# The Theory of the Firm under Perfect Competition

This page contains the NCERT Economics class 12 chapter 4 The Theory of the Firm Under Perfect Competition from Book I Introductory Microeconomics. You can find the solutions for the chapter 4 of NCERT class 12 Economics, for the Short Answer Questions, Long Answer Questions and Projects/Assignments Questions in this page. So is the case if you are looking for NCERT class 12 Economics related topic The Theory of the Firm Under Perfect Competition question and answers.
Exercises
1. What are the characteristics of a perfectly competitive market?
The characteristics of a perfectly competitive market are:
1.
Large Number of Buyers and Sellers: The market consists of a large number of buyers and sellers, which means that each individual buyer and seller is very small compared to the size of the market. No individual buyer or seller can influence the market by their size.
2.
Homogenous Product: Each firm produces and sells a homogenous product, i.e., the product of one firm cannot be differentiated from the product of any other firm.
3.
Free Entry and Exit: Entry into the market as well as exit from the market are free for firms. This condition is essential for the large numbers of firms to exist. If entry was difficult or restricted, then the number of firms in the market could be small.
4.
Perfect Information: All buyers and all sellers are completely informed about the price, quality, and other relevant details about the product, as well as the market.
These characteristics lead to the single most distinguishing characteristic of perfect competition: price-taking behavior. A price-taking firm believes that if it sets a price above the market price, it will be unable to sell any quantity of the good that it produces. Conversely, if the set price is less than or equal to the market price, the firm can sell as many units of the good as it wants to sell.
2. 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, market price (p), and the quantity sold by the firm (q) are related to each other in the following way:
Total Revenue (TR): It is defined as the market price of the good multiplied by the firm’s output. The formula is TR = p × q. This means that the total revenue is directly proportional to the quantity of goods sold and the price at which they are sold. For example, if the market price of a box of candles is ₹ 10, then selling one box results in a total revenue of ₹ 10, selling two boxes results in ₹ 20, and so on.
Market Price (p): This is the price at which the goods are sold in the market. In a perfectly competitive market, the firm is a price taker, which means it accepts the market price for its goods. The market price is constant for all units sold.
Quantity Sold by the Firm (q): This is the number of units of the good that the firm sells. The total revenue increases linearly with the quantity sold because the market price is fixed.
The relationship between these three can be depicted using a Total Revenue Curve, where the quantity sold is on the X-axis and the revenue earned is on the Y-axis. The curve is a straight line because the price is constant in a perfectly competitive market, making the TR curve an upward rising straight line.
Additionally, the Average Revenue (AR) of a firm is defined as total revenue per unit of output, which equals the market price {\left(AR = \dfrac{TR}{q} = p\right)}. The Marginal Revenue (MR) of a firm is the increase in total revenue for a unit increase in the firm’s output, and for a perfectly competitive firm, MR equals the market price (MR = p).
3. What is the ‘price line’?
The ‘price line’ is a concept in economics that refers to a horizontal straight line on a graph that represents the market price of a product in a perfectly competitive market. Here’s how it is related to a firm under perfect competition:
Price Line
Average Revenue (AR): For a price-taking firm, the average revenue equals the market price. This is because the firm can sell as much as it wants at the market price, and thus the total revenue divided by the quantity sold (which is the definition of AR) will always equal the market price.
Demand Curve for the Firm: The price line also depicts the demand curve facing a firm in perfect competition. It is perfectly elastic, indicating that the firm can sell any quantity of its product at the market price.
Marginal Revenue (MR): Marginal revenue is the additional revenue a firm earns by selling one more unit of a product. In a perfectly competitive market, the MR for the firm is equal to the market price, because each additional unit of output is sold at the same constant price.
Therefore, the price line is a graphical representation of the constant price at which a firm can sell its products in a perfectly competitive market. It is horizontal because the price does not change with the quantity of goods sold, reflecting the fact that firms in such markets are price takers.
4. 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 curve of a price-taking firm is an upward-sloping straight line because the total revenue (TR) is calculated by multiplying the market price (p) by the quantity sold (q). In a perfectly competitive market, the price is constant regardless of the quantity sold. Therefore, as the quantity sold increases, the total revenue increases at a constant rate, which is represented graphically by a straight line with a positive slope.
