Question

Please show all your work and show your steps. Clearly explain your answer and the steps you take. If writing, please write neatly, no cursive, and write in a linear fashion. Please draw and demonstrate the appropriate graphs. WRITING ONLY on PEN AND PAPER WITH BLACK PEN. NO TYPING

3. You are the production manager who has been directed to produce 1,280 units of output. What is the minimum cost for you to do so given the price of capital of $10, a wage rate of $20 and a production function where TP = 10KL. (10 marks) к Optimal amount of capital: (5 marks) Optimal amount of labour: (5 marks) Minimum total cost to produce 1,280 units: (7 marks)

Answer 1

In long run, cost minimization

MRTS = MPL/MPK = w/r = 20/10= 2

MRTS = K/L

So, K/L = 2

K= 2L

From Production function

Q= 10KL

1280= 10*2L*L

128/2 = L*L

L= 8

K= 16

so total cost = 320

= 8*20+10*16

= 320