Production

Department of Economics                                                         Prof. Andrew J. Buck

Temple University                                                                                 Economics 201

Name

A.  Swash Buckles

EF Enterprises produces swash buckles (Q) using only labor (L).    Let AP(L) and MP(L) represent EF's average and marginal products of labor at quantity L.   Fill in the blanks in the following table.

 Units of Labor 3 4 5 6 7 Q(L) 165 200 AP(L) 45 40 MP(L) - 0

B.  Apples

The production function for apples on the Eris Island is Q = 8L1/2T1/2, where Q is the quantity of apples produced, L is the quantity of labor, and T is the quantity of land.   This is an example of a Cobb-Douglas production function.  (See Appendix or the WWW for a brief review of exponents.)

B.1.   In 1982, farmers on Eris devoted 900 square miles to apple production.  Write

the equation for the average product of labor as a function of  L in that year.

AP(L)  =    *(L)*(T)

B.2.  The associated marginal product of labor function when T=900 is MP(L)  =  120L-1/2.  (This was

obtained by taking the first derivative of the production function with respect to L at

T = 900.)   When L = 64 what is the marginal product of labor?

C.  Assorted Production Functions

Listed below are five production functions showing output (Q) as a function of labor (L) and capital (K).  In each case, determine whether the production process exhibits increasing (I), decreasing (D), or constant (C) (maginal) returns to scale and then whether it exhibits increasing (I), decreasing (D), or constant (C) returns to labor.   Indicate your choices under the appropriate columns.  Remember that returns to scale calculations require that both factors change by the same proportion, while returns to labor calculations require that L change with K held constant.  The first one is done for you.

 Returns to Scale Marginal Returns to Labor Q = 5K + 23L C C Q = 15K2 +2L3 Q = 6K1/2L1/2 Q = 10KL3/4 Q = K + 7L + 5

D.  Manna

Heavenly Hostess, Ltd. produces manna (low-fat and regular) for sale over the internet using two ingredients, milk and honey.  The entries in the table show how the company's daily output (measured in tons) varies with the quantities of the inputs.

 Milk (tons) 0 1 2 3 ----------- ----------- ----------- ----------- | 0       | 0.0 0.0 0.0 0.0 | 1       | 0.0 1.2 1.8 2.0 Honey   (tons) | 2       | 0.0 1.8 2.4 2.8 | 3       | 0.0 2.0 2.8 3.4

D1.  Does manna production exhibit Increasing, Decreasing, or Constant

returns to milk?

D2.  Does manna production exhibit Increasing, Decreasing, or Constant

returns to scale?