Question

Q1
Consider an industry with one manufacturer M and two retail firms R1 and R2. The manufacturer produces a homogenous good at a marginal cost of 20. The retailer buys the product from the manufacturer and sells to the final consumers. Downstream demand in the industry is given by

D(p) = 260 − p

where p is the final retail price p.

(a) As a benchmark, suppose M and R1 are vertically integrated and stop supplying R2. Which price does the merged company charge to consumers? What are industry profits and consumer surplus? For the remaining subquestions assume that all firms are independent.

(b) Assume the retailers compete in prices downstream and the manufacturer supplies the good at a price w to both retailers. What is the downstream price equilibrium? Give the demand for the manufacturer’s product. Calculate the manufacturer’s optimal price w and his profits.

(c) Compare with the vertical integration outcome in (a). Does the manufacturer have an incentive to foreclose one of the retailers and exclusively sell through just one retailer? Explain in not more than 80 words.

(d) Assume now the retailers compete in quantities downstream. The manufacturer sells the good at w to both retailers. Calculate the downstream Nash equilibrium.

(e) Derive the demand for the manufacturer’s product as a function of w. Calculate his optimal wholesale price and profits at this price. 1

(f) Compare with the vertical integration outcome in (a). How do wholesale and final prices compare? Does the manufacturer have an incentive to foreclose one of the retailers? Explain your result in not more than 80 words.

Answer 1

Q= 260 - p

if M and R1 are merged.

TR = p*(260-p)

MR = 260 - 2p

at max profit level,

MR = MC

=> 260 - 2p = 20

=> p =120

profit = 260p-p^2 - 20p = 240p-p^2 = 240*120 - 14400 = 14400

initially,

P = MC = 20

q = 240 -20 = 220

CS = 0.5*(p2-p1)*(q2-q1) = 0.5 * 20* 20 = 20