1. The short-run production function of a competitive firm is given by () = 62/3, where L is the amount of labour it uses. The cost per unit of labour is = 6 and the price per unit of output is = 3.

a) Plot a few points on a graph of this firm's production function and then sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0,12), the isoprofit line that passes through (0,8), and the isoprofit line that passes through the point (0,4). What is the slope of each of the isoprofit lines? How many points on the isoprofit line through (0,12) are actually possible? Make a squiggly line over the part of the isoprofit line through (0,4) that consists of outputs that are actually possible.

b) How many units of labour will the firm hire? How much output will it produce? If the firm has no other costs, how much will its total profits be?

c) Suppose the wage of labour falls to 4, and the price of output remains at p=3. On the graph, use red ink to draw the new isoprofit line for the firm that passes through its old choice of input and output. Will the firm increase its output at the new price? Explain why, referring to your diagram.