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Apple Inc
Apple Inc. is about to release the Apple Watch. The demand for the Apple Watch in the Bay Area is P = 5,000 - 2Q. Marginal and average costs for producing the Apple Watch is a flat $200.
a. If Apple chooses to sell the watch to everyone at the same price, how many will it sell, and at what price? What will be its profits?
b. If Apple chooses to sell the watch to separate blocks of consumers, how many will it sell to each, and what will the price be for each block of consumers? What will be the profits?
Expert Solution
a) If there's one price for all customers. The company must produce Q Apple Watch at P price when Marginal revenue equals marginal cost (MR =MC). MC=200. To obtain MR, it is necessary to derive the inverse demand function, P= 5,000-2Q. Therefore,
MR = 5,000 - 4Q
MR = MC
5,000 - 4Q= 200
-4Q =200-5,000
Q= -4800/-4
Q*= 1,200 This is the optimal quantity of production.
Substitute Q in the inverse demand
P = 5,000-2(1,200) = 2,600
Calculate profit by subtracting the total cost of total revenue.
?= (P * Q) - (AVC * Q) + TFC
Assume no fixed cost
?= (1200) (2600) -(200x1200) =2,120,000-240,400=2,880,000
?= 2,880,000
b)
P1 = 5,000 -2Q1
P2 = 5000 -2Q2
Calculate the revenue for each price
Revenue = P x Q
for price 1: ?' / Q1'= - 4Q1 +Q2= 0
Q2 = 4Q1 (A)
for price 2 =?' / Q2'= -4Q2 + Q1 + 5000
Q1 = -5,000 + 4Q2 (B)
Q1 = -5,000 +4 (4Q1) = -5,000 + 8Q1
Q1 -8Q1 = -5,000
Q1 = -5,000 /-7 =714.28 is the price for block 1
For block 2
Q2 = 4Q1 = 4(714.28) =2857.14 is the price for block 2
Then with this new function we equal to 0
Cost of production
Cost of production is an essential concept from the producer's point of view. As the price of the commodity fixed by the consumer is always based on the actual cost of that product which was invested by the producer at the initial stages. The cost of production includes various concepts such as average cost, total cost, and the marginal cost of the product.
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