04 Jun Question The Rapid Transit Corporation in a city has estimated the
Question
The Rapid Transit Corporation in a city has estimated the following Cobb–
Douglas production function using monthly observations for the last two years:
ln Q = 2.303 + 0.40 ln K + 0.60 ln L + 0.20 ln G
(3.40) (4.15) (3.05)
R2 = 0.94 D–W = 2.20
Where Q is the number of bus miles driven, K is the number of buses the
Firm operates, L is the number of bus drivers it employs each day, and G is
The gallons of gasoline it uses. The numbers in parentheses below the
Estimated coefficients are t values. With respect to the above results,
Answer the following questions:
(a) Estimate Q if K = 200, L = 400, and G = 4,000.
(b) Find the value of the output elasticity of K, L, and G. By how much does
Output increase by increasing each input by 10 percent, one at a time?
(c) Determine the economies of scale in production. By how much does
Output increase if the firm increases the quantity used of all inputs at the
Same time by 10 percent?
(d) Are the estimated coefficients of the Cobb–Douglas production function
Statistically significant at the 5 percent level? How much of the variation in
Q does the estimated regression explain? Does the D–W statistic indicate
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