The table below shows production costs of a computer chip for the current produc
ID: 1139838 • Letter: T
Question
The table below shows production costs of a computer chip for the current production level of 5 million pounds per year (assume a constant average and marginal cost of production).
The firm currently has an exclusive patent on the computer chip, which makes it the only producer of the technology in the market. The market demand for the computer chip is given as follows:
a) At the current production level of 5 million pounds per year, the firm is charging $11 per pound as shown in the table above. Is the firm maximizing profit? Why or why not?
b) To maximize profit, how much should the firm produce? What price should it charge? How much is the annual profit then?
AVERAGE VARIABLE COST (variable cost per pound) Raw Materials $1.50 Utilities $0.40 Labor $1.10 AVERAGE FIXED COST (fixed cost per pound) Plant and equipment $1.50 Overhead $1.30Explanation / Answer
(a)
Total Average variable cost (AVC) ($) = 1.5 + 0.4 + 1.1 = 3
Since AVC and average fixed costs (AFC) are constant, AVC is equal to Marginal cost (MC).
Profit is maximized when Marginal revenue (MR) equals MC.
MR = Change in total revenue (TR) / Change in output (Q)
When P = $10, TR ($ million) = 10 x 6 = 60
When P = $11, TR ($ million) = 11 x 5 = 55
MR = $(55 - 60) million / (5 - 6) million = -$5 million / -1 million = 5
Since MR is higher than MC, firm is not maximizing profit.
(b)
When Q = 7, TR ($ million) = 9 x 7 = 63
When Q = 6, TR ($ million) = 10 x 6 = 60
MR for (Q = 9) = $(60 - 63) millon / (6 - 7) million = -$3 million / -1 million = 3
Since MR equals MC, profit-maximizing output is 6 million at price of $10 each.
Annual profit ($ million) = (Price - Average variable cost - Average fixed cost) x Output
= [10 - (1.5 + 0.4 + 1.1 + 1.5 + 1.3)] x 6
= (10 - 5.8) x 5
= 4.2 x 5
= 21
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