(d) Regardless of the answers you have obtained above, for the remainder of the question, assume that Apple's total cost for producing iPhones is given by C(y) = 16y²+25. Derive and plot on a diagram the following cost functions for Apple: average cost, average variable cost, and marginal cost. Be sure to solve for and clearly label the level of y where average cost attains on minimum on your graph. (e) Suppose Apple is operating in a perfectly competitive market where it takes the price of iPhones as given. If the price of iPhones is p = 320, how many iPhones will Apple choose to supply to the market if it makes this decision by choosing y to maximize profit? As long as Apple can sell the iPhone for some price greater than zero, will it ever short di (f)
(d) Regardless of the answers you have obtained above, for the remainder of the question, assume that Apple's total cost for producing iPhones is given by C(y) = 16y²+25. Derive and plot on a diagram the following cost functions for Apple: average cost, average variable cost, and marginal cost. Be sure to solve for and clearly label the level of y where average cost attains on minimum on your graph. (e) Suppose Apple is operating in a perfectly competitive market where it takes the price of iPhones as given. If the price of iPhones is p = 320, how many iPhones will Apple choose to supply to the market if it makes this decision by choosing y to maximize profit? As long as Apple can sell the iPhone for some price greater than zero, will it ever short di (f)
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
Related questions
Question
please only solve part d, e, f
Transcribed Image Text:15. Apple uses labour and machines to produce iPhones according to the production function
y = LM, where L is the number of units of labour used and M is the number of machines.
The cost of labour is w = 4 per unit and the cost of using a machine is wM = 16. Apple
faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple chooses
how much labour and machines to employ in order to minimize the cost of producing any
given amount of iPhones y. Apple is therefore solving a cost-minimization problem.
(a) If Apple is cost-minimizing, how many workers will it use for each machine? That
is, find the number of workers per machine that Apple will employ. (Hint: setup the
tangency condition.)
(b)
Continuing to assume that Apple produces any given number of iPhones y in the
cheapest way possible, use the equation defining the number of workers per machine
from part (a) and Apple's production function to find expressions for the cost-minimizing
choices of labour and machines as functions of output produced y.
Now use your answers to part (b) to derive Apple's total cost for producing iPhones
as a function of the number of units produced y.
(d)
Regardless of the answers you have obtained above, for the remainder of the question,
assume that Apple's total cost for producing iPhones is given by C(y) = 16y²+25. Derive
and plot on a diagram the following cost functions for Apple: average cost, average
variable cost, and marginal cost. Be sure to solve for and clearly label the level of y
where average cost attains on minimum on your graph.
(e)
Suppose Apple is operating in a perfectly competitive market where it takes the price
of iPhones as given. If the price of iPhones is p = 320, how many iPhones will Apple
choose to supply to the market if it makes this decision by choosing y to maximize profit?
As long as Apple can sell the iPhone for some price greater than zero, will it ever
choose to shut down?
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