Assume a firm faces a CES production function as Q = (L1/2 + K1/2)2 . Input markets are perfectly competitive so that prices of labour and capital are given as ‘w’ and ‘r’, respectively. 

a. Obtain equations for production expansion paths for this firm. What happens to the capital intensity of production as the firm expands its scale of operation? 

b. Derive the conditional demand functions for labour and capital. Does the demand for each input become more sensitive to output changes as the firm expands? 

c. Obtain long-run cost functions (total, average and marginal costs) for this firm. 

d. Obtain the absolute share of each input in total cost. 

e. Obtain the relative share of each input in total cost. 

f. Specify a linear regression equation that you will use to estimate the cost function obtained in ‘c’ above. 

g. Specify a linear regression equation that you will use to estimate the elasticity of substitution between K and L. What value of elasticity you hypothesize?