Question: Question B2: Consider a firm that produces output, q, using labour, L, and capital, K, and the following production function: q = A (L0.5 +

Question B2: Consider a firm that produces output, q, using labour,

Question B2: Consider a firm that produces output, q, using labour, L, and capital, K, and the following production function: q = A (L0.5 + K05) where A > 1 is the firm's productivity. That is, a higher A means that a firm is able to produce more output with a given combination of labour and capital. For now you can assume that A is constant. Let the wage paid to workers be w = 250 and the rental rate paid to capital owners be r = 1000. (a) (11 marks] Derive this firm's conditional labour and capital demands for an output of qo. How does A affect the conditional demand for labour and capital respectively? (b) [4 marks] Derive an expression for this firm's average cost of production as a function of A. (c) [5 marks] Now suppose that A is no longer constant and instead increases with time. Let t > 0 index time and let the increase in A over time be determined by the following: A(t) = 0.05 where e is a constant that is approximately equal to 2.718. This constant has the prop- erty that ln(et) = t, where In refers to natural logarithm. In addition, suppose that to viably produce this product, the firm has to ensure that AC(q) = P, where AC(q) is its average cost of production and P = 150 is the market price for its product. How long will it take for this firm to viably produce a single unit (i.e. q = 1) of its product at this market price? You can assume that the wage, rental rate, and the market price will remain constant at the values above during the entire period

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