Question

In: Economics

The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten,...

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.

Solutions

Expert Solution

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.)


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