Total Revenue Curve
The total revenue curve passes through the origin because when the quantity sold is zero, the total revenue is also zero. This is intuitive because if a firm does not sell any goods, it does not generate any revenue. The equation TR = p × q translates into a straight line that begins at the origin (0, 0) on a graph where the x-axis represents quantity and the y-axis represents revenue.
To summarize, the total revenue curve is a straight line with a slope equal to the market price (p), and it passes through the origin because the total revenue is zero when no goods are sold.
5. What is the relation between market price and average revenue of a price-taking firm?
The relationship between market price and average revenue for a price-taking firm is direct and straightforward: for a price-taking firm, the average revenue (AR) equals the market price (p). This is because a price-taking firm in a perfectly competitive market has no control over the price of the product it sells; it must accept the market price.
Relationship between Market Price and Average Revenue
The average revenue is calculated as the total revenue (TR) divided by the quantity (q) of goods sold. Since the total revenue is the product of the market price and the quantity sold (TR = p × q), when you divide the total revenue by the quantity, the quantity terms cancel out, leaving you with the market price. Therefore, {AR = \dfrac{TR}{q} = \dfrac{(p × q)}{q} = p}.
This means that the average revenue curve for a price-taking firm is a horizontal line at the level of the market price, which is also referred to as the ‘price line’. This line reflects the fact that the firm can sell any quantity of its product at this price.
6. What is the relation between market price and marginal revenue of a price-taking firm?
For a price-taking firm in a perfectly competitive market, the marginal revenue (MR) is equal to the market price (p). This is because the firm can sell additional units of its product at the market price without affecting the price itself.
Relation between Marginal Price and Marginal Revenue.
Marginal revenue is the additional revenue that a firm earns by selling one more unit of a product. In a perfectly competitive market, when a firm sells one more unit, it does so at the market price, which means the increase in total revenue from selling that additional unit (which is the definition of MR) is exactly the market price.
Therefore,
MR
{= \dfrac{\text{Change in TR}}{\text{Change in quantity}}}
{= \dfrac{p × q_2 - p × q_1}{q_2 - q_1}}
{= \dfrac{p(q_2 - q_1)}{q_2 - q_1}}
{ = p}
This relationship is a key characteristic of perfect competition and indicates that the MR curve for a price-taking firm is also a horizontal line at the market price, just like the average revenue curve.
7. What conditions must hold if a profit-maximising firm produces positive output in a competitive market?
In a competitive market, it is generally the case that for a profit-maximising firm to produce a positive level of output, the market price must be equal to the marginal cost (P = MC). This is because the firm will increase its output until the point where the cost of producing one more unit (marginal cost) is exactly covered by the revenue from selling that unit (price). Producing beyond this point would mean the cost of producing an additional unit is greater than the revenue it would bring, which would decrease profits.
However, there could be a special scenario where a profit-maximising firm produces a positive level of output where the market price is not equal to marginal cost. This could occur if there are constraints or imperfections in the market that prevent the firm from adjusting its output instantly or if there are fixed costs that need to be covered in the short run. For instance, if the firm has already invested in a fixed cost that cannot be recovered in the short term (sunk cost), it might continue to produce as long as the price covers the average variable cost, even if the price does not cover the average total cost, which includes both variable and fixed costs.
In the short run, a firm may decide to produce even if the price is below the average total cost but above the average variable cost, because by contributing to the fixed costs, it reduces losses compared to not producing at all. In the long run, however, the firm would need to cover the full average cost to be profitable and remain in the market.
8. 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 competitive market, a profit-maximising firm will not produce at an output level where the market price is lower than the average cost (AC) in the long run. This is because, at such an output level, the firm’s total revenue (TR) would be less than its total cost (TC), leading to a loss. In the long run, a firm that shuts down production has a profit of zero, and it would choose to exit the market rather than incur a loss.
Therefore, for a profit-maximising firm in a competitive market, the market price must be greater than or equal to the average cost (AC) in the long run for it to produce a positive level of output. If the market price is less than the AC, the firm will not supply any output.
In the short run, however, the condition is slightly different. The price must be greater than or equal to the average variable cost (AVC) for the firm to continue production. If the market price falls below the AVC, the firm is better off shutting down production in the short run.
