Consider a firm with the production functionQ=L2K3. In the short run, the firm has capital fixed at K=64.The firm faces a price of labour w=2 and a rental rater=4.

(a) Find the cost-minimizing factor demand functions in the short-run.

(b) Find this firms short run total cost function (STC(Q)) and indicate the total variable (TVC) and total fixed cost (TFC) components of this curve.

(c) Find the following 4 cost curves: Average Variable Cost (AVC); Average Fixed Cost (AFC); Short Run Marginal Cost (SMC); Short Run Average Cost (SAC)

(d) How does the AFC change as Q increases? Explain this relationship between AFC and Q. (e) Find the firm's short-run supply curve assuming that 200 of the fixed costs are sunk.