Cost-minimization, graph. (10 points) GLS Ch6 P9. Consider the production and cost information...

Question

Cost-minimization, graph. (10 points) GLS Ch6 P9. Consider the production and cost information depicted below: (a) (2 points) Suppose that capital can be hired for $24 per hour. Label each of the isocost lines with the appropriate total expenditure for the firm. (b) (2 points) Suppose that labor can be hired for $36 per hour. Label the horizontal intercept of each isocost line, and determine the slope of each line. (c) (2 points) Can the firm produce 248,000 units of output for exactly $336? (d) (2 points) What is the minimum cost for which 248,000 units of output can be produced? (e) (2 points) Suppose the firm is spending exactly $240 to make 248,000 units of output. If the marginal product of labor is 400 units of output, what must the marginal product of capital be?

David · Accepted Answer

A)  
Cost of capital = $24 
The isocost line with having y-intercept 8 will have label = coost of capital*y-intercept = 24*8 = $192 
The isocost line with having y-intercept 10 will have label =24*10 = $240 
The isocost line with having y-intercept 8 will have label =24*14 = $336
B)  
Labor intercept for isocost $192 = 192/36 = 5.34 
Labor intercept for isocost $240= 240/36 =6.67 
Labor intercept for isocost $336 = 336/36 = 9.34 
Slope of each line = -5.34/8 = -0.6675
C)  
As the isquant curve with production 248000 is intersecting the isocost line with cost $336, it can be 
produced.
D)  
The minimum cost is achieved when the slope of isocost line and isoquant is equal. 
The minimum cost to produce 248000 units = $ 240
E) 
Slope of isocost line = -mpl/mpk 
Mpk = 400/0.6675 = 600

Cost-minimization, graph. (10 points) GLS Ch6 P9. Consider the production and cost information depicted below: (a) (2 points) Suppose that capital can be hired for $24 per hour. Label each of the...

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