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The Theory of the Firm Under Perfect Competition

CBSE · Class 12 · Economics

NCERT Solutions for The Theory of the Firm Under Perfect Competition — CBSE Class 12 Economics.

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An infographic illustrating the four key defining features of a perfectly competitive market: large number of buyers and sellers, homogenous products, free entry and exit, and perfect information. Eac
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27 Questions Solved · 1 Section

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Exercises

1What are the characteristics of a perfectly competitive market?Show solution
A perfectly competitive market has these defining features:

- There are a large number of buyers and sellers.
- Each firm produces a homogeneous product.
- Entry and exit are free for firms.
- There is perfect information about price, quality, and other relevant details.

Because of these features, no single buyer or seller can influence the market price, so firms are price takers.

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2How are the total revenue of a firm, market price, and the quantity sold by the firm related to each other?Show solution
The total revenue (TR) of a firm is the market price of the good multiplied by the quantity sold by the firm.

So, if market price is pp and quantity sold is qq, then

TR=p×qTR = p \times q

If either price or quantity changes, total revenue changes accordingly.

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3What is the 'price line'?Show solution
The price line is a horizontal straight line at the market price pp on the revenue-output graph. It shows that under perfect competition a firm can sell any quantity at the given market price. It is also the firm's average revenue curve and the demand curve facing the firm.

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4Why is the total revenue curve of a price-taking firm an upward-sloping straight line? Why does the curve pass through the origin?Show solution
The total revenue curve of a price-taking firm is an upward-sloping straight line because

TR=p×qTR = p \times q

and in perfect competition the market price pp is constant. So as output qq increases, total revenue rises at a constant rate, which gives a straight line.

The curve passes through the origin because when output is zero, no output is sold and therefore

TR=p×0=0TR = p \times 0 = 0

So at zero output, total revenue is also zero.

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5What is the relation between market price and average revenue of a price-taking firm?Show solution
For a price-taking firm,

AR=TRq=p×qq=pAR = \frac{TR}{q} = \frac{p \times q}{q} = p

So average revenue equals market price.

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6What is the relation between market price and marginal revenue of a price-taking firm?Show solution
For a price-taking firm, when output rises by one unit, that extra unit is sold at the same market price. Therefore the increase in total revenue from one more unit is exactly the market price.

So,

MR=pMR = p

Hence for a perfectly competitive firm, marginal revenue equals market price.

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7What conditions must hold if a profit-maximising firm produces positive output in a competitive market?Show solution
If a profit-maximising firm produces positive output in a competitive market, these conditions must hold at that output level:

1. Price equals marginal cost: p=MCp = MC
2. Marginal cost is non-decreasing at that output level
3. In the short run, p≥AVCp \ge AVC; in the long run, p≥ACp \ge AC

These conditions ensure that the chosen output maximises profit and that producing is better than shutting down.

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8Can 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.Show solution
No. In perfect competition, a positive profit-maximising output must satisfy **p=MCp = MC.

If market price is not equal to marginal cost at some positive output, profit can be increased by changing output:
- If MR>MCMR > MC, increasing output raises profit.
- If MR<MCMR < MC, reducing output raises profit.

Since for a competitive firm MR=pMR = p, profit maximisation requires p=MCp = MC** at the chosen positive output.

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9Will 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.Show solution
No. A profit-maximising firm will not produce a positive output where marginal cost is falling.

The chapter states the second condition for profit maximisation: marginal cost must be non-decreasing at the profit-maximising output level. If the MC curve is falling, then the same price can be matched at another output with higher profit, so that output cannot be the maximum-profit point.

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10Will 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 AVCAVC ? Give an explanation.Show solution
No. In the short run, if market price is less than the minimum of AVC, the firm will not produce positive output.

Reason: at any positive output, total revenue is less than total variable cost, so producing gives a loss larger than the loss from shutting down. If the firm produces zero output, its loss is only TFC. Therefore, it is better to shut down and produce nothing.

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11Will 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 ACAC ? Give an explanation.Show solution
No. In the long run, if market price is less than the minimum of AC, the firm will not produce positive output.

Reason: at any positive output, total cost exceeds total revenue, so the firm makes a loss. In the long run, a firm can exit the market and earn zero profit by shutting down. Hence it will exit rather than continue producing at a loss.

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12What is the supply curve of a firm in the short run?Show solution
The chapter defines a firm's short run supply curve as:

- the rising part of the short-run marginal cost curve (SMC) starting from the point where price is equal to the minimum AVC, and
- zero output for all prices below the minimum AVC.

So the firm supplies positive output only when the market price is at least the minimum AVC.

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13What is the supply curve of a firm in the long run?Show solution
The chapter defines a firm's long run supply curve as:

- the rising part of the long-run marginal cost curve (LRMC) starting from the minimum of LRAC, and
- zero output for all prices below the minimum LRAC.

Thus, in the long run, the firm produces only when price covers at least the minimum long-run average cost.

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14How does technological progress affect the supply curve of a firm?Show solution
Technological progress lowers the firm's marginal cost at any given output level. This causes the MC curve to shift rightward/downward. Since the supply curve is a segment of the MC curve, the firm's supply curve shifts to the right.

Therefore, at any given market price, the firm now supplies more output.

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15How does the imposition of a unit tax affect the supply curve of a firm?
16How does an increase in the price of an input affect the supply curve of a firm?
17How does an increase in the number of firms in a market affect the market supply curve?
18What does the price elasticity of supply mean? How do we measure it?
19Compute the total revenue, marginal revenue and average revenue schedules in the following table. Market price of each unit of the good is Rs 10.
20The 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.
21The 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.
22Consider a market with two firms. The following table shows the supply schedules of the two firms: the SS1SS_1 column gives the supply schedule of firm 1 and the SS2SS_2 column gives the supply schedule of firm 2. Compute the market supply schedule.
23Consider a market with two firms. In the following table, columns labelled as SS1SS_1 and SS2SS_2 give the supply schedules of firm 1 and firm 2 respectively. Compute the market supply schedule.
24There are three identical firms in a market. The following table shows the supply schedule of firm 1. Compute the market supply schedule.
25A 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?
26The 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.
27At 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?

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