Intermediate Microeconomics

Homework 1

Joanne Roberts

1 Question 1

Consider two lotteries, A and B. With lottery A, there is a 0.90 chance that you receive a payoff of

$0 and a 0.10 chance that you receive a payoff of $400. With lottery B, there is a 0.50 chance that

you receive a payoff of $30 and a 0.50 chance that you receive a payoff of $50.

a) Verify that these two lotteries have the same expected value but that lottery A has a bigger

variance than lottery B.

b) Suppose that your utility function is U =√I + 500. Compute the expected utility of each

lottery. Which lottery has the higher expected utility? Why?

c) Suppose that your utility function is U = I + 500. Compute the expected utility of each

lottery. If you have this utility function, are you risk averse, risk neutral, or risk loving?

d) Suppose that your utility function is U = (I + 500)2. Compute the expected utility of each

lottery. If you have this utility function are you risk averse, risk neutral, or risk loving?

2 Question 2

2 Suppose you are a risk averse decision maker with a utility function given by U = 1 − 10(I)−2,

where I denotes your monetary payoff from an investment in thousands. You are considering an

investment that will give you a payoff of $10,000 (thus, I = 10) with probability 0.6 and a payoff

of $5,000 (I = 5) with probability 0.4. It will cost you $8,000 to make the investment. Should you

make the investment? Why or why not?

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3 Question 3

Assume that a monopolist sells a product with a total cost function TC = 400 + Q2. and a

corresponding marginal cost function MC = 2Q. The market demand curve is given by the equation

P = 500−Q.

a) Find the profit-maximizing output and price for this monopolist. Is the monopolist profitable?

b) Calculate the price elasticity of demand at the monopolists profit-maximizing price. Also

calculate the marginal cost at the monopolists profit-maximizing output.

4 Question 4

An economy has 2,000 people. 1,000 of them have utility functions U(x, y) = x + y and 1,000 of

them have utility functions U(x, y) = min(2x, y). Everybody has an initial allocation of 1 unit of x

and 1 unit of y. Find the competitive equilibrium prices and consumptions for each type of person.

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