Question

1. Consider the following production function for bus transportation in a particular city:

Q= aL^B1F^B2K^B3

Where Fuel input in gallons = F

Capital input in number of busses = K

Labor input in worker hours = L

Output in millions of bus miles = Q

We estimate the various parameters as follows using historical data:

                                    α=0.0012, β1=0.45, β2=0.2, β3=0.3

a) Determine output elasticities for Labor.

b) Suppose that labor hours increase by 10%. By what percentage will output increase?

Answer 1

ANSWER::

The following production function for bus transportation in a particular city: Q= a

Where Fuel input in gallons = F

Capital input in number of busses = K

Labor input in worker hours = L

Output in millions of bus miles = Q

We estimate the various parameters as follows using historical data:

                                    α=0.0012, β1=0.45, β2=0.2, β3=0.3

a)

solution:

The output elasticities for labour is

The regression model for the above question is given below

Q =  α + β1*F + β2*K + β3*L

Q = 0.0012 + 0.45*F + 0.2*K + 0.3*L

b)

solution:

Suppose that labor hours increase by 10% then the coefficient of labour hours is 0.3 and L = 10%

then output increases by 0.3%  at all the variable at constant

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