Question

Suppose the wage increases to ​$200.00200.00 but that the firm chooses to keep using the same amount of labor and capital to produce 200 units of output. Given this new set of factor prices ​(w​'equals=​$200.00200.00​, requals=​$100.00100.00​), how much have costs changed if the set of input choices remains at point​ A? ​$nothing. ​(Enter a numeric

Answer 1

Question:

The question is incomplete. See the complete question below and the graph.

You are given the following data;

Cost = C = $12,000.00

w = $100.00 per unit of labor

r = $100.00 per unit of capital

These data are used to construct the isocost line (C) in the diagram to the right. Suppose the wage increases to $200.00 but that the firm chooses to keep using the same amount of labor and capital to produce 200 units of output. Given this new set of factor prices (w'=$200.00, r = $100.00), how much have costs changed if the set of input choices remains at point A? Enter a numeric response using a real number rounded to two decimal places.)

Answer:

Cost change = $6,000

Explanation:

Given Data:

Cost = C = $12,000.00

w = $100.00 per unit of labor

r = $100.00 per unit of capital

Calculating the cost incurred  at point A using the equation of iso-costline C¹, we have;

C = wl + rk

where;

C = total cost

w = price of labor = $100

l =  labor = 60 unit from the graph

k = capital = 60 unit from the graph

r = price of capital = $100

Substituting into the formula, we have

C = wl + rk

  = 100*60 + 100*60

  = 6000+6000

  = $12,000

For increase in wages(w= $200, r = $100) with same amount of labor and capital, the cost incurred becomes;

C = wl + rk

   = 200*60+100*60

  = 12,000 + 6000

  = $18,000

Therefore,

Cost change = 18000-12000

                    = $6,000

See the attached graph.