Tackle the Test: Free-Response Questions

1. Question

   Answer the following questions under the assumption that firms use only two inputs and seek to maximize profit.

   
   

   
   

   1. Would it be wise for a firm that does not have the cost-minimizing combination of inputs to employ more of the input with the highest marginal product and less of the input with the lowest marginal product? Explain.

      
      
   
   

   2. What is the cost-minimization rule?

      
      
   
   

   3. When a firm hires more labor and rents less capital, what happens to the marginal product of labor per dollar and the marginal product of capital per dollar? Explain.

      
      
   
   

   Rubric for FRQ 1 (5 points)

   1 point: No

   1 point: The input with the highest marginal product might be much more expensive than the input with the lowest marginal product, making the marginal product per dollar higher for the input with the lowest marginal product. When that is the case, costs would be lower if the firm employed more of the input with the lowest marginal product (but the highest marginal product per dollar) and less of the input with the highest marginal product (but the lowest marginal product per dollar.)

   1 point: The cost-minimization rule says that firms should adjust their combination of inputs to equalize the marginal product per dollar spent on each input.

   1 point: The marginal product of labor per dollar decreases and the marginal product of capital per dollar increases.

   1 point: Each factor has diminishing marginal returns. So when more labor is hired, the marginal product of labor (and thus the marginal product of labor per dollar) decreases. Likewise, when less capital is rented, the marginal product of capital (and thus the marginal product of capital per dollar) increases because the units of capital that are given up had a lower marginal product than those that remain.

2. Question

   Refer to the table below. Assume that the wage is $10 per day and the price of pencils is $1.

   
   

   
   

   
   

   
   
   
   
   
   
   
   
   
   

   Quantity of labor (workers)	Quantity of pencils produced
   0 1 2 3 4 5 6 7	0 40 90 120 140 150 160 166

   
   

   
   

   
   

   1. What is the MPL of the 4th worker?

      
      
   
   

   2. What is the MPL per dollar of the 5th worker?

      
      
   
   

   3. How many workers would the firm hire if it hired every worker for whom the marginal product per dollar is greater than or equal to 1 pencil per dollar?

      
      
   
   

   4. If the marginal product per dollar spent on labor is 1 pencil per dollar, the marginal product of the last unit of capital rented is 100 pencils per dollar, and the rental rate is $50 per day, is the firm minimizing its cost? Explain. (5 points)

      
      
   
   

   Rubric for FRQ 2 (5 points)

   1 point: 20

   1 point: 10/$10 = 1 pencil per dollar

   1 point: The firm would hire 6 workers.

   1 point: No.

   1 point: The marginal product per dollar spent on capital is 100/$50 = 2 pencils per dollar. Thus, the firm is not following the cost-minimization rule because the marginal product per dollar spent on labor (1) is less than the marginal product per dollar spent on capital (2).