The file provided to you for this section contains time series data on output , capital () and labour () for certain firm. Using this data file:
a) Estimate the Cobb-Douglas production function in its unrestricted form (i.e. impose no restriction on the estimators of coefficients and ). Consider the possibility of a constant growth rate in the technology coefficient, i.e. ; if you decide this feature is relevant in your model, report the estimator of the technology growth rate. Also, report and analyse the rest of your results carefully. (5 Marks)
b) Based on your estimates, plot a map of isoquant curves on the space for Period 30. (5 Marks)
c) Assume you are in Period 30 and the firm wants to know how much output can be produced with a budget of 100 million dollars when the cost of financing the capital production good is $0.05 per $1 (net of depreciation) and the cost of labour is $100,000 per worker (note: considering that is expressed in ‘000s of dollars in your data set, you can use the following cost function expressed in ‘000s of dollars: ). Find the solution using your estimates and the Lagrangian method to solve this output maximization problem. Provide an economic interpretation and represent it in a graph using isocost and isoprofit curves. (5 Marks)
d) Demonstrate that the problem in section (c) has a dual or mirror-image representation, i.e. if you minimise the cost at which you can produce the amount of output found in (c), the answer obtained through the Lagrangian method will be $100,000,000. Prove this result. Also provide an economic interpretation and a graphical representation of the problem. (5 Marks)
e) Estimate the restricted Cobb-Douglas production function . Then, considering the restricted and unrestricted forms, conduct a statistical test to determine whether or not there are constant returns to scale. Explain every step of this test carefully. If you find no evidence of constant returns to scale, explain whether the correct specification has increasing or decreasing returns to scale. (10 Marks)
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