Consider the production function f(L,K) = 2L^1/2K ^1/4, where L is units of labour and K is units of capital employed in production. A profit-maximising firm with this production function sells its output in a competitive market, and so takes the unit price of its output, p, as fixed. The per unit labour cost is w and the per unit capital cost is r.

a. In the short run, the firm has a fixed amount of capital input, . Write down an expression for the firm's use of the variable factor labour, L, in the short run as a function of the factor unit costs, final product price, and .

b. What is the firm's output quantity choice in the short run as a function of factor unit costs, final product price and ?

c. Keeping factor costs the same, if the amount of the fixed factor of production, capital, were twice as high (i.e. equal to 2), would the firm's use of labour also be twice as large, or more, or less than twice as large? What features of the production function give rise to your answer?