Exercise Set 13
PERFECT COMPETITION

I. Objectives

• To determine the optimal quantity for a firm in perfect competition
• To obtain the firm's maximum profits
• To indicate the optimal values on a graph
• To derive a firm's supply curve

II. Data

• A firm in a perfectly competitive market can sell its output at a market price of P.
• The firm's cost function is: C = aQ + bQ² + F.
• The marginal cost function is: MC = a + 2bQ.
• For selected values of P, a, b and F, obtain the firm's optimal output (Q*).
• Compute the firm's average cost at Q*.
• What is the firm's maximum profit?
• Click on Gimme Output and stuff! to confirm your results.

III. Questions

1. Select values for P, a, b and F. Sketch the demand curve facing the perfectly-competitive firm.
2. The horizontal demand curve for the firm's output implies that demand is [ perfectly elastic / perfectly inelastic / unit-elastic ].
3. Sketch the MC and AC curves. Determine and indicate the optimal output (Q*).
4. Compute the firm's total revenue, total cost and profit at Q*. Indicate the corresponding "rectangular areas" on the graph.
5. Suppose the market price increases by 20%. Find the new Q* and profit.
6. Derive a positively-sloped supply curve for the firm.
7. A decrease in the firm's fixed costs will cause the firm to produce [ more / less / the same ] output. Explain.
8. A firm will continue to operate in the short run even if it makes a loss. Using an appropriate value for P, explain when that is true. Provide a sketch.

IV. Additional Questions

1. Consider a firm in a perfectly competitive market.
   (a) What are the characteristics of perfect competition?
   (b) Explain how the firm chooses the optimal output level.
   (c) Indicate your answer to (b) on a graph.
   (d) On the graph in (c), indicate the areas depicting total revenue, total cost, and profit.
   
   
2. Assume that the market for apples is perfectly competitive. The equilibrium price of apples is $2/lb; 3000 lbs of apples are sold in the market; and each (identical) firm is making zero profits.
   (a) Sketch the market demand and supply curves, and indicate the equilibrium price and quantity of apples.
   (b) Sketch the demand curve, marginal cost curve and average cost curve for an individual firm in the industry.
   Suppose consumers' incomes rise, thus causing an increase in the demand for apples.
   (c) In the short run, what is the effect on:
   1. The market price, and
   2. The optimal output produced by a firm in the industry?
   Provide explanations and graphs to support your answers.

3. The industry for gizmos is perfectly competitive. The market price of a gizmo is $10. At this price, a gizmo- making firm maximizes its profits by producing 40 gizmos.
   (a) Describe the optimal rule used by the firm in determining this output level (i.e., 40 gizmos).
   (b) Provide a sketch of: (i) The demand curve facing the firm, and (ii) The firm's marginal cost and average costs curves. Indicate the optimal output level. Also, show the total revenue, total cost and profit on the graph.

4. Explain whether the following statements about firms in perfect competition are true or false. Provide sketches to support your answers.
   (a) The elasticity of demand for an individual firm's output is zero.
   (b) The demand curve for the industry is horizontal at the market price.

5. You are the owner of a business consulting firm. Last year, your revenues were $90,000, and explicit costs (labor costs, costs of materials, rent on office space, taxes, etc.) were $40,000.
   (a) Explain how you would compute your accounting profit.
   (b) Explain how you would compute your economic profit.
   (c) Why is economic profit less than accounting profit?

6. A perfectly competitive nursery grows flowers using labor. Flowers are sold at a price of P_F, while a unit of labor costs P_L. The profit-maximizing amount of labor is obtained at the point where
   (a) P_F = P_L
   (b) P_F = P_L x MP_L
   (c) P_L = P_F x MP_L
   (d) P_L = MP_L / P_F

7. A pound of fertilizers sells for $180. Corn, which is produced using fertilizers, sells for $90 per bushel in a perfectly competitive market. The last pound of fertilizers used by a profit-maximizing farmer will increase the output of corn by
   (a) 0.5 bushels
   (b) 1 bushel
   (c) 2 bushels
   (d) 3 bushels

