## Managerial Economics Midterm exam

Managerial Economics Midterm exam. The exam will have two parts: multiple choice and short answer. The short answer will be a mix of analytical/technical questions and conceptual questions. The multiple choice will reflect key concepts and ideas that we have discussed in class. In addition to this review guide, your first three home works and the lecture notes are excellent study materials. Please bring a simple calculator (no graphing calculators and no phones…) and your writing utensils to the exam. Scantrons are not needed.

Perfect Competition

1. The Green Company produces chemicals in a perfectly competitive market. The current market price is $40; the firm’s total cost is C=100+4Q+Q2.

a. Determine the firm’s profit-maximizing output. More generally, write down the equation for the firm’s supply curve in terms of price, P.

b. Complying with more stringent environmental regulations increases the firm’s fixed cost from 100 to 400. Would this affect the firm’s output in the short run? What about in the long run?

2. Firm Z, operating in a perfectly competitive market, can sell as much or as little as it wants of a good at a price of $16 per unit. Its cost function is C=50+2/3Q^2.

a. Determine the firm’s profit-maximizing level of output. Compute its profit.

b. The industry demand curve is Q=200-5P. What is the total market demand at the current $16 price? If all firms in the industry have cost structures identical to that of firm Z, how many firms will supply the market (hint: each firm will provide the same amount to the market because they are all identical!)?

c. Is this sustainable in the long run? What will be true in the long run, and, qualitatively, how will price, quantity supplied per firm, and number of firm’s change in the long run? Monopoly

3. Consider a monopolist with a cost function of c(Q) = 4 + 2Q. Suppose the market demand function is QD = 24 − 2P.

a) Under uniform pricing (i.e. the basic monopoly problem), find the monopolist’s optimal price and quantity.

b) Calculate and draw a diagram that depicts consumer surplus, producer surplus, profits, and any deadweight welfare loss from the monopolist.

c) How does this compare to the socially efficient outcome? Draw a diagram to compare the equilibrium, consumer surplus, and producer surplus.

4. Consider a monopolist who has a cost function of c(Q) = 10Q. This monopolist faces two consumers, the first having demand q1(P1) = 60 − P1 and the second having demand q2(P2) =50 − P2.

a) Calculate the profit-maximizing price and then the optimal quantity sold to each consumer under uniform pricing, i.e. the monopolist charges the same price for both consumers. What are the monopolist’s profits? (Hint: first you need to find the market demand curve comprised of both consumers. Use horizontal aggregation.)

Production and Cost Analysis

5) Consider the production function Q=10L-0.5L2+24K-K

2 where L is labor and K is capital.

b. Suppose the input prices are $40 for labor and $80 for capital and the price of output is $10. Determine the optimal quantity of each input. Net Present Value, Decision-Making over Time, and Cost-Benefit Analysis

6) Comparing Investment Options Consider the following investment options:

Option 1: invest $100 now and get back $60 in six months $75 in a year, and $90 in 18 months

Option 2: invest $75 now and get back $10 per month at the end of each of the next 18 months

a. If the annual interest rate is 10%, what would be the equivalent monthly interest rate?

b. What option would you choose and why?

7) Consider the problem of how to finance the new purchase of a new van for your small business. There are two options. Option 1 is to make a large up-front payment of $5,000 and then pay $6,000 at the end of each of the next 4 years. Option 2 is to make no up-front payment but to make a payment of $6,500 at the end of each of the next 5 years. The annual interest rate is 15%.

a. Which option should you take and why?

Decision-Making Under Uncertainty

8) Your firm has successfully marketed a package of multitask software. Recently, sales have begun to decline because the software is incompatible with a number of popular application programs. Thus, future profits are uncertain. In the software’s present form, the firm’s managers envision three possible forecasts: (1) maintaining current profits at $2 million, (2) profits slipping to just $0.5 million,

or (3) you incur losses of $1 million. The respective probabilities are 0.2, 0.5, and 0.3. Alternatively, your firm can try to develop an “open”, i.e. compatible, version of the software. This will allow the firm to maintain its market position better, but it is costly to develop the new software. Depending upon the cost of the development, your firm will make $1.5 million in profits, $1.1 million, $0.8 million, or $0.6 million. Each of these outcomes is equally likely. Which action should you take if your objective is to maximize expected profits?

9) Your company is considering the purchase of a small firm that is struggling. You feel that there is a 50-50 chance of turning the firm around and making it profitable if you take it over, and this depends upon how future market conditions will affect your management plan. If conditions are good, and the firm becomes profitable, it will make you $500,000 in profits. If conditions are bad, and the firm

continues to operate at a loss, the firm will generate a loss of $400,000. (Assume these figures include the cost of purchasing the company).

a. Construct a decision tree to represent your company’s problem. Use it to decide whether or not you should make the purchase (assuming that your objective is to maximize expected profits).

b. Suppose now that you can pay a market research company for a perfect forecast of future conditions so that you know with certainty if the firm will be profitable or not. Use a decision tree to show your decision-making process. What is the most you would be willing to pay for this market research, i.e. what is the value of the information?

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