A profit-maximising, competitive, firm has the following production function:

where Q is output, K the quantity of input capital, and the quantity of input labour. The price of the output is P. the price of K is r, the price of L is w. This means that costs are given by: C - wL rk

(a)

(b)

(c)

Minimise costs subject to the production function, to find the conditional, on Q. factor demands. These are cost minimising K and I expressed in terms of Q. w and r. Do not check the second order conditions,

(9 marks)

Now solve for the cost function by substitution, finding optimal C in terms of Q. w and r.

(6 marks)

ac

Now set marginal cost all equal to price and solve for Q. (2 marks)