Topic:Profit Maximization

EC 200 Practice problems for MT3

PERFECT COMPETITION Practice Problems

Answer Key

12 ATC MC P

To the right of the vertical line, there are diminishing marginal returns 0 4 8 12 16 20 24 28 32 36 Q

a. On the graph, identify each curve. – See graph. b. On the graph, indicate the amount of output at which the Law of Diminishing Marginal Returns starts working. – See graph. (We know the Law of DMR is in action when MC is increasing in output) c. If the firm operates in a perfectly competitive market, and the price in that market is $11, should it stay in the market or should it leave? Why?

It should stay since it will be earning positive economic profit. We know this because at the firm’s optimal output (the point where MC intersects P) price exceeds average total cost.

d. If it stays, what will be its economic profit?

Profit = (P – ATC) · Q*, where Q* is the optimal output.

Profit = ($11 – $10) · 13 = $13. See the shaded area on the graph.

e. In which range of prices the best thing for this firm to do would be to shut the production down? Why?

The firm should shut down when the revenue from sales doesn’t cover the production (variable) cost. In other words, when P < min AVC. Therefore, the firm should shut down if the price falls below $6.

1 EC 200 Practice problems for MT3

2. True, false, or uncertain? Explain. a. Under perfect competition, a firm is always guaranteed to earn positive economic profits if it produces where marginal cost equals price. False. Producing the quantity at which MC = P is in many cases a good idea, since itwill maximize the firm’s profit or minimize its losses. Which of the two is the case will depend on the location of price and the ATC curve relative to each other. If the firm’s cost is higher than the price, its economic profit will be negative. b. A firm working in a perfectly competitive industry can always be better off by raising the price of its good a little. False. A firm working in a perfectly competitive industry has no control over price. It can sell only at the present market price. If the firm will raise its price above the market price, it will lose all its customers.

3. If a firm operates in a perfectly competitive market, then it will most likely a) advertise its product on television. b) settle for whatever price is offered. c) have a difficult time obtaining information about the market price. d) have an easy time keeping other firms out of the market.

4. Which of the following is not true under perfect competition? a) The firm's demand curve is horizontal. b) The firm's demand curve is the average revenue curve. c) The firm's demand curve is the marginal revenue curve. d) The firm's demand curve is inelastic.

5. a. The condition for the long run equilibrium in a perfectly competitive industry. P = MC = ATC b. Suppose a perfectly competitive market was initially in the long run equilibrium, and after that market demand has increased. What is the immediate effect of this event on the profit of a single firm? Explain using the graphs for the market and for the firm.

On the diagram below, the long-run equilibrium is shown by bold lines. An increase in demand (see shift 1) will increase the market price. The firm will respond to that by producing more. It will also start earning positive economic profit.

Q Q Market Firm

c. What do you predict will happen in this market after that (in the long run)?

The events described in part b will gradually attract other firms into this market. This process of new firms’ entry corresponds to an increase in supply (shift 2). It will push the price back down. This will continue until the price is again equal to the minimum of ATC of a representative firm, so all firms in the industry earn zero economic profit.

6. Your firm produces baseball gloves using two inputs: capital and labor. Every glove is sold at $10 per unit. Suppose capital is fixed and you can vary only the amount of labor. The table below shows the number of baseball gloves you can produce using different amount of labor.

Number of Output Marginal Marginal Marginal workers produced Product Revenue, $ cost, $ 0 0 ------1 7 7 70 2 18 11 110 3 31 13 130 4 42 11 110 5 50 8 80 6 56 6 60 7 59 3 30 8 60 1 10 a. When does the Law of Diminishing Returns start working in this example? Explain.

At the fourth worker (after the third worker), because this is when the marginal product starts decreasing. b. State the profit maximization rule.

MR = MC c. If the wage you pay each worker is $50 a day, how many workers is it optimal for you to hire? (To answer this question, you will need to do some calculations and fill a few columns in the table.)

In this case each cell in the last column will read ‘50’. Going down the column and comparing MR to MC, we can see it is optimal to continue hiring up to the 6th worker. In other words, hiring 6 workers will be the best for the firm. d. How will your optimal decision change if you have to pay each worker $75 a day?

Using the same approach, but with $75 in the last column, we can see the optimal number of workers is 5. e. How many workers will you hire if each worker has to be paid $100 a day?

Same approach – 4 workers. f. Sketch your firm’s demand for labor on the graph below, using your answers to parts c, d and e.

1 2 3 4 5 6 7 Number of workers

The three dots on the graph represent the answers to questions c-e. The rest is up to you: you can do it rigorously, as we did on slide 59 to get a graph that looks like a stair, or just draw a line through these points. g. (3 points) State the Law of Demand. Is the curve you’ve plotted consistent with the Law of Demand?

The higher is the price of a good, the lower is the quantity of this good demanded in the market. No matter how you answered question f, your graph should slope downwards, therefore it is consistent with the law of demand.