In summary, for a profit-maximising firm in a competitive market:
In the long run, the firm will not produce a positive output if the market price is less than the AC.
In the short run, the firm will not produce a positive output if the market price is less than the AVC.
9. 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.
A profit-maximizing firm in a competitive market will not produce a positive level of output at a point where the marginal cost (MC) is falling. This is because, for profit maximization, the firm’s output level must satisfy three conditions:
1.
The price (P) must equal the marginal cost (MC).
2.
The marginal cost must be non-decreasing at the profit-maximizing output level (q0).
3.
In the short run, the price must be greater than the average variable cost (AVC); in the long run, the price must be greater than the average cost (AC).
Specifically addressing the second condition, the document states that the marginal cost curve cannot slope downwards at the profit-maximizing output level. If the marginal cost were decreasing, it would imply that for output levels slightly less than the profit-maximizing output level, the marginal cost would be higher than the price, which contradicts the profit-maximizing principle that marginal revenue (MR) should equal marginal cost (MC).
Therefore, a profit-maximizing firm in a competitive market will not produce a positive level of output in the range where the marginal cost is falling because it would not satisfy the necessary condition for profit maximization—that the marginal cost must be non-decreasing at the profit-maximizing output level.
10. 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.
A profit-maximising 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). The explanation for this is based on the concept of the shutdown point.
The shutdown point is the level of pricing at which a firm ceases to produce in the short run. This occurs at the price-output combination where the price is equal to the minimum of the AVC. If the market price falls below this minimum AVC, the firm’s total revenue from producing any positive output would not cover its variable costs. Producing at a loss is not sustainable, even in the short term, because the firm would lose less money by shutting down and avoiding variable costs altogether.
In essence, if the market price is below the minimum AVC, the firm would incur a smaller loss by not producing anything, as its loss would be limited to its fixed costs, which have to be paid regardless of the level of output. Therefore, in the short run, a profit-maximising firm will produce zero output if the market price is less than the minimum AVC.
11. 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.
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). The explanation for this is grounded in the firm’s need to cover all of its costs in the long run to remain in business.
In the long run, all costs are variable, and there are no fixed costs. Therefore, the average cost includes all costs associated with production. If the market price is below the minimum average cost, the firm cannot cover its production costs, let alone make a profit. Producing under these conditions would lead to a loss with each unit of output sold because the revenue from selling the product at the market price would be less than the cost of producing it.
Consequently, in the long run, a firm will exit the market if it cannot produce at a level where the market price is at least equal to the minimum average cost. This ensures that the firm can cover its costs and make a non-negative economic profit. If the market price is below this level, the firm’s best response is to produce zero output and potentially shut down, as any production would result in a loss.
12. What is the supply curve of a firm in the short run?
The supply curve of a firm in the short run represents the quantity of goods that a firm is willing and able to produce and sell at each possible market price, given its existing plant size and fixed factors of production.
Short Run Supply Curve of a Firm (highlited in bold red)
Here are the key characteristics of a firm’s short run supply curve:
1.
Portion of the Marginal Cost Curve: The short run supply curve of a firm is the portion of its marginal cost (MC) curve that lies above the minimum average variable cost (AVC).
2.
Rising Part of SMC: It includes the rising part of the short run marginal cost (SMC) curve from and above the minimum point of the AVC curve.
3.
Market Price and Supply: When the market price is greater than or equal to the minimum AVC, the firm will supply the amount of output where the market price equals the firm’s marginal cost. If the market price is less than the minimum AVC, the firm will not supply any output and may shut down in the short run.
4.
Shutdown Point: The minimum point of the AVC curve is known as the shutdown point. If the market price falls below this point, the firm is better off shutting down and not producing anything because the revenue from selling the product would not cover the variable costs of production.
5.
Positive Output: A firm will produce a positive output in the short run as long as the price is equal to or greater than the AVC, and it will produce at the output level where price equals marginal cost.
6.
Zero Output: For all prices strictly less than the minimum AVC, the firm’s short run supply curve corresponds to zero output.
In summary, the short run supply curve of a firm in a competitive market is the upward-sloping part of the marginal cost curve that lies above the average variable cost curve.
