Question

Suppose that a foreign firm with monopoly power exports its product to Canada. That is, the firm is the only source of the product for Canadian consumers.

Canada’s market demand curve for the product is P = 80 – Q.

Assume that the firm’s total cost function is: TC(Q) = 20Q

1. A) Calculate the monopoly’s profit maximizing price and quantity. Calculate also the consumer surplus to Canada.

   Now suppose that Canada decides to impose a tariff,  per unit, on the product.

2. B) Describe the monopoly’s profit maximizing behavior under the tariff.
   Calculate the consumer surplus to Canada and also total tariff revenue to Canada. (Hint: Your answers will be functions of .)

3. C) Assume that the Canadian government tries to maximize its social welfare. Find out the optimal size of the tariff.

Answer 1

Suppose that a foreign firm with monopoly power exports its product to Canada. That is, the firm is the only source of the product for Canadian consumers.

P = 80 - Q

C(Q) = 20Q

Total revenue, TR = P x Q = 80Q - Q2

Marginal revenue, MR = dTR / dQ = 80 - 2Q

Marginal cost, MC = dC(Q) / dQ = 20

Monopolist will maximize profits by equating MR with mC:

80 - 2Q = 20

2Q = 60,

Q = 30

P = 80 - Q = 50

(a) Tariff of t is imposed.

MC curve becomes (MC + t) = 20 + t

Since we don't have exact value of t, we need a graphical solution (explanation) as follows.

Monopolist's new MC is (20 + t). Profit maximizing output is QT & Price is higher, at PT.

Increase is price < t.

(b)

Consumer surplus is the area between demand curve & price.

So, before tariff, CS = Area of triangle PCPM = (1/2) x $(80 - 50) x 30 = 450

After tariff, CS = Area PDPt = (1/2) x (80 - PT) x QT

Tariff revenue = Area of rectangle EBGF = QT x (20 + t - 20) = QT x t

(c)

In the graph the social welfare loss (deadweight loss) is area of triangle CDH, that is,

DWL = (1/2) x (PT - 50) x (30 - QT).

To maximize social welfare, government will want to minimize deadweight loss, that is, minimize the value of [(PT - 50) x (30 - QT)]. A tariff rate t* that minimizes this value will be the optimal tariff rate.

Exact value is not possible to compute unless value of t is known.graph draw chesi upload cheiiIf you do not get anything in this solution, please put a comment and I will help you out.