Question

The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten, a perfectly competitive firm that produces children’s mittens in a competitive market.

Smitten's Production Costs

Quantity (pairs of mittens)	Marginal Cost (dollars)	Average Total Cost (dollars)
20	$1.60	$1.25
25	2.00	1.40
30	2.45	1.58
35	3.55	1.86
40	4.00	2.13
45	5.50	2.50
50	6.00	2.85
55	8.50	3.36

Instructions: In part a, enter your answer as a whole number. In parts b–d, round your answers to two decimal places.

a. If the market price of children’s mittens is $6.00 per pair, how many pairs of children’s mittens should Smitten produce per week to maximize its profits?

     pairs of mittens

b. What is Smitten’s average total cost at the profit-maximizing quantity of children’s mittens?

   $

c. What are Smitten’s weekly profits if the market price is $6.00 per pair and the firm produces the profit-maximizing quantity of mittens?

   $

d. What are Smitten’s weekly profits if the market price is $5.50 per pair and the firm produces the profit-maximizing quantity of mittens?

     $

e. The price at which Smitten would earn a normal profit is where:

• average cost equals average revenue at the minimum of average cost.

• marginal cost equals average cost.

• marginal cost equals average cost at the minimum of average cost.

• marginal cost equals marginal revenue at the minimum of marginal cost.

Answer 1

a. Profit is maximized at the quantity where P = MC
P = MC = 6 at Q = 50. So, Smitten will produce 50 pairs.

b. At Q = 50, ATC = 2.85

c. Profit = Total Revenue - Total cost = P*Q - ATC*Q = (P-ATC)*Q = (6-2.85)*50 = 3.15*50 = $157.5

d. P = MC = 5.5 at Q = 45. So, Smitten will produce 50 pairs. And ATC = 2.5
So, Profit = (P-ATC)*Q = (5.5 - 2.5)*45 = 3*45 = 135

e. average cost equals average revenue at the minimum of average cost.
(There are normal profits when P = AR = minimum of AC.)