8. The daily wage rate for a farm laborer is $120. A farmer hires laborers to produce wheat which sells for $30 per bushel in a perfectly competitive market. The last worker hired by the profit-maximizing farmer will increase the daily output of wheat by
   (a) 0.25 bushels
   (b) 2 bushels
   (c) 4 bushels
   (d) 30 bushels
   (e) 150 bushels

9. A firm in perfect competition will discontinue production in the short run if:
   (a) Price is less than marginal cost
   (b) Price is less than average variable cost
   (c) Price is less than average total cost
   (d) Price is less than marginal revenue
   (e) None of the above

10. A firm reaches a break-even point where:
    (a) Marginal revenue cuts the horizontal axis
    (b) Marginal cost intersects the average variable cost curve
    (c) Total revenue equals total variable cost
    (d) Total revenue and total cost are equal

11. In the short-run, a purely competitive firm will shut down:
    (a) At any point where price is less than the minimum AVC
    (b) Between the two break-even points
    (c) At any point where total revenue is less than total cost
    (d) At any point where the firm is not making an economic profit
    (e) At any point where price is less than the minimum ATC

12. In a purely competitive industry:
    (a) There will be no economic profits in either the short or the long run
    (b) Economic profits may persist in the long run if consumer demand is strong
    (c) There may be economic profits in the short run, but not in the long run
    (d) There may be economic profits in the long run, but not in the short run
    (e) None of the above

13. Suppose that a firm faces a horizontal demand curve P = $10 and it produces Q = 5,000 units in order to maximize its profit. Then:
    a. the firm's marginal cost is less than $10.
    b. the firm's marginal revenue is less than $10.
    c. the firm's marginal revenue is $10.
    d. the firm's marginal revenue is more than $10.
    e. none of the above.

14. The basic characteristic of the short run is that:
    a. barriers to entry prevent new firms from entering the industry.
    b. the firm does not have sufficient time to change the size of its plant.
    c. the firm does not have sufficient time to cut its rate of output to zero.
    d. a firm does not have sufficient time to change the amounts of any of the resources it employs.
    e. none of the above.

15. In the long run:
    a. all costs are variable costs.
    b. all costs are fixed costs.
    c. variable costs tend to be greater than fixed costs.
    d. fixed costs tend to be greater than variable costs.
    e. none of the above.

16. A firm in perfect competition faces the demand function P = $40. This implies that it:
    a. can sell any quantity at $40 a unit.
    b. can sell some quantity at prices higher than $40 a unit.
    c. will have the incentive to "cut" the market and sell at less than $40 a unit.
    d. must price its product based on its own marginal cost function.
    e. none of the above.

17. When the demand function is given by P = $51, the marginal revenue:
    a. is less than the price.
    b. is greater than the price because the demand is flat.
    c. is equal to the price because all units are sold at the same price.
    d. can never be equal to the price.
    e. none of the above.

18. A firm in perfect competition is selling Q = 500 at the price P = 20. The marginal revenue at this point:
    a. cannot be determined from the given data.
    b. is 15.
    c. is 10.
    d. is 5.
    e. none of the above.

19. The demand curve confronted by a firm in a purely competitive market is:
    a. relatively elastic, that is, the elasticity coefficient is greater than unity.
    b. perfectly elastic.
    c. relatively inelastic, that is, the elasticity coefficient is less than unity.
    d. perfectly inelastic.
    e. none of the above.

20. Which of the following is a characteristic of a purely competitive seller's demand curve?
    a. Price and marginal revenue are equal at all levels of output.
    b. Average revenue is less than price.
    c. Its elasticity is "1" at all levels of output.
    d. It is the same as the market demand curve.
    e. None of the above.

21. The Ajax Manufacturing Company is selling a purely competitive market. Its output is 100 units which sell at $4 each. At this level of output total cost is $600, total fixed cost is $100, and the marginal cost is $4. The firm should:
    a. reduce output to about 80 units.
    b. expand its production.
    c. continue to produce 100 units.
    d. produce zero units of output.
    e. none of the above.

22. Answer Questions 23 and 24 on the basis of the following cost data for a purely competitive seller:

    Output	Total Cost
    0	$50
    1	90
    2	120
    3	140
    4	170
    5	210
    6	260
    7	330

    
    
    
23. If product price is $60, the firm will:
    a. produce five units and realize a loss
    b. produce four units and realize a $120 profit.
    c. produce six units and realize a $100 profit.
    d. produce three units and realize a $40 loss.
    e. none of the above.

