A small company produces only violin bows. The company has to pay a monthly rent
ID: 1099259 • Letter: A
Question
A small company produces only violin bows. The company has to pay a monthly rent of $500 for the location; its variable cost function is given by C(Q) = 5Q2, where Q denotes the quantity of output. The market demand function is given by Q = 1,200 ? P , where P denotes the price.
(a) Suppose that the market is perfectly competitive, with 110 identical bow companies. How many bows does each company produce in equilibrium, if its goal is to maximize profits? Find the price associated with this output, and the profit for each company. Hint: Use an individual company
Explanation / Answer
Let quantity produced by single company is q
110*q= Q
Total cost of an inividual company = 5*q^2 +500
Marginal Cost = 10q
Q = 1200-P
110*q = 1200-P
Revenue = P*q = (1200-110q)*q
Marginal Revenue = 1200-220q
For profit maximization, MR = MC
10q = 1200-220q
q = 5.22 or 6
each company produce in equilibrium = 6 bows
P= 1200-110*6 = $540
Profit for each company =540*6 -(5*6^2 +500) = $2560
b) Total cost of the company = 5*Q^2 +500
Marginal Cost = 10Q
Q = 1200-P
Revenue = P*Q = (1200-Q)*Q
Marginal Revenue = 1200-2Q
For profit maximization, MR = MC
1200-2Q= 10Q
Q = 100
the company produce in order to maximize profit = 100 bows
Price = 1200-100 = 1100
the company