The management of Cobb and Douglas Ltd are trying to work out if they should

expand their business. Their accountants and engineers have provided them with

details of their company which they are working through to make a capital investment

decision. The engineers have informed them that the overall production structure of

the company can be described by y = 4K^1/2L^1/2, where y is output, K is capital, and L is labour. The engineers also report that this implies that:

MPK = 2L^1/2 / K^1/2 .

The managers have a statement from the company's accountants reporting that the

price of capital is currently $50 per unit, the price level is 8, the rate of depreciation

is 20%, the current real interest rate is 3%, and the firm currently owns 64 units of capital, and employs 25 hours of labour input.

a) If you were one of the managers trying to maximise Cobb and Douglas Ltd's profits

would you want to alter its current capital stock, and if so, in what direction? Explain

your answer.

b) Say that in a subsequent meeting reviewing the original decision, that managers now

know that the research and development work of the engineers of Cobb and Douglas

has recently led to a technological innovation that means that the company can

produce more output with the same level of resources. The engineers report that the

overall production structure of the company can now be described by y = 6K^1/2L^1/2

and MPK =3L^1/2 / K^1/2 .

Would the managers' decision in a) change? What would the explanation would they

give for changing or not changing their decision?

c) Last year, the Reserve Bank repeatedly cut the Official Cash Rate in an attempt to

prevent an economic recession in New Zealand. Would this make the decision reached about how much to invest or disinvest in Cobb and Douglas Ltd's capital seem wise

in retrospect?