A firm has a production function given by 
. Suppose that each unit of capital costs R and each unit of labor costs W.
a. Derive the long-run demands for capital and labor.
b. Derive the total cost curve for this firm.
c. Derive the long-run average and marginal cost curves.
d. How do marginal and average costs change with increases in output? Explain.
e. Confirm that the value of the Lagrange multiplier you get from the cost minimization problem is equal to the marginal cost curve.
Definitions:
Population Standard Deviation
A measure of the dispersion or spread of a set of data points in a population, showing how much variation exists from the average.
Square Root
A mathematical function that produces the original number when multiplied by itself.
Null Hypothesis
A hypothesis that suggests there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
Standard Error of the Mean
A statistical measure that estimates the sampling variability of the mean from different samples drawn from the same population.
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