Question

The Southern Mail produces local newspapers. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at R52 per hour and labour can be hired at R12 per worker hour. The company has allocated R150 000 for the intial run of newspapers. The production function using available technology can be expressed as Q= 0.25K⁰.²⁵L⁰.⁷⁵: a) Construct the isocost equation? b) Determine the combination of labour and capital to get the greatest output for an outlay of R150 000 for an intial run of newspapers. Determine the level of output? c) Graphically illustrate this using isoquant and isocost lines.

Answer 1

Solution:

a.). Isocost function:

TC = wL + rK

TC = 12L + 52K

 

b.). MP_L = $\frac{\partial Q} {\partial L}$ = 0.1875K^0.25L^-0.25

 

MP_K = $\frac{\partial Q} {\partial K}$ = 0.0625K^-0.75L^0.75

 

MRTS = $\frac{MP_{L} }{MP_{K}} = \frac{w}{r}$

= $\frac{0.1875K^{0.25}L^{-0.25} }{0.0625K^{-0.75}L^{-0.75}} = \frac{3K}{L}$

$\frac{3K}{L} = \frac{12}{52}$

L = 13K

150,000 = 0.25K^0.2513K^0.75

K = 46,154

L = 13K = 13 x 46,154 = 600,000

Q = 0.25(461534^0.25) 600,000^0.75

Q = 78,997

 

c.). The graph is as below: