NCERT Solutions for Class 11 Economics Chapter 4 - The Theory Of The Firm Under Perfect Competition
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31. How are the total revenue of a firm, market price, and the quantity sold by the firm related to each other?
Ans. The total revenue is the product of output sold at market price, whereas the market price is the ratio of total revenue and quantity sold.
TR = Price × Quantity
Hence, P=TR/Q
32. Why is the total revenue curve of a price-taking firm an upward-sloping straight line? Why does the curve pass through the origin?
Ans. For a price-taking firm, Average Revenue is constant. If AR is constant, MR is also constant.
Hence, TR increases at a constant rate and it forms a straight line sloping upward. It passes through the point of origin, simply because TR is zero when the output is zero.
33. What is the relation between market price and average revenue of a pricetaking firm?
Ans. The market price and the average revenue of a price-taking firm are equal. Graphically, they are indicated by a horizontal straight line as the market price is constant for a price-taking firm.
34. What is the relation between market price and marginal revenue of a pricetaking firm?
Ans. For a perfectly competitive firm, marginal revenue is equal to the market price per unit of output. Marginal revenue is the change in the total revenue that occurs due to the sale of one more unit of output.
35. 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.
Ans. It is not possible for any perfect competitive firm to produce a positive level of output in a range where MC is falling. According to one of the conditions of profit-maximization, the MC curve should be upward sloping or the slope of the MC curve should be positive at the equilibrium level of output.
36. 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.
Ans. The market price must be greater than or equal to the AVC at that output level. Hence, when the price is less than the minimum AVC, the firm produces zero output.
37. 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.
Ans. If the market price falls short of the minimum of A. As, in the long run there is a free entry and exit of firms and all firms earn normal profit. Therefore, any firm making losses in long run will stop production.
38. What is the supply curve of a firm in the short run?
Ans. The firm’s short‐run supply curve is the portion of its marginal cost curve that lies above its average variable cost curve. One of the factors in the short-run is variable and others are fixed.
39. What is the supply curve of a firm in the long run?
Ans. Starting from the break-even point, when price = average cost the rising segment of the firm’s MC curve represents the firm's supply curve in the long run.
In long run, all factors are variable, period in which supply can be changed by changing all the factors of production.
There is no difference between fixed and variable factors. In the long run, the firm produces only at minimum average cost.
40. How does technological progress affect the supply curve of a firm?
Ans. The supply curve of a firm is a positive function of a state of technology. Which means if the technology available to the firm appreciates, more amount of output can be produced by the firm with the given levels of capital and labour. Due to the technological advancements, the firm will experience lower cost of production, which will lead the MC curve to the rightward or downward. Thus, due to the appreciation and advancement of production techniques, the firm will produce more and more output that will be supplied at a given market price.
41. How does the imposition of a unit tax affect the supply curve of a firm?
Ans. When there is a imposition of a unit tax on the production of goods, the unit cost of production will rise and therefore, the firm would supply less than before at the given price and accordingly supply curve would shift to the left.
42. How does an increase in the price of an input affect the supply curve of a firm?
Ans. An increase in input price shifts the marginal cost curve of the firm upward. Accordingly, the supply curve shifts upward.
43. How does an increase in the number of firms in a market affect the market supply curve?
Ans. When the number of firms increases in the market, the market supply curve shifts to the right.
44. What does the price elasticity of supply mean? How do we measure it?
Ans. Price elasticity of supply is the percentage change in quantity supplied caused by a given percentage change in own price of the commodity. It is measured as the ratio between the percentage change in quantity supplied and the percentage change in the price of the commodity.
