Question

Consider an investment fund that builds its portfolios with help of humans H and robots R. The human employees receive a wage w = 40 per hour. The rental rate of robots r = 60 per hour. Suppose that inputs H and R are perfect substitutes and a portfolio can be created by 2 humans only, one robot only or any combination in between (assuming for computational reasons that humans and robots can contribute part-time also).

a) Draw isoquants for F(H,R) = {10,20,30}, i.e. production levels of 10, 20 and 30.

b) To produce 20 portfolios, the company chooses to employ 10 humans and 15 robots. Does this input combination minimise cost and, therefore, optimise production ? Add the corresponding isocost line to your graph of isoquants !

c) Whichinputcombinationwilloptimiseproduction

Answer 1

a)

b) $10\times40+15\times 60=1300$

To produce 10 portfolios, the company chooses to employ 7 humans and 12 robots

C)$7\times40+12\times 60=1000$

To produce 30 portfolios, the company chooses to employ 15 humans and 20 robots

$15\times40+20\times 60=1800$