A firm's production function is given by Q = √LK . The price of labour is w and the price of capital is r.
a. The price of labour is $5 and the price of capital is $20. What is the cost minimising combination of labour and capital if the firm wants to produce 1000 units per year?
b. Derive the total cost function, as a function of Q, w and r.Substitute the values w = $5 and r = $20 into the cost function and illustrate LRTC(Q), LRAC(Q) and LRMC(Q) using a suitably labelled diagram (LR = long run). Why is the LRTC function shaped the way it is?
c. Now assume that capital is fixed at K' , derive the short run total cost function, using w = $5 and r = $20.Illustrate the SRTC(Q), SRAC(Q) and the SRMC(Q) functions using a suitably labelled diagram (SR = short run).