1. ECON 3020: Final Exam
Due: Tuesday, December 15, 2015 at 10:30am.
Use additional sheets of paper or a blue book to answer the
following questions and turn in your own work. You now have
the skills to analyze more interesting economic phenomena and
this exam should push you in that direction. Feel free to utilize
your available resources—the Learning Commons, me, your
textbooks and your classmates to get over whatever bumps you
encounter.
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
(a) Find the profit maximizing choice of output for the
monopoly? How much profit does the monopolist make?
(b) 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.
(c) How much profit does the monopolist make when it is forced
to behave like a perfectly competitive firm?
(d) 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

2. 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.
a. Rewrite the budget constraint using our traditional prices. In
other words, how much does c0 cost? What is the price of
consuming tomorrow, c1?
b. Solve for the Walrasian demand functions.
c. What relationship between δ and r causes the individual to
consume the same amount today and tomorrow?
d. 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
e. 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

3. r=0. Give a value for δ such that consumption is held constant
in each period and the agent exactly consumes his production.