Question:
1)This problem is an introduction to welfare analysis, essentially figuring out why anticompetitive behavior is socially negative and perfect competition is good for society.
A monopolist has a cost function of c(y)=(1/2)y2+4y+100. It faces the following demand curve:
Q=100-p
Find the profit maximizing choice of output for the monopoly? How much profit does the monopolist make?
The government would like to force the monopolist to behave as though it were in a perfectly competitive market. In that market, what would the supply curve be? What would the demand curve be? Find the equilibrium price and quantity in that market.
How much profit does the monopolist make when it is forced to behave like a perfectly competitive firm?
Draw the graph depicting the monopolist's marginal cost, marginal revenue and demand curves. Draw a second graph depicting the market supply and market demand when the government forces the monopoly to behave as a perfectly competitive firm. Illustrate and calculate the consumer and producer surpluses on each graph. What is the deadweight loss of the monopolist? Describe the welfare implications for consumers and producers of monopoly behavior as opposed to competitive behavior.
2)This problem is an introduction to intertemporal choice and equilibrium theory.
Consider and agent who values consumption in period 0 and 1 according to the following utility function:
U(c0, c1)=ln(c0)+δln(c1).
Where δ is a discount rate, <1, that indicates the agent prefers to consume today than consume tomorrow. Given the laws of natural logs, we can rewrite the utility function in the familiar form
U(c0, c1)=(c0)(c1δ)
Suppose the agent is given a total wealth today of w and he may save any portion of w to consume tomorrow. If he saves any of w, he is paid interest r. Thus, we can write the budget constraint as
c0+()=w.
Rewrite the budget constraint using our traditional prices. In other words, how much does c0 cost? What is the price of consuming tomorrow, c1?
Solve for the Walrasian demand functions.
What relationship between δ and r causes the individual to consume the same amount today and tomorrow?
Suppose instead of being given a fixed income, the individual has production technology to produce x and y. The technology is limited by the constraint,
x2 + y2 = 2.
Because the agent is maximizing profits, we can show
Use these two equations to solve for x* and y*, the optimum levels of production as functions of px and py
Suppose x is the amount of production in period 0 and y is the amount of production in period 1. Suppose px=1, py=1 and r=0. Give a value for δ such that consumption is held constant in each period and the agent exactly consumes his production.