45. 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 |
Ans.
| Quantity (Units) | TR = P × Q (₹) | MR = TR n – TR n – 1 (₹) | AR = Price (₹ 10) |
| 0 | 10 × 0 = 10 | — | — |
| 1 | 10 × 1 = 10 | 10 – 0 = 10 | 10 |
| 2 | 10 × 2 = 20 | 20 – 10 = 10 | 10 |
| 3 | 10 × 3 = 30 | 30 – 20 = 10 | 10 |
| 4 | 10 × 4 = 40 | 40 – 30 = 10 | 10 |
| 5 | 10 × 5 = 50 | 50 – 40 = 10 | 10 |
| 6 | 10 × 6 = 60 | 60 – 50 = 10 | 10 |
46. 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 |
Ans.
| Quantity (Units) | TR (₹) | TC (₹) | Profit (₹) | MR (₹) |
| 0 | 0 | 5 | -5 | - |
| 1 | 5 | 7 | -2 | 5 |
| 2 | 10 | 10 | 0 | 5 |
| 3 | 15 | 12 | 3 | 5 |
| 4 | 20 | 15 | 5 | 5 |
| 5 | 25 | 23 | 2 | 5 |
| 6 | 30 | 33 | -3 | 5 |
| 7 | 35 | 40 | -5 | 5 |
47. 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.
| Quantity Sold | TC (₹) |
| 0 | 5 |
| 1 | 15 |
| 2 | 22 |
| 3 | 27 |
| 4 | 31 |
| 5 | 38 |
| 6 | 49 |
| 7 | 63 |
| 8 | 81 |
| 9 | 101 |
| 10 | 123 |
Ans.
| Quantity (Units) | Price (₹) | TC (₹) | TR (₹) | Profit |
| 0 | 10 | 5 | 0 | -5 |
| 1 | 10 | 15 | 10 | 5 |
| 2 | 10 | 22 | 20 | -2 |
| 3 | 10 | 27 | 30 | 3 |
| 4 | 10 | 31 | 40 | 9 |
| 5 | 10 | 38 | 50 | 12 |
| 6 | 10 | 49 | 60 | 11 |
| 7 | 10 | 63 | 70 | 7 |
| 8 | 10 | 81 | 80 | -1 |
| 9 | 10 | 101 | 90 | -11 |
| 10 | 10 | 123 | 100 | -23 |
Firm is earning profit of ₹12 as the profit maximising level is at 5 units sold.
48. 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 (₹) | SS 1 (units) | SS 2 (units) |
| 0 | 0 | 0 |
| 1 | 0 | 0 |
| 2 | 0 | 0 |
| 3 | 1 | 1 |
| 4 | 2 | 2 |
| 5 | 3 | 3 |
| 6 | 4 | 4 |
Ans.
| Price (₹) | SS1 (unit) | SS2 (unit) | SS (Market Supply Schedule) |
| 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 |
49. 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 |
Ans.
| Price (₹) | SS1 (kg) | SS2 (kg) | SS (Market Supply Schedule) |
| 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 |
| 3 | 1 | 0 | 1 |
| 4 | 2 | 0.5 | 2.5 |
| 5 | 3 | 1 | 3 |
| 6 | 4 | 1.5 | 5.5 |
| 7 | 5 | 2 | 7 |
| 8 | 6 | 2.5 | 8.5 |
50. 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 |
Ans.
| Q | Total cost | Total cost by all 3 firms | Quantity Supplied |
| 0 | 0 | 0 × 3 = 0 | 0 |
| 1 | 0 | 0 × 3 = 0 | 3 |
| 2 | 2 | 2 × 3 = 6 | 6 |
| 3 | 4 | 4 × 3 = 12 | 9 |
| 4 | 6 | 6 × 3 = 18 | 12 |
| 5 | 8 | 8 × 3 = 24 | 15 |
| 6 | 10 | 10 × 3 = 30 | 18 |
| 7 | 12 | 12 × 3 = 36 | 21 |
| 8 | 14 | 14 × 3 = 42 | 24 |
51. 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 Rs 150. What is the price elasticity of the firm’s supply curve?