13. What is the supply curve of a firm in the long run?
The supply curve of a firm in the long run reflects the quantity of goods that a firm is willing to produce and sell at each possible market price when all factors of production are variable, and the firm can adjust all inputs freely. This means the firm can change its plant size and enter or exit the industry in response to market conditions.
The Long run Supply Curve of a Firm
Here are the key characteristics of a firm’s long run supply curve:
1.
Portion of the Long Run Marginal Cost Curve (LRMC): The long run supply curve of a firm is the portion of its long run marginal cost curve that lies above the minimum point of the long run average cost curve (LRAC).
2.
Market Price and Supply: When the market price is greater than or equal to the minimum LRAC, the firm will supply the amount of output where the market price equals the firm’s long run marginal cost. If the market price is less than the minimum LRAC, the firm will not supply any output and may exit the market in the long run.
3.
Rising Part of LRMC: The firm’s long run supply curve is the rising part of the LRMC curve from and above the minimum LRAC.
4.
Zero Output Below Minimum LRAC: For all prices less than the minimum LRAC, the long run supply curve corresponds to zero output because the firm cannot cover its total costs at these prices and would therefore choose not to produce.
5.
Adjustment of Plant Size: In the long run, firms can adjust their plant sizes. This means that the long run supply curve can also reflect changes in the scale of production that are not possible in the short run.
6.
Entry and Exit: The long run supply curve takes into account the ability of firms to enter or exit the market. If firms are experiencing economic losses (where price is less than LRAC), they will exit the market, and if they are experiencing economic profits (where price is greater than LRAC), new firms will enter the market, which can affect the overall market supply curve.
In essence, the long run supply curve of a firm in a competitive market is the segment of the LRMC curve that is above the minimum point of the LRAC curve, indicating the range of prices at which the firm is willing to supply output when it is free to adjust all of its inputs and production capacity.
14. How does technological progress affect the supply curve of a firm?
Technological progress affects the supply curve of a firm by shifting it to the right (or downward). This shift occurs because technological advancements typically lead to improvements in production efficiency. Here’s how it works:
1.
Increased Productivity: Technological progress often means that a firm can produce more output with the same levels of capital and labor, or produce the same level of output with fewer inputs.
2.
Lower Marginal Costs: As a result of increased productivity, the marginal cost of producing each additional unit of output decreases. This is represented by a rightward (or downward) shift of the marginal cost (MC) curve.
3.
Shift in Supply Curve: Since a firm’s supply curve is essentially a segment of its marginal cost curve that lies above the average variable cost, a rightward shift in the MC curve translates into a rightward shift of the supply curve.
4.
Increased Supply at Given Prices: With a lower marginal cost, the firm can now supply more units of output at any given market price, which is the definition of a rightward shift in the supply curve.
5.
Impact on Market Supply: If many firms in the market experience technological progress, the market supply curve will also shift to the right, potentially leading to lower market prices and increased quantity supplied.
In summary, technological progress typically leads to a more efficient production process, which lowers the marginal cost of production and results in a rightward shift of the firm’s supply curve. This means that at any given price level, the firm is able to supply a greater quantity of goods.
15. How does the imposition of a unit tax affect the supply curve of a firm?
The imposition of a unit tax affects the supply curve of a firm by shifting it to the left (or upward). A unit tax is a tax imposed by the government on each unit of a good produced by the firm. Here’s the impact of a unit tax on the firm’s supply curve:
Effect of Unit Tax on Supply Curve of a Firm
1.
Increased Costs: The unit tax adds an additional cost to each unit of the good produced by the firm. This effectively increases the firm’s marginal cost and average cost by the amount of the tax for each unit produced.
2.
Shift in Cost Curves: The long run marginal cost (LRMC) curve and the long run average cost (LRAC) curve both shift upward by the amount of the tax.
3.
Shift in Supply Curve: Since the supply curve of a firm in the long run is the rising part of the LRMC curve from and above the minimum LRAC, the imposition of the unit tax shifts the firm’s long run supply curve to the left.
4.
Decreased Supply at Given Prices: With higher costs due to the tax, the firm now supplies fewer units of output at any given market price, which is the definition of a leftward shift in the supply curve.
