Please show full workings

2. Suppose that the demand for pogo sticks is given as Q = 1500 - 50p . Entrepreneurial talent for pogo-stick making is scarce. The supply of entrepreneurs is given as E = w, where w denotes the annual wage paid. Suppose further that each firm in the perfectly competitive pogo-stick industry requires one (and only one) entrepreneur so that the number of entrepreneurs hired E is equal to the number of firms n. Each firm's long-run total cost function is C(q, w) = 292 - 10q + w . (a) State the equilibrium condition for the pogo-stick entrepreneur market and use it to derive w(n), the annual wage paid as a function of the number of firms. (b) Determine the long-run marginal and average cost functions of each firm. (c) Characterize the long-run equilibrium condition for each firm in the pogo-stick market and use it to derive q(n), p(n), and total quantity supplied Qs and demanded QD as functions of n