Answer to Question #193597 in Microeconomics for Paul Hackman

Question

The production of Fresh Milk at the University of Ghana's LIPREC is characterized by the following production function:

1.75K^1.4 L^0.6

a Compute the factor intensity ratios and comment on each.

b. The Fresh Milk production function is characterized by decreasing returns to scale.Do you agree with this statement? Why?

c. Compute the marginal product of capital (MPk) and the Marginal product of labour (MPl)

d. Compute the MRTS l,k

e. What is the magnitude in the efficiency parameter of the Fresh Milk production technology?

What does this efficiency parameter imply.

Answer 1

a.

Factor intensity ratio (for L)$= \frac{Coefficient \space of\space Labor}{Coefficient \space of \space Capital} = \frac{0.6}{1.4 }= 0.42$

Factor intensity ratio (for K) =$\frac{Coefficient \space of \space Capital}{Coefficient \space of\space Labor} = \frac{1.4}{0.6} = 2.33$

Since, factor intensity ratio is more for capital, therefore, production technique is capital intensive.

b.

No, since the sum of coefficient of labor and coefficient of capital is greater than one, i.e.

$0.6 + 1.4 = 2$ , which is greater than 1,

therefore, this shows there are increasing returns to scale.

c.

$MP_K = \frac{\delta X}{\delta K} = \frac{\delta (1.75K^{1.4}L^{0.6})}{\delta K} = 1.75 \times 1.4 \times K^{0.4} \times L^{0.6}$

$MPL = \frac{\delta X}{\delta L }=\frac { \delta (1.75K^{1.4}L^{0.6})}{\delta L} = 1.75 \times0.6 \times K^{1.4 }\times L^{-0.4}$

d.

$MRTS_{(L,K) }=\frac{ MPL}{MPK} =\frac {Coefficient\space of\space Labor}{Coefficient \space of\space Capital} \times \frac{ K}{L}$

$MRTS_{(L,K)}=0.42 \times \frac{ K}{L}$

e. 

Value of efficiency parameter = 1.75

The efficiency parameter implies the effect of the scale on production, i.e. it signifies the level of technology in the production.

Higher the value of the efficiency parameter, higher the value of output (if inputs are kept constant).