Consider a single firm facing inverse demand function p=100-10q where q is the q
ID: 1167571 • Letter: C
Question
Consider a single firm facing inverse demand function
p=100-10q
where q is the quantity of the good produced and p is the price for the good.
The firm has linear cost function C(q)=10q .
Suppose now there are two firms facing inverse demand function
p = 100 - 10Q
where Q=q_1 + q _ 2 is the total quantity of the good produced and p is the price for the good.
Each firm has linear cost function C(q) = 10q .
Compare the monopoly price in Q1, call it p^M , to the competitive equilibrium price in Q2, call it p^CE,
What is p^M - p^CE
Explanation / Answer
Finding price in monopoly
P = 100 – 10q Hence, Marginal Revenue = 100 – 20q
Marginal Cost = 10q + 10 – 10q = 10
Marginal Cost = Marginal Revenue
10 = 100 – 20q
20q = 90 Therefore, q = 90 / 20 = 4.5
P = 100 – 10q = 100 – 45 = 55
Finding price in competitive equilibrium
Demand = Marginal Cost
10 = 100 – 10(q1 + q2)
q1 = q2
Hence, 10 = 100 – 20q1 or q2
Solving as above we get q1 = q2 = 4.5
Price = 100 – 10(4.5 + 4.5) = 100 – 90 = 10
P^M – P^CE = 55 – 10 = 45