Assume that the price of silk ties in a perfectly competitive market is $21 and

Question

Assume that the price of silk ties in a perfectly competitive market is $21 and that the typical firm confronts the following costs:

Instructions: Enter your response as a whole number.

(a) What is the profit-maximizing rate of output for the firm? (Use the highest level of output.)

ties/day

(b) How much profit does the firm earn at that rate of output?

$

(c) If the price of ties falls to $15, how many ties should the firm produce?

ties/day

(d) At what price should the firm shut down?

Quantity (ties per day) 0 1 2 3 4 5 6 7 8 9 10 Total Cost $10 $17 $26 $37 $50 $65 $82 $101 $122 $145 $170

Explanation / Answer

Working notes:

(1) Marginal cost (MC) = Change in total cost (TC) / Change in output (Q)

(2) A perfect competitor maximizes profit by equating price with MC.

(3) Profit = Total revenue (TR) - TC = (P x Q) - TC = (21 x Q) - TC

(4) Shut down price is the point where price equals average variable cost (AVC).

(5) AVC = Total variable cost (TVC) / Q

(6) TVC = TC - Fixed cost (FC), where

FC = Total cost when Q equals 0 = $10

Therefore,

(a) Price = $21. When P = MC = $21, Q = 8

(b) When Q = 8, Profit = $21 x 8 - $122 = $(168 - 122) = $46

(c) When P = $15, P = MC = $15 when Q = 5

(d) When P = $21, P = AVC = $21.

Q TC FC TVC AVC MC 0 10 10 0 0 1 17 10 7 7 7 2 26 10 16 8 9 3 37 10 27 9 11 4 50 10 40 10 13 5 65 10 55 11 15 6 82 10 72 12 17 7 101 10 91 13 19 8 122 10 112 14 21 9 145 10 135 15 23 10 170 10 160 16 25

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