Following is a statically estimated demand Curve for Apple’s next I-phone. The m
ID: 1111033 • Letter: F
Question
Following is a statically estimated demand Curve for Apple’s next I-phone. The marginal cost of producing an I-Phone is given as $40. If Apple decides to produce 20 million next year, what will be its profit? Or Loss? Can you verify that they are maximizing profits or not? Furthermore, due to some advancement in Nano technology Apple is able to reduce their production cost (e.g., Marginal cost) down to $30. What might that mean to their sales and profits? Is the demand for Apple’s I-phone elastic? What is that elasticity?
I-Phone Demand Curve: Q = 1040 - 0.5P; where Q represents Quantity demanded; and P is the price per phone
Explanation / Answer
Demand: Q = 1,040 - 0.5P
0.5P = 1,040 - Q
P = 2,080 - 2Q
MC = $40
(1) When Q = 20, P = 2,080 - (2 x 20) = 2,080 - 40 = 2,040
Profit ($ Million) = Q x (P - MC) = 20 x (2,040 - 40) = 20 x 2,000 = 40,000
(2) Profit is maximized when Marginal revenue (MR) equals MC.
P = 2,080 - 2Q
Total revenue (TR) = P x Q = 2,080Q - 2Q2
MR = dTR / dQ = 2,080 - 4Q
Equating MR & MC,
2,080 - 4Q = 40
4Q = 2,040
Q = 510 (Million)
P = 2,080 - (2 x 510) = 2,080 - 1,020 = $1,060
Since current production is less than profit-maximizing output, Apple is not maximizing profit.
(3) When MC = $30,
Sales will remain unchanged unless Apple's demand curve changes, since sles is a function of demand and not of cost of production. Therefore, price and output remaining unchanged, lower MC will signify that profit will increase.
(4) For profit-maximizing (Equilibrium) Q = 510 & P = $1,060,
Elasticity = (dQ / dP) x (P / Q) = - 0.5 x (1,060 / 510) = - 1.04
Since absolute value of elasticity is higher than 1, demand is elastic.