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Sharjah Electronics Company possesses substantial market power in the market for advanced wireless stereo headphones in UAE
Sharjah Electronics Company possesses substantial market power in the market for advanced wireless stereo headphones in UAE. The manager of the electronics estimated demand for its headphones is Q = 100 000 - 1000P Where Q is the number of wireless headphones and P is the price of a headphones. a) What is the inverse demand function? b) Write the marginal revenue function? Average Variable Cost (AVC) function for headphone is estimated to be AVC = 28 -0.005Q + 0.00000122 Where AVC is average variable cost (in AED), and Q is number of wireless stereo headphones. Sharjah Electronics' fixed costs each month are AED 270, 000. c) If the Sharjah Electronics Company wishes to maximize its profit, how many headphones should Sharjah Electronics produce? d) What price should Sharjah Electronics Company charge for headphones? e) How much profit Sharjah Electronics Company earns?
Expert Solution
a) Q = 100,000 - 1,000P
Inverse demand function: P = 100 - 0.001Q
b) TR = P * Q
TR= 100Q - 0.001Q^2
MR = 100 - 0.002Q
c) AVC = 28 - 0.005Q + 0.000001Q^2
VC = 28Q - 0.005Q^2 + 0.000001Q^3
TC = VC + FC = 28Q - 0.005Q^2 + 0.000001Q^3 + 270,000
MC = 28 - 0.01Q + 0.000003Q^2
Electronics should produce at a point when MR = MC
100 - 0.002Q = 28 - 0.01Q + 0.000003Q^2
0.000003Q^2 - 0.008Q - 72 = 0
Q = 6,410
d) When Q = 6,410, P = 100 - 0.001 * 6,410 = 93.59
e) Total revenue = 93.59 * 6,410 = 599,911.9 while total cost is 507,414.22 which result in profit of 599,911.9 - 507,414.22 = 92,497.68
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