Question Revisit Q1) A manufacture abs sells a product in a non-competitive market at a unit wholesale prICe w* through a retailer

Question

Revisit

Q1) A manufacture abs sells a product in a non-competitive market at a unit wholesale

prICe

w* through a retailer. The manufacturer's unit production cost is "$10". The

retailer sets a market price a

"p" to sell the product. The retailer observes a market

demand function as follows.

Q = 100-20p

Assume that the manufacturer is the Stackelberg leader and the retailer is the

Stackelberg follower. Calculate the following

(i) Write the profit functions for the retailer and the manufacturer

(if) Derive the optimal wholesale price, the optimal market price and the optimal

demand which can maximize the total profit functions for the supply chain

members.

(in) Derive the optimal profit functions for the retailer, manufacturer and the total

supply chain profit.