Download 6Review questions 2

Econ (Mgec) 330
Spring 2007
These are some example for numerical questions that you will need to do at the exam.
1. Consider a competitive industry where each firm has the same cost function c(q) =
12.5 + 12 q2. The market inverse demand is P = 1005 – 2Q.
a. Show that the long-run equilibrium price is 5. (assume that there are many potential entrants
with access to the same technology, and use the “zero-economic-profit condition.)
b. Suppose that currently there are 90 firms active in this market. Compute the
equilibrium price.
c. Compute the price elasticity of the market demand at the equilibrium price. Is it
elastic or inelastic?
d. Write the equation for the residual demand for firm j. Assume that all firms other than
j produce their equilibrium output levels. (repeat what we did in class)
e. Suppose that firm j behaves like a monopoly over its residual demand. What price
will it charge to maximize profit? Is this price very different than the equilibrium price
you found in part (d)?
2. THE DOMINANT FIRM MODEL
There are 12 fringe firms with cost function c(q) = 4q +q2. The dominant firm’s cost
function is Cd(q) = 2q. The inverse market demand is p = 100 − Q.
a. Compute the monopoly price and quantity in the absence of the fringe.
b. Compute the profit maximizing price the dominant firm will charge taking into
account the effect of the fringe firms. What is the market share of the fringe?
c. Compare the Part (a) price and the Part (b) price.
d. Now suppose that new fringe firms can enter the market but only after paying a onetime entry cost CE =1. Find the equilibrium in this new set up. Note that the number of
fringe firms may increase if there is entry.
3. Consider the following two industries
Industry A
Firm
1
2
3
4
5
6
Market
share (%)
55
10
10
5
5
5
Industry B
Firm
1
2
3
4
5
Market
share (%)
25
25
25
24
1
7
8
5
5
Which industry is more concentrated? Use CR4 and HHI.
How do the concentration indexes change if the two largest firms in both industries
merge?
4. Suppose that a monopolist produces and sells in each of two periods: t = 1 and t = 2.
Let the interest rate be r%. Demand for its product is linear in each period and
independent of sales in the other period: P(q) = A – q. Production experiences learning
by doing across the periods. Current production cost is given by:
C(qt, Qt) = (c − Qt)qt
where qt is production in period t, Qt is cumulative production up to—but not
including—period t. More specifically, Q1 = 0, and Q2 = q1. Finally, c > 0 denotes the
baseline constant marginal cost.
a. Find monopoly price and profits in period t = 2 given production q1 in period t = 1.
b. Compute profit-maximizing production in the two periods, that is, q1 and q2.
c. How does production in period t = 1 depend on the interest rate r?
d. Compare prices charged by the monopolist in each period to current production cost
and to the baseline marginal cost of c. How does the markup evolve over time?
5. Regulation of a natural monopoly
Compare and contrast the two methods of regulating a natural monopoly, rate of return
(average cost pricing) regulation vs price-cap regulation. What are the advantages and
drawbacks of each method?