run, p ≥ AVC; in the long run, p ≥ AC.
Graphical Representation
Profit maximisation can be represented graphically where the firm’s marginal cost curve intersects with its marginal revenue curve.
Deriving the Supply Curve
Short Run Supply Curve
The short run supply curve is derived from a firm's marginal cost curve. It is the part of the marginal cost curve that lies above the minimum average variable cost.
Long Run Supply Curve
The long run supply curve also originates from the marginal cost curve but considers the average cost in the long run.
Market Supply Curve
The market supply curve is an aggregate of individual firms' supply curves. It’s derived by horizontally summing up the supply curves of all firms in the market.
Shutdown and Break-Even Points
Short Run Shutdown Point
A firm will cease production in the short run if the market price falls below its minimum average variable cost.
Long Run Shutdown Point
In the long run, the shutdown point is where the market price is below the minimum average cost.
Normal Profit and Break-Even Point
Normal profit is the minimum profit necessary for a firm to stay in business, considered an opportunity cost. The break-even point is where the firm earns only normal profit, with no economic profit.
Determinants of a Firm's Supply Curve
Technological Progress
Technological advancements reduce production costs, shifting the supply curve to the right, allowing firms to supply more at any given price.
Input Prices
Increases in input prices shift the supply curve to the left, as production becomes costlier, reducing the quantity supplied at any given price.
Price Elasticity of Supply
Definition and Calculation
Price elasticity of supply measures how much the quantity supplied responds to changes in price. It’s calculated as:
[ e_s = \frac{\text{Percentage change in quantity supplied}}{\text{Percentage change in price}} ]
Provide a numerical example to illustrate.
Numerical Example
Consider a situation where the price of a cricket ball rises from ₹10 to ₹30, and the quantity supplied increases from 200 to 1,000. The price elasticity of supply would be:
[ e_s = \frac{\Delta Q / Q_1}{\Delta P / P_1} = \frac{(1000-200)/200}{(30-10)/10} = 2 ]
By understanding these core principles and graphical representations, students can grasp the theory of the firm under perfect competition, preparing them for exams and practical applications in economics.
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