Q. In a market, each firm has a marginal cost(MC) of $ 4, and the inverse demand
ID: 1186285 • Letter: Q
Question
Q. In a market, each firm has a marginal cost(MC) of $ 4, and the inverse demand
function is given by: P=16-2Q where P is the market price and Q is the total
market quantity, find each of the following:
1. Market price and quantity in a perfect competitive market?
2. Monopoly price and quantity?
3. Oligopoly market price and total quantity (hint: assume two firms are
operating in this market with the same MC=$4).
4. In a diagram, show the marginal cost (MC) curve, marginal revenue (MR)
curve, Demand curve, and show the points corresponding to your answers in
1,2,&3.
5. Calculate the consumer Surplus, Producer Surplus, and Dead Weight Loss
from moving between monopoly and perfect competition, and show that in a
separate diagram?
Explanation / Answer
Perfect Competition,
MC = P
4 = 16-2q
q = 6
price = 4, quantity=6
Monopoly,
MC = MR
TR = P*Q = 16Q-2Q62
MR = 16-4Q
16-4Q = 4
Q = 3
P = 10
price = 8, quantity=3
Oligopoly,
firm 1 :
Profit = (16-2(Q1+Q2))*Q1 - 4*Q1
dp/dq1 = 12 - 4q1 - 2q2 = 0
firm 2:
dp/dq2 = 12 - 4q2 - 2q1 = 0
q1 = 2
q2 = (12-4q1)/2 = 2
price = 8, quantity=4
DWL = .5*change in price*change in quantity
= .5*4*3
= 6
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