(a) A firm's inverse demand and total cost functions are given as: P = 700 - TC = 202 + 100Q + 5000 1. Find the firm's total revenue and profit functions. [2 marks] ii. Find the firm's profit maximising quantity, price, and level of profit. Demonstrate that it is a maximum using second-order condition. (5 marks] iii. Using differential of total revenue function, find the approximate change in total revenue if the level of output increases by 4% from the level obtained in (ii). Comment on the accuracy of your finding. [3 marks] iv. Do you think total profit will increase, if the level of output is increased by 2% from the profit maximising level obtained in part (11)? Briefly explain. [1 mark] (b) Suppose the production function of a firm is given by: Q = 30KL) where Q is weekly output, and K and L are weekly inputs of machine-hours and worker- hours respectively. i. Find marginal product of labour and marginal product of capital when K=125 hours and L=216 hours. [2 marks] il. Using your answers in part (1), find the marginal rate of technical substitution and interpret the results. [2 marks] (a) A firm's inverse demand and total cost functions are given as: P = 700 - TC = 202 + 100Q + 5000 1. Find the firm's total revenue and profit functions. [2 marks] ii. Find the firm's profit maximising quantity, price, and level of profit. Demonstrate that it is a maximum using second-order condition. (5 marks] iii. Using differential of total revenue function, find the approximate change in total revenue if the level of output increases by 4% from the level obtained in (ii). Comment on the accuracy of your finding. [3 marks] iv. Do you think total profit will increase, if the level of output is increased by 2% from the profit maximising level obtained in part (11)? Briefly explain. [1 mark] (b) Suppose the production function of a firm is given by: Q = 30KL) where Q is weekly output, and K and L are weekly inputs of machine-hours and worker- hours respectively. i. Find marginal product of labour and marginal product of capital when K=125 hours and L=216 hours. [2 marks] il. Using your answers in part (1), find the marginal rate of technical substitution and interpret the results. [2 marks]