21-23. A monopoly firm producing a rare cheese has demand for its output given b
ID: 1119811 • Letter: 2
Question
21-23. A monopoly firm producing a rare cheese has demand for its output given by P = 116 - 2Q. The firm’s costs are given by TC = q2 + 20q + 256. Q or q represents the number of wheels of cheese produced by this firm and consumed by consumers. P indicates the price of a wheel of cheese. You can use this information in answering questions 21 through 23.
21. At what price will the monopolist sell its output if it wishes to generate the maximum amount of profit?
(A) $52 (B) $64 (C) $70 (D) $72 (E) $80
(F) $84 (G) $88 (H) $92 (I) $96 (J) none of the above
22. Imagine now that a tax of $24 per wheel of cheese is imposed on this industry. What will be the excess burden caused by this tax?
(A) $82 (B) $94 (C) $120 (D) $128 (E) $160
(F) $172 (G) $188 (H) $192 (I) $196 (J) none of the above
23. By how much is the profit of the monopolist reduced by this tax?
(A) $176 (B) $224 (C) $308 (D) $336 (E) $348
(F) $412 (G) $448 (H) $484 (I) $512 (J) none of the above
Explanation / Answer
1. TC = Q2 + 20Q+256 , MC= 2Q+20
P= 116-2Q, MR = 116-4Q
At Monopolist profit maximization , MR = MR
116-4Q = 2Q+20
6Q = 96, Q = 16,
P= 116-2(16) = 84 , Answer is F
2. Tax levied $24 for wheel of cheese
So MC including tax = 2Q+20+24 = 2Q+44
At MR=MC, 116-4Q = 2Q+44
6Q = 72, Q = 12
P= 116-2(12) = 92
Substitute Q= 16, After tax Q= 12,
P= 2(16)+20 = $52
P= 2(12)+20 = $ 44
Excess tax burden is the dead weight loss on imposing tax = 1/2 * [(82-52)+(92-44)] *(16-12) = $160
Answer is E
3. Profit before the tax = (84*16)- [(16*16)+(20*16)+256] = $512
Profit after tax = (92*12)- [(12*12)+(44*12)+256] = $176
Change in the profit = $512- $176 = $336
Answer is D
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