1. Consider a single firm facing inverse demand function p=100-10q where q is th
ID: 1167556 • Letter: 1
Question
1. 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 .
Find the firm's profit maximizing quantity, q*.
2. 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 .
Find the competitive equilibrium output, Q *
3. 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
4. Consider the alcohol consumption problem (e.g., Tadelis 1.4) and suppose your payoff is given by
v (a ; theta)= (theta*a) - c*a^2
where c > 0 is the cost of consuming amount a and theta belongs to [1,6] is your tolerance for alcohol.
Find your optimal consumption a when theta is distributed uniformly on the interval [1,6].
Explanation / Answer
(1)
P = 100 - 10Q
Total revenue, TR = P x Q = 100Q - 10Q2
Marginal revenue, MR = dTR / dQ = 100 - 20Q
C(Q) = 10Q
Marginal cost, MC = dC / dQ = 10
It is not mentioned if the firm operates in a competitive or monopolistic industry, so I shall consider both market structures.
(a) A competitive firm will equate its price with MC.
Or
100 - 10Q = 10
10Q = 90,
Q = 9
(b) But a monopolist will equate its MR )and not price) with MC.
100 - 20Q = 10
20Q = 90
Q = 4.5
Note: Quantity is lower under monopolistic structure.
NOTE: Out of 4 questions, the 1st question has been answered.
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