4. Consider the production function f(L, K) = L + K. Suppose the capital is fixed at K = 1. Compute the average product of labor AP, and the marginal product of labor MPL. Draw the two functions on the same graph.
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- 1. A firm can manufacture a product according to the production function Q = F(K,L) = K³/4L¹/4 a. Calculate the average product of labour, when the level of capital is fixed at 16 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 81 units of labour? b. Find an expression for the marginal product of labour when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labour depends on the amount of labour hired by calculating the marginal product of labour for 16 and 81 units of labour. c. Suppose capital is fixed at 16 units. If the firm can sell its output at a price of £100 per unit and can hire labour at £25 per unit, how many units of labour should the firm hire to maximise profits?Suppose the production function is given by 0 = 2K - 5L What is the marginal product of labor when 15 units of capital and 10 units of labor are employed?A firm can manufacture a product according to the production function:Q=F(K,L)=K^(3/4) L^(1/4).a.Calculate the average product of labour, AP_L, when the level of capital is fixed at 81 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 256 units of labour? b.Find an expression for the marginal product of labour, MP_L, when the amount of capital is fixed at 81 units. Then, calculate the marginal product of labour for 16 and 81 units of labour. c.Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit and can hire labour at $50 per unit, how many units of labour should the firm hire in order to maximize profits?
- Suppose a firm’s production function is given by q = 2KL + L , where K is capital and L is labor. What is the average product of labor (APL) when 5 units of capital are employed?A firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?Grease Tech produces oil changes. The production of oil changes reles on both capital (K) and labor (L) and is combined in the following production function F (K, L) = KILL Take the derivative of this production function with respect to capital. What is the marginal product of capital evaluated at (le. just plug in the numbers) 64 units of capital used and 16 units of labor?
- Consider the following production function: Q = (6L + 3K)¹/2 1. What is the Marginal Product of Labor (MPL)? What is the Marginal Product of Capital (MPK)? Are they diminishing? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (MPK)? 3. What is the TRSL,K? Is the absolute value of TRSLK diminishing in L or K? 4. Are there constant, decreasing, or increasing returns to scale?1. Assume that a firm has the following production function: q = L0.5K0.6 d. Determine, both, the marginal product of labour and capital functions (ignore c.). e. Calculate, both, the marginal product of labour and capital when L = 64, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 64, K = 32 and interpret your answer.Underground Sandwiches, a sandwich shop, has the following marginal product curve (labeled MP) for its hourly production. MARGINAL PRODUCT (Sandwiches per worker) 80 72 64 56 48 40 32 24 m 16 B When labor increases from three to four workers, total product increases by 00 18 8 16 Use the orange points (square symbol) to plot the production function on the following graph. Assume that if there are no workers, Underground Sandwiches does not have any output. 0 12 Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. 9 m 2 0 0 O 2 3 LABOR (Workers) 0 O MP QUANTITY OF LABOR (Workers) 5 per hour. Production Function