Ans. Initial price (P1) = ₹10
Final price (P2) = ₹15
ΔP = P2 – P1
= 15 – 10 = ₹5
P1 = ₹10
Revenue = ₹50
$$Q_1=\frac{R}{P_1}=\frac{50}{10}=5\text{unit}\\P2=₹15\\\text{Revenue}=₹150\\Q_2=\frac{R}{P_2}=\frac{150}{10}=10\text{units}\\\Delta Q=Q_2–Q_1\\= 10 – 5 = 5\text{units}\\e_s=\frac{\Delta Q}{\Delta P}×\frac{P}{Q}=\frac{5}{5}×\frac{10}{5}\\e_s=2$$
52. 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.
Ans. P1 = ₹5, P2 = ₹20, ΔP = P2 – P1 = 20 – 5 = ₹15
ΔQ = 15 units
es = 0.5
$$e_s=\frac{\Delta Q}{\Delta P}×\frac{P}{Q}=\frac{15}{15}×\frac{5}{Q}=0.5\\Q=\frac{5}{0.5}=10\text{unit}$$
Initial quantity (Q1) = 10 units
Final Quantity (Q2) = ΔQ = Q2 – Q1
Q2 = DQ + Q1
= 15 + 10 = 25 units
53. 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?
Ans. P1 = ₹10, Q1 = 4 units, P2 = ₹30 Q1 = ?
$$e_s=\frac{\Delta Q}{\Delta P}×\frac{P}{Q}=\frac{\Delta Q}{20}×\frac{10}{4}=1.25$$
ex = 1.25
ΔP = P2 – P1 = 30 – 10 = ₹20
ΔQ = 1.25 × 8 = 10 units
Q2 = ΔQ + Q1 = (10 + 4) units
= 14 units
39. What are the characteristics of a perfectly competitive market?
Ans. The characteristics of a Perfectly Competitive Market are:
- Large number of buyers and sellers: A large number of buyers and sellers exists in a perfectly competitive market. The number of sellers is so large that no individual firm owns control over the market price of a commodity.
Therefore,
perfect and free competition exists due to a large number of sellers in the market. A firm acts as a price taker while the price is determined by the forces like the demand for’ and ‘supply of’ goods. Thus, we can conclude that under a perfectly competitive market, an individual firm is a price taker and not a price maker. - Homogenous products: In a perfectly competitive market, all the firms produce homogeneous products. This signifies that the output of each firm is perfect substitute to others’ output in terms of quantity, quality, colour, size, features, etc. This implies that the buyers are indifferent to the output of different firms. Due to the homogenous nature of products, the existence of uniform prices is guaranteed.
- Free entry and exit of firms: In the long run, there is free entry and exit of firms. However, in the short run, some fixed factors obstruct the free entry and exit of firms. This ensures that all the firms in the long run earn normal profit or zero economic profit which measures the opportunity cost of the firms either to continue production or to shut down. If there are abnormal profits, new firms will enter the market and if there are abnormal losses, a few existing firms will exit the market.
- Perfect knowledge among buyers and sellers: In a perfectly competitive market, both buyers and sellers are fully aware of the market conditions, such as the price of a product at different places. The sellers should be cautious of the prices at which the buyers are willing to buy the product.
The implication of this feature is that if any individual firm is charging a higher (or lower) price for a homogeneous product, the buyers will shift their purchase to other firms (or shift their purchase from the firm to other firms selling at a lower price).
40. What is the ‘price line’?
Ans. Price line also known as firm’s demand curve is a line showing different combinations of two commodities that a consumer can obtain at a given income and the given market price of the goods.
41. What conditions must hold if a profit-maximising firm produces positive output in a competitive market?
Ans. The following three conditions must hold if a profit-maximising firm produces a positive level of output (says equilibrium output Q) in a competitive market:
4. Perfect
(i) MR must be equal to MC at Q*. (ii) MC should be upward-sloping or rising at Q*.
(iii) The price must be greater than or equal to AVC. i.e., P ≥ AVC at Q in the short-run and price must be greater than or equal to LAC in the long-run.
42. 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.
Ans. There cannot be a positive level of output for profit-maximizing firms when average revenue is not equal to marginal cost because the output will be produced at equilibrium, where marginal revenue is equal to marginal cost.
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