Answer true or false to the following: If adding a unit of labor increases output (q) then AP must be increasing [Select] If MP is greater than AP then AP is decreasing [Select] If output (q) is at its maximum then MP=0 [Select] 4
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![Answer true or false to the following:
If adding a unit of labor increases output (q) then AP must be increasing
[Select]
If MP is greater than AP then AP is decreasing [Select]
If output (q) is at its maximum then MP=0 [Select]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa11c203b-6b40-4f2b-8057-ba60f0bdfa13%2F09078e39-722a-4828-ba8f-5efc1c7a2dce%2Fieh8rgj_processed.png&w=3840&q=75)
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- 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?Suppose a soap-manufacturing production process is described by the following equation: Y = a + b log K + с log L Where, Y= Output (number of soaps produced) K=Capital L=Labor a, b and c are constants Suppose 0<a<1, 0< b<1 a. Find the Marginal Product of Labor (MPL) and Marginal Product of Capital (MPK) in the production of soap b. Is MPL diminishing, increasing or constant as L increases? c. Is MPK diminishing, increasing or constant as K increases?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?
- Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. Draw isoquants for q = 1, q = 2 and q = 3 on a diagram with labour on horizontal axisand wool on vertical axis.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?Suppose a firm is planning to replace a labor intensive production process with an automated robot production line. Calculate the marginal rate of technical substitution (MRTS) using the following information. Labor Intensive Production: 24 workers / 3 machines Automated Robot Production: 10 workers / 30 machines Assume both production process can produce the same level of output.
- Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. Draw an expansion path on a diagram and derive an expression for the expansion path. How does it depend on the wage and the price of wool?Suppose the productionfunction is given by Q = 5K + 3L. What is the average product of capital when10 units of capital and 10 units of labor are employed? 5 8 3 30Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?
- A firm can manufacture a product according to the production function Q = F(K, L) = K3/4 L1/4 a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. How does the average product of labor change when the firm uses 256 units of labor? b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units. Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor. c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at $50 per unit of labor, how many units of labor should the firm hire in order to maximize profitWe can describe inputs as either fixed or variable. Thinking about a company that assembles cars, which of the following would be an example of a fixed input that could not be changed in the short run? Group of answer choices A)The robots that help assemble the cars. B)The building where the assembly takes place. C)The electricity required to support the assembly activity. D)The employees that work for the company.Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q=min{L/3, K0.5}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q = 2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. = $5 per kg. b) Let the price of labour-hour be given by w = $18 and the price of fruit by p What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of kiwi?
