Section 3 Firms and market structures (40 Marks) Assume that a rm has the following (perfect substitutes) production function: Q1. Q2. Q3. Q4. q = 5L + 10K. (a) Calculate output when L = 20 and K = 5. (b) Calculate the marginal product of labour and interpret your answer. (0) Calculate the marginal product of capital and interpret your answer. (d) Calculate the marginal rate of technical substitution (MRTS) and interpret your answer. (e) If the wage and rental rates are given by: w = r = $20 then what combination of capital and labour would produce output of q = 100 the cheapest? Assume that a rm has the following short run cost function; C(q) = 1001:;r + 3:.)2 +75. (a) (b) (0) (d) (e) Calculate total cost if Output is 10 units. Determine the short run xed and variable cost functions. Determine the average, average variable, and average xed cost functions. Determine the marginal cost function. Calculate the lowest average cost, and associated quantity, that the rm can produce this good for in the short run. Assume that a rm in perfect competition faces the following market price and cost function: p = 12 c = 4 + 2:;2 (a) Derive the rm's revenue function. (b) Derive the rm's marginal revenue and marginal cost functions. (0) Calculate the prot maximising (loss minimising) quantity (q*) for this firm. (d) Calculate this rm's prot based on your answer to (c). (e) Should this rm stay open or shut down in the short run? (i) What would you expect to happen to this rm's prots (losses) in the long run? Explain your answer. Assume that a monopoly rm faces the following prot function: (a) (b) (0) (d) nag) = 4800 302 653 Calculate this rm's xed costs (F). Calculate this rm's prot if it produces 37 units of output, Q = 37. Calculate the prot maximising (loss minimising) quantity (Q') for this rm. Calculate this rm's prot based on your answer to (c)