Question

A local factory making greeting cards employs only workers and machines. Let x1 represent workers and x2 represent machines. The firm’s production function is: f(x1, x2)=10*min(x1, 1/2x2)

a) Draw an isoquant representing a quantity of 100 units and an isoquant representing a quantity of 200 units. Label two points on each isoquant.

b) Suppose the firm wants to produce 300 cards. The price of an hour of labor is $20 and the price of a machine hour is $30 per hour. What will be the firm’s costs?

c) Suppose you notice the firm is using 45 worker hours and 100 machine hours. What could you recommend to the firm in order for them to decrease costs without decreasing output? How much money would you save the firm?

Answer 1

A) isoquant are L shaped, kinked along,

X1= .5X2

B) so at eqm, x1= .5*X2 = q

So q= 300, x1*= 300, x2*= 300*2= 600

w1= 20, w2= 30

Total cost C*= 20*300 + 30*600

= 6,000 + 18,000

= 24,000

C) x1= 45, x2= 100

Then x2/2= 50

So, Maximum possible output = Min(45,50) = 45

So firm could reduce X2 by 10 units,

So that x2'= (100-10)= 90

& x2'/2= 45

& Still output produced is 45 units ,

So money saved = 10*30= 300