1) Sweaters are produced using machines and labour. The following table shows the isoquants associated with producing 10, 20, 30 and 40 sweaters. The first number in the input bundle is units of labour, the second is units of capital.

The price of one unit of labour is $2.00. The price of one unit of capital is $3.00.

(a) Show graphically, using an isoquant diagram, the optimal way to produce 10, 20, 30 and 40 sweaters.

(b) Using the results obtained above, derive a table for the long run costs of the various levels of production of sweaters (10, 20, 30, 40). The table should show: quantity, total cost, average cost and marginal cost.

(c) Assume that the firm has built the optimal plant (i.e., purchased the optimal amount of capital) to produce 30 sweaters. In the short run, how would the firm produce 10, 20 and 40 sweaters. Use this information to produce a table showing the short run costs facing this firm for various levels of output (10, 20, 30, and 40 sweaters). The table should include quantity, total cost, average variable cost and marginal cost.