ECON 3050 Problem Set Unit 17 Prof. Rodet Unit 17: Leadership I A market has an
ID: 1124451 • Letter: E
Question
ECON 3050 Problem Set Unit 17 Prof. Rodet Unit 17: Leadership I A market has an inverse demand curve P = 65-5a-SQF and two firms: the leader and the follower. Suppose that firm costs are: C(Q)-5Q1,Cr(s) 5Qr for the leader and follower, respectively. For the problems below, recall that firms choose quantities simultaneously according to the Cournot model; firms choose sequentially in the Stackelberg model where the leader has a first-mover advantage. 1. a. Derive the Cournot Best-response functions (BRF) for each firm. b. Calculate the Cournot profit-maximizing price and quantities. c. Calculate the Cournot equilibrium profit for cach firm. d. Calculate the Stackelberg leader's profit-maximizing price and quanity Calculate the Stackelberg follower's profit-maximizing quantity. Calculate the Stackelberg equilibrium profit for each firm and compare to results in e. f. part c. Do firms have an incentive to be the leader even when competing against just one other firm? g. Suppose the market is made up of one leader and a group of small, price-taking firms. How would prices and profits compare to those found in f (Hint: you don't have to calculate them- in fact you don't have enough information to do so... Why are they different?Explanation / Answer
First 3 subparts related to Cournot are answered below.
1. To find best response functions, set MR = MC for each firm separately
Firm 1: MR = 65-10QL-5QF
MC = 5
Set MR1 = MC1
65-10QL-5QF = 5
60-5QF=10QL
QL* = 6-0.5QF ..... (1)
This is best response function of Leader
Similarly, best response function of follower will be: QF* = 6-0.5QL .... (2)
2.
To find Cournot prices and quantities, set (1) = (2)
This gives QL* = QF* = 4 units and P* = $20
3.
Profit of each firm = (P-MC)Q = (20-5)4 = $60 each
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