Please answer all parts neatly and clearly and draw the appr

Please answer all parts neatly and clearly, and draw the appropriate graphs/diagrams for each part! Thank you

Suppose the factory price of iPhone X is suppressed by Apple to P\'_x = $500 as a result of competition from the newly launched Samsung Galaxy Note 8?

(a) Is Foxconn still willing to operate the iPhone X assembly lines in the short run? Why or why not?

(b) Could Apple reduce the factory price to any level other than 0 and maintain Foxconn’s willingness to continue production in the short run? Why or why not?

(c) Which curve would be the short run output supply curve?

(d) Now suppose Foxconn needs to make a long-term investment decision in terms of how much capital and labor it should hire to produce iPhones for Apple. Suppose Foxconn has the same production function for all models of iPhone as that of iPhone X, and all capital and labor hired could be used to produce any version of iPhone without any need to adjust. On average, the factory price of iPhones is related with the number of iPhones that Apple wants to order, captured by the following function: P_x = 1,000 - 0.1x. How much capital and labor should Foxconn hire with long-term contracts?

Suppose the electronic manufacturer Foxconn\'s production function of iPhone X is where a denotes the amount of iPhones as output, k and I are the amounts of capital and labor as inputs. Let the factory price(the price that Apple offers to Foxconn) of iPhone X be given as Pa $700 price of capital r $900 and price of labor w $400

Solution

Production function:

X = 2(kl)1/2

To find the long run total cost

MRTS = w/r

MRTS = k/l

So at equilibrium , k/l = 400/900

k = (4/9)*l

Put this in production function. x = (4/3)*l

l = (3/4)x

k = (1/3)*x

So Long run cost = w*l + r*k

LRTC= 300x + 300x

=600x

LRMC = dLRTC/dx = 600

LRAC =LRTC/x = 600

e) Given k= 100

x = 20l^1/2

Profit in short run

? = 14000l^1/2 – 400l -90000

d?/dl = 7000l^-1/2 – 400

l* = 306.25

Short run cost = SRTC = 400*l + 90000

SRTC = 212,500

SRMC = dSRTC/dx =

SRAC = SRTC/x = 212500/350 = 607.14