5.
Impact on Market Supply: If all firms in the market are subject to the unit tax, the overall market supply curve will shift to the left as well, which could lead to higher market prices and a decreased quantity supplied.
In essence, a unit tax increases the cost of production per unit, which causes the firm to supply a smaller quantity of goods at any given price level, resulting in a leftward shift of the supply curve.
16. How does an increase in the price of an input affect the supply curve of a firm?
An increase in the price of an input affects the supply curve of a firm by shifting it to the left (or upward). Here’s how this works:
1.
Increased Production Costs: When the price of an input rises, the cost of production for the firm increases. This is because the firm has to spend more to acquire the same amount of input or has to reduce the quantity of input used, which can affect productivity.
2.
Shift in Marginal Cost (MC): The increase in input prices leads to an increase in the firm’s marginal cost at any level of output. This is because the marginal cost reflects the cost of producing one more unit of output, and if input prices are higher, the cost of producing that additional unit will also be higher.
3.
Shift in Supply Curve: Since the supply curve of a firm is essentially a segment of its MC curve that lies above the average variable cost (AVC), an upward shift in the MC curve translates into a leftward shift of the supply curve.
4.
Decreased Supply at Given Prices: With a higher marginal cost, the firm will now supply fewer units of output at any given market price, which is the definition of a leftward shift in the supply curve.
5.
Impact on Market Supply: If the increase in input prices affects all firms in the market similarly, the overall market supply curve will shift to the left as well, which could lead to higher market prices and a decreased quantity supplied.
In summary, an increase in the price of an input leads to higher production costs, which in turn increases the marginal cost of production. This results in a leftward shift of the firm’s supply curve, indicating that the firm will supply less at every price level.
17. 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 affects the market supply curve by shifting it to the right (or downward). Here’s the rationale behind this shift:
1.
More Producers: With more firms entering the market, there are more producers making the same type of goods.
2.
Increased Aggregate Supply: Each new firm contributes to the total supply of the good in the market, increasing the aggregate quantity of goods available at each price level.
3.
Shift in Market Supply Curve: The market supply curve, which represents the total quantity supplied by all firms at different price levels, shifts to the right as the total market supply increases.
4.
Potential Price Reduction: The increased supply in the market, assuming demand remains constant, may lead to a reduction in the market price of the good due to the greater availability.
5.
Enhanced Competition: More firms can also lead to increased competition, which might drive firms to become more efficient, potentially lowering costs and prices further.
In essence, an increase in the number of firms in a market typically leads to a rightward shift in the market supply curve, indicating that a larger quantity of the good will be supplied at each price level.
18. What does the price elasticity of supply mean? How do we measure it?
The price elasticity of supply (ES) measures the responsiveness of the quantity supplied of a good or service to a change in its price. It is a measure of how much the supply of a good is affected by changes in its price.
Here’s how the price elasticity of supply is defined and measured:
1.
Definition: PES is defined as the percentage change in quantity supplied divided by the percentage change in price.
2.
Formula: The elasticity of supply is calculated using the formula:
Price Elasticity of Supply (ES)
{= \dfrac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}}
{= \dfrac{\dfrac{ΔQ}{Q} × 100}{\dfrac{ΔP}{P} × 100}}
{= \dfrac{ΔQ}{Q} × \dfrac{P}{ΔP}}
Where
ΔQ is the change in quantity supplied.
Q is the original quantity supplied.
ΔP is the change in price.
P is the original price.
3.
Interpretation:
If PS > 1, supply is considered elastic. This means that the quantity supplied is highly responsive to price changes.
If PS < 1, supply is considered inelastic. This means that the quantity supplied is not very responsive to price changes.
If PS = 1, supply is unit elastic. This means that the quantity supplied is proportionately responsive to price changes.
If PS = 0, supply is perfectly inelastic. This means that the quantity supplied is completely unresponsive to price changes (this is rare and theoretical).
If PS is infinite, supply is perfectly elastic. This means that any small change in price would lead to an infinite change in quantity supplied (also a theoretical extreme).
4.
Calculation: To calculate PES, you need data on how the quantity supplied changes in response to price changes. This can be observed over time or across different producers.
5.
