2. Consider a firm with the following short-run total cost curve: STC(q) = 0.1q2
ID: 1108421 • Letter: 2
Question
2. Consider a firm with the following short-run total cost curve: STC(q) = 0.1q2 + 10q + 50. a. Identify SMC, SVC, SFC, SAC and SAVC. b. If the selling price is S20, what is the firm's profit maximizing output level? c. How much profit would the firm earn? d. Suppose the firm is required to pay a flat fee of $100 independent of the amount of output it produces. How would this affect the profit e. Alternatively, suppose it is assessed a tax of 50% of its profits. f. If, instead, it is required to pay a tax of S2 per unit of output maximizing quantity and the maximal profits? How would this affect the profit maximizing output level? how would this affect marginal costs? How would it affect the profit umuasxinization decision and the level of profits? g. Finally, suppose the firm were taxed 10% of its revenue (rather than a percentage of profits). How would this affect the profit maxi- mization decision? Compare your answer to part eExplanation / Answer
STC(q) = 0.1q2 + 10q + 50
(a)
SMC = dSTC(q) / dq = 0.2q + 10
SVC = 0.1q2 + 10q
SFC = 50
SAC = STC(q) / q = 0.1q + 10 + (50 / q)
SAVC = SVC / q = 0.1q + 10
(b) Profit is maximized when SMC = Price.
0.2q + 10 = 20
0.2q = 10
q = 50
(c) When q = 50,
Total revenue (TR) = Price x q = 20 x 50 = 1000
STC(q) = (0.1 x 50 x 50) + (10 x 50) + 50 = 250 + 500 + 50 = 800
Profit = TR - STC(q) = 1000 - 800 = 200
(d) Profit is maximized by equality of Price and MC. Since fixed cost does not impact MC, the profit maximizing quantity will remain unchanged at 50 units, but profit will fall because STC(q) will increase by $100.
Decrease in profit ($) = 100
New profit ($) = 800 - 100 = 700
NOTE: As per Chegg answering guidelines, only 1st 4 parts are answered.
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