Production and Costs

Production and Costs explains how a firm turns inputs such as labour and capital into output and what it costs to do so. In this chapter you will study the production function, the distinction between the short run, when at least one factor is fixed, and the long run, when all factors can be varied, and the concepts of total product, average product and marginal product. You will learn the law of variable proportions, or law of diminishing marginal product, with its three phases, and the idea of returns to scale, increasing, constant and decreasing, using the Cobb-Douglas production function. The second half of the chapter deals with costs. You will calculate total fixed cost, total variable cost, total cost, average fixed cost, average variable cost, average cost and marginal cost from schedules, and explain why the AFC curve is a rectangular hyperbola and why the AVC, AC and MC curves are U-shaped. You will also study the relationship between marginal and average cost and the shapes of the long run average and marginal cost curves.

Detailed Worksheet: Production and Costs Section A - Definitions (10 marks) 1. Define the production function. Distinguish between the short run and the long run. (2 marks) 2. Define marginal product of labour and average product of labour. (2 marks) 3. State the law of variable proportions. (2 marks) 4. What are returns to scale? Distinguish between increasing and decreasing returns to scale. (2 marks) 5. Distinguish between fixed costs and variable costs with one example of each. (2 marks) Section B - Calculations and Applications (15 marks) 6. With fixed capital, a firm's total product for 1 to 6 units of labour is 10, 24, 36, 44, 48 and 48. Calculate the MP and AP at each level. Identify the phases of the law of variable proportions. (3 marks) 7. The production function of a firm is q = 5 L^0.5 K^0.5. Calculate output when L = 16 and K = 25. What type of returns to scale does it show? Find output if both inputs are doubled. (3 marks) 8. A firm's total fixed cost is Rs 60 and its total cost for output 0 to 5 units is Rs 60, 90, 110, 120, 140 and 180. Calculate TVC, MC, AVC, AFC and AC for each positive level of output. (3 marks) 9. The production function is q = L^0.6 K^0.6. Find the returns to scale. By what factor does output increase when both inputs are doubled (take 2^1.2 = 2.30)? (3 marks) 10. A firm's AFC is Rs 20 at 10 units of output, and its AVC at 10 units is Rs 15. Calculate TFC, TVC, TC and AC at 10 units, and AFC at 40 units of output. (3 marks) Section C - Diagrams (10 marks) 11. Draw the TP, AP and MP curves on one diagram and mark the three phases of the law of variable proportions. (4 marks) 12. Draw the AFC, AVC, AC and MC curves on one diagram. Show that MC cuts AVC and AC at their minimum points. (3 marks) 13. Draw the TFC, TVC and TC curves. Explain why TC and TVC are parallel. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Explain the reasons for increasing returns to a factor in the first phase and diminishing returns in the second phase of the law of variable proportions. Why does a rational producer operate only in the second phase? (5 marks) 15. Explain the relationship between (i) MP and AP, (ii) MC and AC and (iii) TP and MP, with diagrams. Why is the AC curve U-shaped in the short run? (5 marks) 16. Distinguish between the law of variable proportions and returns to scale. Explain an isoquant and why it slopes downward. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Show schedules and working in calculations. Draw neat, labelled cost and product curves.