Factors Influencing PES:
Time Period: Supply is usually more elastic in the long run than in the short run because producers have more time to adjust their production levels.
Flexibility of Production: If a firm can easily increase production without a significant rise in costs, supply is more elastic.
Availability of Substitutes for the Input: If there are readily available substitutes for the inputs required in the production process, the supply is more elastic.
Spare Capacity: If a firm has spare capacity, it can increase production more easily when prices rise, making supply more elastic.
Understanding the price elasticity of supply is crucial for businesses and policymakers as it affects pricing strategies, taxation policies, and how markets respond to changes in supply conditions.
19. Compute the total revenue, marginal revenue and average revenue schedules in the following table. Market price of each unit of the good is ₹ 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 at a market price of ₹ 10, we can use the following formulas:
Total Revenue (TR)
= Quantity Sold (Q) × Market Price (P)
Marginal Revenue (MR)
{= \dfrac{\text{Change in Total Revenue}}{\text{Change in Quantity Sold}}}
Average Revenue (AR)
{= \dfrac{\text{Total Revenue}}{\text{Quantity Sold}}}
Given that the market price is constant at ₹ 10, the Marginal Revenue (MR) will be equal to the market price for each additional unit sold, because the addition to total revenue by selling one more unit is just the price at which that unit is sold.
Let’s compute the values for each quantity sold:
Quantity Sold
Q
Total Revenue
TR = Q × P
Marginal Revenue
{MR = \dfrac{ΔTR}{ΔQ}}
Average Revenue
{AR = \dfrac{TR}{Q}}
0
0 × 10 = 0
1
1 × 10 = 10
{\dfrac{10 - 0}{1 - 0} = 10}
{\dfrac{10}{1} = 10}
2
2 × 10 = 20
{\dfrac{20 - 10}{1} = 10}
{\dfrac{20}{2} = 10}
3
3 × 10 = 30
{\dfrac{30 - 20}{1} = 10}
{\dfrac{30}{3} = 10}
4
4 × 10 = 40
{\dfrac{40 - 30}{1} = 10}
{\dfrac{40}{4} = 10}
5
5 × 10 = 50
{\dfrac{50 - 40}{1} = 10}
{\dfrac{50}{5} = 10}
6
6 × 10 = 60
{\dfrac{60 - 50}{1} = 10}
{\dfrac{60}{6} = 10}
In this case, because the price is constant, the Marginal Revenue and Average Revenue remain constant at ₹ 10, which is equal to the market price. Total Revenue increases by ₹ 10 for each additional unit sold.
20. 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 (₹)
TC (₹)
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
Profit is calculated as Total Revenue (TR) minus Total Cost (TC). Let’s calculate the profit at each output level:
Quantity Sold
TR (₹)
TC (₹)
Profit (₹)
= TR – TC
Market Price
{MP = \dfrac{RT}{Q}}
0
0
5
0 – 5 = -5
1
5
7
5 – 7 = -2
{\dfrac{5}{1} = 5}
2
10
10
10 – 10 = 0
{\dfrac{10}{2} = 5}
3
15
12
15 – 12 = 3
{\dfrac{15}{3} = 5}
4
20
15
20 – 15 = 5
{\dfrac{20}{4} = 5}
5
25
23
25 – 23 = 2
{\dfrac{25}{5} = 5}
6
30
33
30 – 33 = -3
{\dfrac{30}{6} = 5}
7
35
40
35 – 40 = -5
{\dfrac{35}{7} = 5}
Now, to determine the market price of the good, we look at the total revenue for each additional unit sold. In a competitive market, the price per unit is constant, and the total revenue increases by this price with each additional unit sold.
From the table, we can see that the total revenue increases by ₹ 5 for each additional unit sold (from ₹ 0 to ₹ 5, ₹ 5 to ₹ 10, and so on). This implies that the market price of the good is ₹ 5 per unit.
Also, we can see that the firm makes a profit at quantities 3, 4, and 5, with the highest profit of ₹ 5 occurring at a quantity of 4 units sold. At other quantities, the firm either breaks even (quantity 2) or incurs a loss.
21. The following table shows the total cost schedule of a competitive firm. It is given that the price of the good is ₹ 10. Calculate the profit at each output level. Find the profit maximising level of output.
