Mike Air produces sneakers according to the production functionF(L,K)=L0.25K0.25.The wage rate, w, and the rental rate, r, are both equal to 1.Note: only part a) is about production, so even if you don't get part a) you can keep going here.

a) What is Mike Air's MRTS? What is the optimality condition for the cost-minimizing production of sneakers (note: this means you don't have to do the whole cost-minimization)?

b) Mike Air's minimized cost function isC(Q)=2Q2. Assuming that Mike Air also has $800 in fixed costs, what is Mike Air's average (total) cost function?

c) Assuming there are 200 identical firms in the sneaker industry, what is the (short-run) market supply for sneakers (either the supply function or supply curve will do)? If the market demand curve isp=8000QD30, what is the short-run equilibrium price and market quantity of sneakers?

d) What is the long-run equilibrium price in the sneaker market (hint:startwith your answer from part b)?

e) In the (Q,p) plane, graph the short-run and long-run market supply curves for sneakers, and the market demand curve. Label the quantity and price at each equilibrium: you will have to calculate the long-run equilibrium market quantity to do this.Add the short-run market supply curve that shows firms entering or exiting to bring the market from short-run to long-run equilibrium, making a note of whether exit or entry is occurring.