Answer to Question #125445 in Microeconomics for Ss

Question

Consider a toy making firm’s long run production choices. The following table shows the marginal products of capital (K) and labour (L) for various methods of producing 10,000 toys per day.

Production

Method MPK MPL

A 100 4

B 90 18

C 80 30

D 70 40

E 60 48

F 50 55

G 40 60

Capital costs $5.25 per unit and labour costs $3.00 per unit.

a) Suppose the firm is currently producing 10,000 toys per day by using production method E. To

minimize the cost of production, should the firm adjust its employment of capital and/or labour? If so,

why should it hire more or less capital and/or labour?

b) Calculate, if possible, which method minimize costs.

Answer 1

a)Current Output=10,000 toys per day

Marginal Product=MP

Price of Labor=P_l   

Price of Capital=P_c

For Method E; $MPl/pl$ =$\frac{48}{3}$ =16

                         $MPc/Pc$=$\frac{60}{5.25}$=11.42

Hence the firm should hire more labor since it gets an output of 16 per dollar as compared to capital that gives 11.42 per dollar.

b) Method A=Capital=$\frac{100}{5.25}$=19

                       Labor=$\frac{4}{3}$=1.33

   Method B=Capital=$\frac{90}{5.25}$=17.14

                       Labor=$\frac{18}{3}$=6

   Method C=Capital=$\frac{80}{5.25}$=15.24

                       Labor=$\frac{30}{3}$=10

    Method D=Capital=$\frac{70}{5.25}$=13.33

                        Labor=$\frac{40}{3}$=13.33

     Method F=Capital =$\frac{50}{5.25}$=9.52

                         Labor=$\frac{55}{3}$=18.33

      Method G=Capital=$\frac{40}{5.25}$=7.62

                          Labor=$\frac{60}{3}$=20

In this case the method that minimizes costs is Method D since the firm will be indifferent between bringing in more capital versus labor since in either case every dollar brings the same output.