Question

Suppose that there is a single producer of a good and a single retailer. The producer's marginal cost is 14 and the retailer's marginal cost is the wholesale price w plus a unit retail cost equal to 4 . The producer chooses the wholesale price and the retailer the retail price. The demand function is 26-p.

(a) Write down the retailer's profit function as a function of the retail price p and the wholesale price w.

(b) What is the optimal retail price choice as a function of the wholesale price?

(c) What is the corresponding quantity?

(d) What is the producer's profit as a function of w ?

(e) What are hence the equilibrium values of w, p, q ?

(f) What are the equilibrium producer and retailer profits (both separate and in aggregate)?

(g) Now suppose that the producer and retailer merge without a change in retail or production costs. Then what would be the new equilibrium price, quantity, and profit?

(h) Provide a brief intuitive explanation for why the retail price is now less but profits are higher.

(i) If the producer and retailer are still separate firms, then how much of a $ 1 increase in the unit producer cost gets passed through to the retailer and how much to the consumer?

(j) How would a $ 1 increase in the unit retail cost affect the wholesale and retail prices? Please explain.

(k) Now suppose that the producer offers to sell its products to the retailer at the producer's marginal cost (w=14) in return for a fixed fee R . So the retailer pays the producer 14 per unit plus R . What would be the equilibrium retail price in this example?

(l) What would be the profit of the producer and that of the retailer? Express the profit in terms of R.

(m) Show that R should be between 8 and 12 (both inclusive) for both producer and retailer to be ok with this arrangement.

(n) What is the relevance of the nonlinear pricing example for mergers?

Answer 1

As per the HOMEWORKLIB POLICY, answering the first four parts,