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Assigment Essay

585 words - 3 pages

Assignment #2  Production economics  Exercise 1: Production function  In the Deep Creek Mining Company example described in class suppose that capital is fixed at 500 brake  horse power, while labor is a variable input.  a) Complete the following table  Labor input L   (n. of workers)  1  2  3  4  5  6  7  8  9  10    b) Plot the (i) total product, (ii) marginal product and (iii) average product functions  c) Determine the boundaries of the three stages of production  Exercise 2. Optimal input level in short‐run  The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the  boat. Based on past data, the following production schedule was developed:  Crew size (number of workers)  2  3  4  5  6  7  8  9  10  11  12    a) ...view middle of the document...

 Determine the optimal crew  size if the trawler owner wants to maximize profits.  Exercise 3. Optimal input levels in long‐run  A firm uses two variable inputs, labor (L) and raw materials (M), in producing its output. At its current  level of output:  CL = $10/unit     MPL = 25  CM = $2/unit    MPM = 4  a) Determine whether the firm is operating efficiently, given that its objective is to minimize the  cost of producing the given level of output.  b) Determine what changes (if any) in the relative proportions of labor and raw material need to be  made to operate efficiently.  Exercise 4. Optimal use of labor  Consider the following short‐run production function for a firm, where L is labor, and Q is output.  Q = 20∙L ‐ .25∙L2  Suppose that the good is sold for $5 per unit.  Also assume that the firm can obtain as much of labor (L), as  it needs at $81.25 per unit.  a) Determine the marginal revenue product of labor.  (This is a function. Start from 1 up to 10 workers)  b) Determine the marginal factor cost function.  c) Determine the optimal value of L, given the objective is to maximize profits.  Exercise 5. Returns‐to‐scale  Consider the following production function for FFS railways:  Q =  L∙Eß∙W  where  L = labor input in man‐hours; E = electricity in KWh; W = capital input in number of wagons; and Q =  output measured in millions of kilometers.   Suppose that the parameters (, ß, and ) of this model  were estimated using a log linear regression model with annual data for the past 40 years.  The following  results were obtained:   = .42    ß = .37     = .31  a) What type of returns to scale appears to characterize this railways system?  b) Suppose that all inputs increase by 5% next year.  Determine the approximate percentage change in  output. [Hint: multiply by 1.05 …..]   

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