1. Consider the following Cobb-Douglas production function for the bus transportation system in a particular city:

Q = L¹F²B³

Where L = labour input in worker hours

F = fuel input in gallons

B = capital input in number of buses

Q = output measured in millions of bus miles

Suppose that the parameters (, 1, 2 and 3) of this model were estimate using annual data for the past 25 years. The following results were

obtained: 1 = 0.45, 2 = 0.20 and 3 = 0.30

i.Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticities (2 points)

ii.Suppose that labour input (worker hours) is increased by 2 percent next year (with the other inputs held constant), determine the

approximate percentage change in output. (2 points)

iii.Suppose that capital input (number of buses) is decreased by 3 percent next year (which, certain older buses are taken out of

service). Assuming that the other inputs are held constant, determine the approximate percentage change in output. (2 points)

iv.What type of returns to scale appears to characterize the transportation system (ignore the issue of statistical significance)?

(2 points)

v.Discuss some of the methodological and measurement problems one might encounter in using time-series data to estimate the

parameters of this model. (2 points)

[Total: 20 marks]