Section B There is only ONE question in this section, which you must answer. 1. Consider a firm with the following production function: F(K,L)=4K0.5+L0.5 where K is the amount of capital and L is the amount of labour used in the production process. The cost of capital is r per unit, the cost of labour is w per unit and the price of the output is p. i) Write down the firm's profit function. [15\%] ii) Find the firm's marginal product of labour (MPL). marginal product of capital (MPK), and marginal rate of technical substitution of labour for capital (MRTS [15\%/ iii) Maximize the profit function from part i) above to find the firm's demand for labour and demand for capital. [30\%] iv) Using your answer to part iii) above, find the firm's output function and graph the firm's (long run) supply curve (you must label this graph properly). [20\%]] v) If there was a reduction in the cost of capital (r), what effect would this have on the firm's demand for labour? [10\%] vi) Say that the firm was able to change their technology so that capital became more productive. To be precise, say that the production function charrges to this: P(K,L)=8K0=Las. What effect would this have on the firm's demand for labour? [10% ] Section B There is only ONE question in this section, which you must answer. 1. Consider a firm with the following production function: F(K,L)=4K0.5+L0.5 where K is the amount of capital and L is the amount of labour used in the production process. The cost of capital is r per unit, the cost of labour is w per unit and the price of the output is p. i) Write down the firm's profit function. [15\%] ii) Find the firm's marginal product of labour (MPL). marginal product of capital (MPK), and marginal rate of technical substitution of labour for capital (MRTS [15\%/ iii) Maximize the profit function from part i) above to find the firm's demand for labour and demand for capital. [30\%] iv) Using your answer to part iii) above, find the firm's output function and graph the firm's (long run) supply curve (you must label this graph properly). [20\%]] v) If there was a reduction in the cost of capital (r), what effect would this have on the firm's demand for labour? [10\%] vi) Say that the firm was able to change their technology so that capital became more productive. To be precise, say that the production function charrges to this: P(K,L)=8K0=Las. What effect would this have on the firm's demand for labour? [10% ]