1 Problems on theory of production (Chapter 6) 1. A Company has an assembly line of fixed size A. Total output is a function of the number of workers as shown in the following schedule: No. of Workers (L) Total Output (Q) 0 0 1 10 2 30 3 50 4 56 5 59 6 60 7 60 8 58 (a) Determine schedules for marginal productivity of labor and average productivity of labor. (b) Determine the rage of employment that show the three stages of production (c) Indicate the level of employment at which the law of diminishing returns first occurs. (d) Suppose the market price of the output $15 and the wage rate is $90, how many workers would this firm hire? What if the market price decreases to $10? (e) Suppose the market price increases to $25, what is the highest wage rate the firm would be willing to pay to employ 4 units of labour? 2. A certain production process employs two inputs ⎯ labor (L) and raw materials (R). Output (Q) is a function of these two inputs and is given by the following relationship: Q = 6L 2 R 2 − .10L 3 R 3 Assume that raw materials (input R) are fixed at 10 units. (a) Determine the total product function (TP L ) for input L. (b) Determine the marginal product function for input L. (c) Determine the average product function for input L. (d) Find the number of units of input L that maximizes the total product function. (e) Find the number of units of input L that maximizes the marginal product function. (f) Find the number of units of input L that maximizes the average product function. (g) Determine the boundaries for the three stages of production. 3. Indicate whether each of the following statements is true or false. (a) If the marginal product of capital increases as capital usage grows, the returns to capital are decreasing. (b) Marginal revenue product measures the output gained through expanding input usage. (c) Increasing returns to scale and declining average costs are indicated when ε Q > 1. (d) When the law of diminishing returns takes effect, a firm's average product will start to decline.
2 (e) Decreasing returns to scale occurs when a firm has to increase all inputs at an increasing rate to maintain a constant rate of increase in its output. (f) stage I of the production process ends at the point where the law of diminishing returns
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