Suppose that a firm’s production function is given by Q = ( K1/3 + L1/3 ) a , here α is a given parameter.(a) Find the marginal product of capital and labor.(b) Find the average product of capital and labor.(c) Does this production function have increasing, constant or decreasing re- turns to scale? Explain.(d) Find the marginal rate of technical substitution (RTS)(e) Use your result in (d) to find the elasticity of substitution.(f) Suppose a = 3. Set up the cost minimization problem of the firm and solve for the conditional demand for K and L

Acompany that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. prior to buying the new equipment, the company used 6 workers, who produced an average of 79 carts per hour. workers receive $16 per hour, and machine coast was $49 per hour. with the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $11 per hour while output increased by four carts per hour. a) compute the multifactor productivity (mfp) (labor plus equipment) under the prior to buying the new equipment. the mfp (carts/$) = (round to 4 decimal places). b) compute the productivity changes between the prior to and after buying the new equipment. the productivity growth = % (round to 2 decimal places)

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Adisadvantage of corporations is that shareholders have to pay on profits.