Question

I ONLY WANT ANSWERS TO LETTERS "i" and "j"

4) Start with the following production function: q=10K1/2 [1/2 a) Calculate the cost minimizing amounts of K and L (Hint: K and L* will be functions of q, v and w) b) Compute the TC function (Hint: TC will be functions of q, v and w) c) Compute the TC function if w = v = $4. (Hint: TC will now be function only of q) d) If K is fixed at Kı, then the production function is: q=10K2L"2 q” Show that the STC function is: STC = vK, +w. ** 100K, For the remainder of question (4) assume K1 = 4 and if w = v = $4. e) Calculate the short-run marginal cost . f) Calculate the firm's short-run variable cost function and the short-run average variable cost function. g) What is the firm's shut-down price? (Hint: Think about average variable costs) h) Calculate the firm's short-run average total cost function. i) At what price with the firm break even? j) Will the firm produce in the short run if the price is $0.60? Why or why not?

Answer 1

Using previous parts,

STC = (q2/100) + 16

SAC = (q/100) + (16/q)

SMC = dSTC/dq = q/50

(i)

In break-even, TR = TC and P = SAC = SMC.

(q/100) + (16/q) = q/50

q/50 = 16/q

q2 = 800

q = 28.28

Break-even price = SMC = 28.28/50 = $0.57

(i)

SVC = (q2/100)

SAVC = SVC/q = q/100

When P = $0.6, Setting P = SMC,

0.6 = q/50

q = 30

SAVC = 30/100 = $0.3

Since P > SAVC, firm will produce in short run.