Question

1. a) Suppose a manufacturing company can use either Humans or Robots to produce output (Q) (consider Humans and Robots to be substitutes). The Marginal Product of Humans is 10 units of output per hour and the Marginal Product of Robots is 32.5 units of output per hour. Humans cost $7 per hour and Robots cost $20 per hour. What is the firm's Total Cost Function?

b) Suppose the firm is producing 50 units of output. Using a graph, draw the firm's isoquant for Q = 50. Also, on the same graph, draw the isocost line associated with the total cost of producing Q = 50.

Your graph should be accurate and carefully labeled.  Please put the number of pounds of hours of Humans (H) on the vertical axis, and the number of hours of Robots (R) on the horizontal axis. Make sure to clearly indicate the cost-minimizing combination of Humans and Robots that the firm should use to make 50 units of output, and to clearly label both the isocost line and the isoquant.

Answer 1

A) Production function

Q = 10*H +32.5*R

PH = 7, PR = 20

MRTS = MPR/MPH = 32.5/10 = 3.25

PR/PH = 20/7 = 2.85

As MRTS > PR/PH

MPR/PR > MPH/PH

only R is used ,

total cost = R*PR

Q = 32.5R, R = Ql32.5

total cost = 20Q/32.5

C = Q/1.625

B) isoquant : 10H +32.5R = 50

Total cost to produce 50 units = 50/1.625

So Isocost : 7H +20R = 50/1.625

Graph