Question: 1. Consider the production function =(X 1 , X 2 ) = X 1 1/3 X 2 3/6 . Prove that the technical rate of
1. Consider the production function =(X1, X2) = X11/3X23/6. Prove that the technical rate of substitution is decreasing. [4]
2. True or false? If the law of diminishing marginal product did not hold, the world's food supply could be grown in a flowerpot. Explain. [3]
3. Profit Maximisation (Chapter)
Consider a short-run production function = () = 62/3 where refers to labour. Let the price of output be expressed by and the price of labour by .
3.1 Find the factor demand for labour and the amount of output it will produce. Show all calculations. [5]
3.2 How many units of labour will the firm hire, if p = R3 and w = R6? [1]
3.3 Using your answer in (3.2), how much output will it produce? [1]
3.4 If no other costs are incurred, how much total profits will it earn? [1]
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