Demand for a good can be characterized by P = 100 âˆ’ Q. There are two firms: Firm 1 and Firm 2. They have identical cost functions.
TC1 =5+10q1 TC2 =5+10q2
1. Suppose that each firm make the output decision simultaneously (Cournot model). What are the equilibrium outputs by each firm, q1 and q2? What is the equilibrium price? What are each firmâ€™s profits? (3 points)
2. Suppose that both firm collude with each other and share the profits equally (Monopoly model). What is the equilibrium output and price in this market? What are each firmâ€™s profits? (3 points)
Suppose that Jake considers two alternative investment plans of $1,000 for one-year. Investment A is a no-risk plan: deposit into a bank account with interest rates with 5%. That is, it makes $1,050 in a year for sure. Investment B is a risky plan: buying stocks. This plan could make $1,500 in a year if the economy is good, but if the economy is bad in a year, it could make only $600. According to recent forecases by economists, the probability that the economy is good in a year is 1/2.
1. Find the expected income and standard deviation of Investment B. (3 points)
Suppose Jakeâ€™s utility function is U = âˆšI, where I is the income. Find the expected utility from each investment. (3 points)
Which investment would Jake choose? Why?(2 points)
Is Jake risk-loving? Explain why shortly. (2 points)
(Bonus Questions) How much of certain income would he give up to avoid risk? (Hint: What is a certain income that yields the same utility as an uncertain income yields?) (4 points)
Michael has the following utility function:
U(X,Y ) = log(X) + log(Y ),
where the price of X is $3 and the price of Y is $1. He has decided to allocate $120 on X and Y. What is his utility maximizing combination of X and Y? (5 points)