**Consider a monopolist that faces a linear inverse demand of**

1. Consider a monopolist that faces a linear inverse demand of:

P(q) = 304 4q

The rm has the cost function:

C(q) = 100 + 4q + 2q2

What are the monopolistic market price (pM), quantity(qM), and pro ts (M)? Show deriva-

tions (neatly!) below. (30 points)

pM =

qM =

M =

2. Imagine a textbook company has a monopoly over a textbook in both the U.S. and India.

If they can price discriminate by charging a separate price in each of the two markets (each

country prohibits importation from the other market), nd the optimal quantities and prices

they would charge in those markets.

The rm's cost function is C(q1+q2) = C(q) = 2q2+30. In the U.S. (which we'll call Market

1), the inverse demand function is p(q1) = 1296 30q1 and in India it is p(q2) = 400 38q2

(a) What quantity does the rm sell in each market? What is the total quantity sold? (10

points)

q

1 =

q

2 =

q(total for rm) =

(b) What price does the monopolist charge in each market? (8 points)

P

1 =

P

2 =

(c) What is the total pro t for the monopolist? (2 points)

(d) In equilibrium, what is the monopolist's elasticity of demand in each of the two markets?

(6 points)

j1(q

1)j =

j2(q

2)j =

(e) Circle the correct choice:

Comparing your answers to (b) and (d), this rm charges a higher price in the market

in which its demand curve is more (elastic / inelastic). (4 points)

3. Consider a Cournot duopoly with both rms producing a homogeneous good and facing linear

demand of the form: P(Q) = 124 30Q, where Q = q1 + q2. Assume both rms have the

same costs: C(q) = 4q.

(a) For each rm, derive the best response function below. Show all work. (8 points)

(b) Graph the best response functions for both rms on the axes below. As in class, q1

should be on the y axis and q2 should be on the x axis. (4 points)

0

0

(c) Solve for the Nash Equilibrium output of each rm. (6 points)

(d) Solve for the equilibrium market price. (4 points)

(e) Solve for the equilibrium pro ts of each rm. (4 points)

4. Stackelberg Duopoly with Heterogeneous Costs.

Now consider a Stackelberg duopoly with both rms producing a homogeneous good and

facing a linear demand of the form P(Q) = 138 6Q where Q = q1 + q2. Assume the rms

have di erent costs. Firm 1 has costs C1(q) = 3q+3 and Firm 2 has costs of C2(q) = 6q+12.

Firm 1 will be the rst mover in this case.

(a) What is the Equilibrium output of each rm under Stackelberg Competition? (10 points)

(b) What are the equilibrium pro ts of each rm? (4 points)

**Category:**Accounting, General Accounting

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