24. If product price is $45, the firm will:
    a. produce four units and realize a $120 profit.
    b. produce five units and realize a $15 profit.
    c. produce six units and realize a 100 profit.
    d. do none of the above.

25. Assume a purely competitive firm is selling 200 units of output at $3 each. At this output its total fixed cost is $100 and its total variable cost is $350. On the basis of this information we can say that the firm:
    a. is maximizing its profits
    b. is making a profit, but not necessarily the maximum profit.
    c. is incurring losses.
    d. is doing none of the above.

26. Answer Questions 27 - 30 based on the following cost data for a competitive seller.

    Total Output	Total Fixed Cost	Total Variable Cost	Total Cost
    0	$50	$ 0	$50
    1	50	70	120
    2	50	120	170
    3	50	150	200
    4	50	220	270
    5	50	300	350
    6	50	390	440

27. These data are for:
    a. the long run.
    b. the short run.
    c. both the short and the long run.
    d. none of the above.

28. At five units of output, average fixed cost, average variable cost, and average total cost are:
    a. $10, $60 and $70 respectively.
    b. $50, $40 and $90 respectively.
    c. $10, $70 and $80 respectively.
    d. $5, $25 and $30 respectively.
    e. none of the above.

29. The marginal cost of the fifth unit of output:
    a. is $80
    b. is $90
    c. is $50
    d. cannot be determined from the information given.
    e. none of the above.

30. If product price is $75, the firm will:
    a. produce three units of output
    b. produce four units of output
    c. produce five units of output
    d. produce six units of output

31. The marginal revenue product of an input is defined as:
    (a) The additional output produced by the firm by using 1 more input
    (b) The additional revenue earned by the firm by using 1 more input
    (c) The additional revenue earned by producing 1 more unit of output
    (d) None of the above

32. A firm in perfect competition maximizes profits at the point where:
    (a) Marginal profit = 0
    (b) The difference between TR and TFC is the greatest
    (c) The slope of the total profit curve is positive
    (d) The slope of the total profit curve is negative

33. Which of the following indicates that the amount of a particular input being used is greater than its optimal level?
    (a) Marginal Revenue Product = Price of input
    (b) Marginal Revenue Product > Price of input
    (c) Marginal Revenue Product < Price of input
    (d) Marginal Product < Price of input

34. Which of the following is not true of perfect competition?
    (a) Numerous sellers
    (b) Differentiated product
    (c) Perfect information
    (d) No barriers to entry and exit
    (e) Both (c) and (d)

35. The daily wage rate for a farm laborer is $120. A farmer hires laborers to produce wheat which sells for $30 per bushel in a perfectly competitive market. The last worker hired by the profit- maximizing farmer will increase the daily output of wheat by

    (a) 0.25 bushels
    (b) 2 bushels
    (c) 4 bushels
    (d) 30 bushels
    (e) 150 bushels

36. A firm in perfect competition will discontinue production in the short run if:

    (a) Price is less than marginal cost
    (b) Price is less than average variable cost
    (c) Price is less than average total cost
    (d) Price is less than marginal revenue
    (e) None of the above

37. A firm reaches a break-even point where:

    (a) Marginal revenue cuts the horizontal axis
    (b) Marginal cost intersects the average variable cost curve
    (c) Total revenue equals total variable cost
    (d) Total revenue and total cost are equal

38. In the short-run, a purely competitive firm will shut down:

    (a) At any point where price is less than the minimum AVC
    (b) Between the two break-even points
    (c) At any point where total revenue is less than total cost
    (d) At any point where the firm is not making an economic profit
    (e) At any point where price is less than the minimum ATC

39. In a purely competitive industry:

    (a) There will be no economic profits in either the short or the long run
    (b) Economic profits may persist in the long run if consumer demand is strong
    (c) There may be economic profits in the short run, but not in the long run
    (d) There may be economic profits in the long run, but not in the short run
    (e) None of the above

	6c	7c	8c	9b	10d	11a
	12c	13c	14b	15a	16a	17c
	18e	19b	20a	21d	22
	23c	24b	25b	26	27b	28a
	29a	30b	31b	32a	33c	34b