Exam practice question:

Suppose that a firm's production function involves two inputs, labour (L) and capital (K) which are perfect substitutes of each other. You are informed that an input bundle involving only 60 units of labour and no capital can produce an output of 180 units. You are also told that an input bundle involving only 20 units of capital and no labour can produce 40 units of output. Based on this, answer the following questions:

i) Work out the firm's production function given the information above and show your working.

ii) Suppose you are told that labour is half as expensive as capital to hire and labour is kept on the horizontal axis while capital is kept on the vertical axis. What will be the absolute gradient of the isocost family? Using the production function in part (i), determine the absolute gradient of an isoquant.