1) Suppose that market demand is linear, q = 70 - p. Marginal costs are constant and equal to 10. The upstream firm, which is a manufacturer, does not sell directly but through a single downstream firm, which is a retailer. The manufacturer set the wholesale price w at stage 1. At stage 2, the retailer who is assumed not to incur any costs except wholesale price (w), observes the wholesale price and sets the retail price p. Find the optimal wholesale price (w*): Find the optimal retail price (p∗): Find the quantity demanded (q∗) that corresponds to p∗: Find the manufacturer’s profit (π*M
1) Suppose that market demand is linear, q = 70 - p. Marginal costs are constant and equal to 10. The upstream firm, which is a manufacturer, does not sell directly but through a single downstream firm, which is a retailer. The manufacturer set the wholesale price w at stage 1. At stage 2, the retailer who is assumed not to incur any costs except wholesale price (w), observes the wholesale price and sets the retail price p.
Find the optimal wholesale price (w*):
Find the optimal retail price (p∗):
Find the quantity demanded (q∗) that corresponds to p∗:
Find the manufacturer’s profit (π*M) that corresponds to p∗:
Find the retailer’s profit (π∗R) that corresponds to p∗:
Find the overall channel profit (Π∗ = π*M+ π*R):
Next, consider a case that the integrated firm produce the product and sell directly to consumers. Suppose the market demand is q = 70 - p. Marginal costs are constant and equal to 10.
Find the optimal retail price (pi):
Find the quantity demanded (qi) that corresponds to pi :
Find the firm’s profit (πi) that corresponds to pi :
Step by step
Solved in 4 steps
