Question

Microeconomics

a Suppose the production function of a restaurant is as followssQ-1o L Assume it is the long run. (ao points) a) Carefully draw isoquants for Q 40, Q-so, and Q-io. Show all your work b) Suppose the price of labor is sio and the price of capital is sio. Draw the isocost lines for TC-8o, 10o, and so. Briefly explain how you drew the lines How much capital and how much labor will be used to produce at each output? Label the cost-minimizing combinations for each output c) d) What kind of returns to scale it is?

Answer 1

a) Isoquants refer to the curve where the same quantity of output is produced while changing the quantities of input.

b)Price of Labor(P _L) = 10

Price of Capital(P_K)= 10

Isocost line = P_LL + P_KK = TC(Total Cost)

=> 10L+ 10K= TC(Isocost line)

At TC=80 , If K=0 L=8 and vice versa

At TC=100, If k = 0 L= 10 and vice versa

Similarly for TC = 120.

c) Production Function = $Q=10\sqrt{KL}$

At Q= 40, KL = 16 .

=> K= 16/L

Using this in Isocost line when TC= 80 we get

10L+ 10(16/L)=80

10L^2 + 160=80L

L^2-8L +16=0

L= 4 and K= 4

Similarly At Q= 50 and TC= 100 K and L are 5 and 5.

At Q= 60 and TC= 120 K and L are 6 and 6.

d) This is constant returns to scale because of %age increase in input i.e. labor and capital is equal to %age increase in Output which is 25%