Suppose that market demand is linear, q = 70 - p. Marginal costs are constant and equal to 10. The upstream firm, which

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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 :