(1) Suppose the production function for widgets is given by q = kl-0.8k -0.212 where q is the annual quantity of widgets produced, k is the annual capital input and 1 is the annual labor input. (a) Suppose k=10; Find the average productivity of labor. At what level of labor input does the average productivity reach a maximum? (b) Suppose k-=10; Find the marginal productivity of labor, At what level of labor input does the marginal productivity reach a maximum? Is the average product equal to the marginal product at the point where average product reaches its maximum? Please show it.

Q: The productivity of a certain country with the utilization of x units of labor and y units of…

A: Given, ​f(x,y)=100x0.65y0.35

Q: A firm has the production function, Q=15L^1/3 K^2/3 where ? is output, ? is labour units and ? is…

A: The degree of homogeneity measures the relationship between change in inputs and change in output…

Q: Consider the following production function: q = (KL)ª, where a > 0. Answer the following questions:…

A: Given  Production function: q=KLα where α>0             ............ (1)

Q: P = 21 + 3k? %3D Find the marginal productivity with respect to capital for 4 units c labor and 3…

A: To calculate marginal-productivity of labor we find the partial derivative of P with respect to L.…

Q: iii) Find the ratio of the marginal productivities of two inputs, at L =2 and K = 3 when the…

A: MPL = ∂Q/∂L = 8K - 2L MPK = ∂Q/∂K = 8L - 2K

Q: A firm's production function is given by Q=K²L. The wage rate is w=$10 and the rental rate of…

A: Detailed explanation: (1).Given, Production function = Q = K2Lwe need to produce Q = 27,000 units of…

Q: Suppose the production function is given by Q = 5K - 3L What is the average product of capital when…

A: Economics is a branch of social science that describes and analyzes the behaviors and decisions…

Q: A firm has the following production function: f(x) = ax? – bx³, where x is the only input, a=2 and…

A: The production function is the maximum output that can be produced with the given technology and the…

Q: Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an…

A: The Cobb-Douglas production function is a mathematical equation that represents the relationship…

Q: Suppose a soap-manufacturing production process is described by the following  equation: Y = a + b…

A: The marginal product of labor measures the change in output due to change in labor. Mathematically,…

Q: (2) The general Cobb-Douglas production function for two inputs is given by q = f(k,I) = Ak*7® where…

A: In 1928, Charles Cobb and Paul Douglas claimed that output is determined by the amount of labor and…

Q: Suppose that capital and labour are perfect complements in a one-to-one ratio in a firm's production…

A: For creation of any good or service, we require inputs and such inputs are Known as factor of…

Q: The Cobb - Douglas production function is a classic model from economics used to model output as a…

A: a) Maximize f = 5L0.25C0.75    s.t. 25L + 75C ≤ 80,000    L, C ≥ 0 b)The results for such…

Q: (b) Prove that the per-worker production function has the following properties: f'(k) > 0, lim f'…

A: We know, f(k)≡F(k,1) Where k=K/L,   Y=Lf(k)                    {if f(k)=y} So that:…

Q: Q(K, L) = 4K²L2 Type your answers in all of the blanks and submit The production function of good x…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the…

A: The production function shows the output produced with given resources. Marginal cost is the…

Q: Consider a firm that produces car repairs. All inputs are fixed except the number of workers hired…

A: Marginal Product = Change in Total Product / Change in Number of Workers The marginal product of…

Q: Which of the following equations does not represent a plausible production function?  a. F(K,L) =…

A: Production function, in the study of economics, helps in establishing a relation between maximum…

Q: Production is described by the function f(K, L) = AL0.3K 0.3, A > 0.a. Interpret the exponents of…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: (A) Suppose the production function for T-shirts can be represented as q = L0.5 KO.5. Show that the…

A: Production Function for T-shirts:q=L^0.5*K^0.5 The marginal productivity of labor depicts how the…

Q: A software firm has only two inputs to production: domestic programmers based in the firm's U.K.…

A: A production function states the mathematical link of quantities of production factor and the…

Q: A farmer can produce f(x,y) = 208-√4x² + y² units of produce by utilizing x units of labor and y…

A: To calculate the marginal productivity of labor at a specific point, we can take the partial…

Q: If the production function is Q = 30 + 22L + 44K, what’s the most you can produce with 9 workers (L)…

A: Production function is the explanation of procedure used in producing the goods and services in the…

Q: If a firm’s production function is Y = KαL1-α, show that it can earn at most zero profit. Use this…

A: Production function highlights the relationship between the different combinations of inputs used to…

Q: If a firm has 5 units of capital, 10 units of labor, and the production function is  Q = 4L + 3K…

A: The average product of capital is nothing but the output per unit of capital.

Q: For each of the production functions below, find the marginal products of both inputs, and indicate…

A: A brief introduction to the production function: A production function portrays the functional…

Q: The productivity of a manufacturing company is given approximately by the function f(x, y) = 20x…

A: Given: The production function for a company is: X = units of labor Y = units of capital To Find:…

Q: Which of the production function has diminishing marginal returns to labor? (Choose ONE). O F(K, L)…

A: In economics, a production function is a means of examining the relationship between input and…

Q: Let a firm's production function Q (L)=12L^2-1/20L^3 (i.e. output as TL or the amount of production…

A: It is given that Q (L) =12L2-1/20L3 and  0 ≤ L ≤ 200

Q: If the production function is Q = 30 + 22L + 30K, what's the most you can produce with 5 workers (L)…

A: As given Production Function Q = 30 + 22L + 30K Also K( capital) = 7 units L(workers) = 5

Q: The total number of output obtained per hour (q) is given by q =KT where L is labor input per hour…

A: The average productivity of labor is qL calculating it using the production function and formula:…

Q: A firm can manufacture a product according to the production function Q = F(K, L) = K0.>L0.5. (a)…

A: Q = F(K,L) = K0.5L0.5 K¯ = 36 L ¯ = 16

Q: Consider a production function: x(l, k) = Alªkº. Showing all of your work: (a) Under what conditions…

A: Production function  is Cobb Douglas production function.The marginal product of labor for…

Q: Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a)…

A: The production function for widgets is given by:

Q: If the optimal quantities of labour and capital were employed, then the total output is…

A: The production function is given as: Q = 100L0.5K0.5subject to5L+10K=75or L+2K=15

Q: Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they…

A: The production function of the Cobb-Douglas form is given as The production function for Hannah and…

Q: Does the MRTS of the production functions Q=L,K decrease? In this case, does the marginal product of…

A: Answer -