Output
TC (₹)
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, we need to subtract the total cost (TC) from the total revenue (TR) at each level of output. Since the price of the good is given as ₹ 10, the total revenue at each output level can be calculated by multiplying the output by the price (P).
Total Revenue (TR)
= Output (Q) × Price (P)
Profit
= Total Revenue (TR) – Total Cost (TC)
Let’s calculate the profit for each output level:
Output
TC (₹)
TR (₹)
Output × 10
Profit (₹)
= TR – TC
0
5
0 × 10 = 0
0 – 5 = -5
1
15
1 × 10 = 10
10 – 15 = -5
2
22
2 × 10 = 20
20 – 22 = -2
3
27
3 × 10 = 30
30 – 27 = 3
4
31
4 × 10 = 40
40 – 31 = 9
5
38
5 × 10 = 50
50 – 38 = 12
6
49
6 × 10 = 60
60 – 49 = 11
7
63
7 × 10 = 70
70 – 63 = 7
8
81
8 × 10 = 80
80 – 81 = -1
9
101
9 × 10 = 90
90 – 101 = -11
10
123
10 × 10 = 100
100 – 123 = -23
Now, to find the profit-maximising level of output, we look for the output level with the highest profit. From the table, we can see that the maximum profit of ₹ 12 is at an output level of 5 units.
Therefore, the profit-maximising level of output for the firm is 5 units.
22. Consider a market with two firms. The following table shows the supply schedules of the two firms: the SS~1~ column gives the supply schedule of firm 1 and the SS~2~ column gives the supply schedule of firm 2. Compute the market supply schedule.
Price (₹)
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
The market supply schedule is obtained by adding the supply schedules of the individual firms at each price level. To compute the market supply schedule, we simply sum the quantities supplied by firm 1 (SS1) and firm 2 (SS2) at each price.
Here is the market supply schedule based on the given data:
Price
(₹)
SS1
(units)
SS2
(units)
Market Supply
= SS1 + SS2
(units)
0
0
0
0 + 0 = 0
1
0
0
0 + 0 = 0
2
0
0
0 + 0 = 0
3
1
1
1 + 1 = 2
4
2
2
2 + 2 = 4
5
3
3
3 + 3 = 6
6
4
4
4 + 4 = 8
So, at a price of ₹ 3, the market supply is 2 units; at a price of ₹ 4, the market supply is 4 units; and this pattern continues, with the market supply increasing by 2 units for each ₹ 1 increase in price.
23. 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 (₹)
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, we add the supply from firm 1 (SS1) and firm 2 (SS2) at each price level. Here’s the market supply schedule based on the given data:
Price (₹ )
SS1 (kg)
SS2 (kg)
Market Supply
= SS1 + SS2 (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
The market supply at each price level is the sum of the supplies from both firms.
24. There are three identical firms in a market. The following table shows the supply schedule of firm 1. Compute the market supply schedule.
Price (₹)
SS1 (units)
0
0
1
0
2
2
3
4
4
6
5
8
6
10
7
12
8
14
If there are three identical firms in the market, each with the same supply schedule as firm 1, then the market supply schedule is simply three times the supply of firm 1 at each price level. We can calculate the market supply by multiplying the supply from firm 1 (SS1) by 3.
Here’s the market supply schedule based on the given data:
Price (₹)
SS1 (units)
Market Supply
= SS1 × 3 (units)
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
The market supply at each price level is the aggregate of the supplies from all three firms.
25. A firm earns a revenue of ₹ 50 when the market price of a good is ₹ 10. The market price increases to ₹ 15 and the firm now earns a revenue of ₹ 150. What is the price elasticity of the firm’s supply curve?
The price elasticity of supply (ES) measures the responsiveness of the quantity supplied to a change in price. It is calculated using the formula:
{E_S = \dfrac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}}
First, we need to calculate the percentage change in quantity supplied and the percentage change in price.
