Call Us demand function is Q = 70 – 0.25P; MC = 16Q and total fixed cost (TFC) i
ID: 1114096 • Letter: C
Question
Call Us demand function is Q = 70 – 0.25P; MC = 16Q and total fixed cost (TFC) is 22% of total revenue (TR) at the revenue maximizing level.
(i) Derive the AFC (average fixed cost) at the profit maximizing level.
(ii) What is the profit at the profit maximizing level?
b) Ear Us (producer of hi–tech hearing aid) production function is Q = L0.5K0.5. The company over the years uses input rates of 50 and 75 for labour (L) and capital (K) respectively. If the price of labour and capital is $20 each; is there efficiency in production? Explain!
Explanation / Answer
(Question 1)
Demand: Q = 70 - 0.25P
0.25P = 70 - Q
P = 280 - 4Q [Inverse demand]
(i) Total revenue (TR) = P x Q = 280Q - 4Q2
Revenue is maximized when dTR / dQ = 0
280 - 8Q = 0
8Q = 280
Q = 35
P = 280 - (4 x 35) = 280 - 140 = 140
TR = P x Q = 140 x 35 = 4,900
Total fixed cost (TFC) = TR x 22% = 4,900 x 22% = 1,078
AFC = TFC / Q = 1,078 / 35 = 30.8
(ii) When Q = 35, MC = 16 x 35 = 560
Total cost (TC) = TFC + (MC x Q) = 1,078 + (560 x 35) = 1,078 + 19,600 = 20,678
Profit = TR - TC = 4,900 - 20,678 = - 15,778 (Loss)
NOTE: As per Chegg answering guidelines, first question is answered.
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