Suppose the inverse production function is: L = x - x2 x3 Where L is labour per period and x is output per period. (5 marks to each part) i. Derive the firm's supply curve [p=f(x)] if w =1.

ii. How much will the firm produce per period if p = 1? And if p = 12?

iii. Howmuchprofitismadeifp=1?Howmuchifp=12? iv. What will the firm do if p =1 and a profit tax of 85 percent is imposed on all firms in the industry?

v. What will the firm do if a levy of 0.2 per period is made on all firms in the industry?

vi. For what values of x are returns to scale increasing, decreasing, constant? How does this tie up with your answer to 'i'? vii. Suppose that p = 1/2 but the firm is required by law to employ 1/3 unit of labour at a wage w = 1. What output, if any, will it supply?