Please only answer parts d e f g I provided the whole questi

?Please only answer parts (d), (e), (f), (g). (I provided the whole question for reference) Draw the appropriate graphs/diagrams and answer each question. Thank you!

(a) What’s the equation for an isoquant curve which represents an output level of 20? In a (k,l) input space, identify 5 points of this isoquant and connect them in a smooth way; call that Diagram 1.

(b) What’s the equation for an iso-cost line which represents a total cost of $18,000? Plot it in Diagram 1.

(c) To produce an output equal to 20, what’s the cost-minimizing basket of inputs? How much does it cost? What is the difference between the short run and long run?

(d) Derive the long-run total cost function(LRTC) as a function of the output level x. Then derive the long-run marginal cost(LRMC) and long-run average cost(LRAC) functions.

(e) Derive the short-run total cost (SRTC) functions for k = 100 and k = 225 respectively. Then derive the two sets of short-run marginal cost(SRMC) and short-run average cost(SRAC) functions respectively.

(f) In a single diagram(call that Diagram 2), carefully plot all the cost curves except the total cost curves. Do you discover any characteristics in terms of their relative positions?

(g) With capital being fixed at k = 100, what’s Foxconn’s optimal level of output? How much is profit at that level of output? With capital being fixed at k = 100, derive the short-run average variable cost(SAVC) function and plot it in Diagram 2.

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

d) 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