From the information given:
Initial Price P1
= ₹ 10
Final Price P2
= ₹ 15
Initial Revenue R1
= ₹ 50
Final Revenue R2
= ₹ 150
Since Revenue = Price × Quantity, we can calculate the initial and final quantities supplied Q1 and Q2:
Initial Quantity Supplied Q1
{= \dfrac{R_1}{P_1}}
{= \dfrac{50}{10}}
= 5 units
Final Quantity Supplied Q2
{= \dfrac{R_2}{P_2}}
{= \dfrac{150}{15}}
= 10 units
Now we calculate the percentage changes:
Percentage Change in Quantity Supplied
{= \dfrac{Q_2 - Q_1}{Q_1} × 100}
Percentage Change in Price
{= \dfrac{P_2 - P_1}{P_1} × 100}
Substituting the values:
Percentage Change in Quantity Supplied
{ = \dfrac{10 - 5}{5} × 100}
{ = \dfrac{5}{5} × 100}
= 100%
Percentage Change in Price
{= \dfrac{15 - 10}{10} × 100}
{= \dfrac{5}{10} × 100}
= 50%
Finally, we calculate the ES:
ES
{= \dfrac{100\%}{50\%}}
= 2
The price elasticity of the firm’s supply curve is 2, which means the supply is elastic. For every 1% increase in price, the quantity supplied increases by 2%.
26. The market price of a good changes from ₹ 5 to ₹ 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.
The price elasticity of supply (ES) is given by the formula:
{E_S = \dfrac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}}
We are given:
ES
= 0.5
Initial Price P1
= ₹ 5
Final Price P2
= ₹ 20
Change in Quantity Supplied ΔQ
= 15 units
First, we need to calculate the percentage change in price:
Percentage Change in Price = {\dfrac{P_2 - P_1}{P_1} × 100}
Substituting the values:
Percentage Change in Price
{= \dfrac{20 - 5}{5} × 100}
{= \dfrac{15}{5} × 100}
= 3 × 100
= 300%
Now we can use the ES formula to find the percentage change in quantity supplied:
{0.5 = \dfrac{\text{Percentage Change in Quantity Supplied}}{300\%}}
Solving for the percentage change in quantity supplied:
Percentage Change in Quantity Supplied
= 0.5 × 300%
= 150%
This means the quantity supplied increased by 150% of the initial quantity supplied. To find the initial quantity supplied Q1, we use the fact that a 150% increase corresponds to the 15 units increase we have:
1.5 × Q1 = 15 units
Solving for Q1:
Q1
{= \dfrac{15 \text{ units}}{1.5}}
= 10 units
Now that we have the initial quantity supplied, we can find the final quantity supplied Q2 by adding the change in quantity supplied to the initial quantity:
Q2
= Q1 + ΔQ
= 10 units + 15 units
= 25 units
So, the initial output level of the firm was 10 units, and the final output level was 25 units.
27. At the market price of ₹ 10, a firm supplies 4 units of output. The market price increases to ₹ 30. The price elasticity of the firm’s supply is 1.25. What quantity will the firm supply at the new price?
The price elasticity of supply (ES) is given by the formula:
{E_S = \dfrac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}}
We are given:
ES
= 1.25
Initial Price P1
= ₹ 10
Final Price P2
= ₹ 30
Initial Quantity Supplied Q1
= 4 units
First, we need to calculate the percentage change in price:
{\text{Percentage Change in Price} = \dfrac{P_2 - P_1}{P_1} × 100}
Substituting the values:
Percentage Change in Price
{= \dfrac{30 - 10}{10} × 100}
{= \dfrac{20}{10} × 100}
= 2 × 100
= 200%
Now we can use the PS formula to find the percentage change in quantity supplied:
{1.25 = \dfrac{\text{Percentage Change in Quantity Supplied}}{200\%}}
Solving for the percentage change in quantity supplied:
Percentage Change in Quantity Supplied
= 1.25 × 200%
= 250%
This means the quantity supplied increased by 250% of the initial quantity supplied. To find the change in quantity supplied ΔQ, we use the fact that a 250% increase corresponds to the change in quantity supplied based on the initial quantity:
ΔQ = 2.5 × Q1
Since Q1 = 4 units:
ΔQ
= 2.5 × 4
= 10 units
Now we can find the final quantity supplied Q2 by adding the change in quantity supplied to the initial quantity:
Q2
= Q1 + ΔQ
= 4 units + 10 units
= 14 units
So, at the new price of ₹ 30, the firm will supply 14 units of output.