Stanford airline's production function is given by a Cobb-Douglas form: where: Y = number of passengers...

Stanford airline's production function is given by a Cobb-Douglas form:

where:

Y = number of passengers carried per year

L = number of pilots (labor)

K = number of aircraft (capital)

a) show that the product elasticity for labor is given by E_YL = a,

and that the product elasticity for capital is given by /•'. ,.=/?.

b) show that MP_L > 0, MP_K >0, and that tfY / âl: < 0 , &Y / cK^₂ < 0.

c) show that the marginal rate of substitution between labor and capital depends only on the ratio of K and L, but NOT on the level of production Y.

d) based on the above, do you think that the Cobb-Douglas form is a realistic production function for the airline industry ? Please explain. Problem

Solutions

Expert Solution

Y=number of passengers carried per year

L=number of pilots( labor)

K= number of aircrafts (capital)

Part a)

Part b)

Part c)

Marginal rate of technical substitution is ratio of marginal product of labor to marginal product of capital.MRTS is not dependent on level of output "Y"

Part d)

Since product elasticities of labor and capital are constant. This means increase in aircrafts and increase in pilots leads to constant increase in output in both cases. This is applicable in real life also. For example increase in fleet of a airline increases the output by product of number of aircrafts added in fleet and sitting capacity of each aircraft.

Aircrafts and pilots are important for the airline to operate and are required in specific proportions.

Therefore, cobb-douglas function is realistic production function for airline industry.

Rahul Sunny answered 1 year ago

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