Suppose that the production function is ƒ(x1,x2) = (xĩ + x²)º, where a and b are positive constants. For what values of a and b is there a diminishing technical rate of substitution (TRS)?
Q: For the production function Q = 4LK, returns to scale: is decreasing O Can be increasing,…
A: Returns to scale decribes how output changes when inputs change by a certain percentage.
Q: On separate axes, draw typical production isoquants for each of the following production functions.…
A: For Isoquants, we have to take f(x,y)= c a constant
Q: What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = (b)…
A:
Q: For the production functions of (1) and (2) create the isoquants for q = 100, and for q = 144 with K…
A: Isoquant curve represents the influence of all inputs on the level of output.
Q: You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run…
A: “Since you have posted a question with multiple sub-parts, we will provide the solution only to the…
Q: If the production function is F(K,L) = AKºL¹-ª , then the Marginal Rate of Technical substitution…
A: To determine the Marginal Rate of Technical Substitution (MRTS), we have to determine the partial…
Q: Consider the following production function: Q = (6L +3K)¹/2 1. What is the Marginal Product of Labor…
A: The production function gives the value of output that can be produced with given inputs and…
Q: A firm can manufacture a product according to the production function Q = 2(K)1/2 (L)1/2 where K…
A: The marginal productivity of labor can be found by differentiating the production function with…
Q: If the production function is F(K,L) = A * K0.4L0.6 then the Marginal Rate of Technical Substitution…
A: Marginal Rate of Technical Substitution(MRTS) measures the rate at which one input is substituted…
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: You have been hired by Kia as manager for its Pakistan operations. Assume following is the…
A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
Q: 56, K=103, the marginal product of labor is 2 and the marginal product of capital is 2. What is…
A: Marginal rate of technical substitution alludes to the rate at which the inputs are substituted in…
Q: (a) Suppose we have the following production function: Q = min [10 K, L]. Confirm the technology…
A: Returns to scale refers to the proportionate change in output scale when the input levels are…
Q: In this typical production function, where output is increasing at a decreasing rate and has a slope…
A: The markets are the place where the buyers, and sellers of different commodities meet and interact…
Q: Let c(x) be the cost of producing a product of x units. Given that c(x) follows the experience cost…
A: Experience curve is the known as Henderson's law which states that more the firm produces , firm…
Q: Suppose that a firm has the following production function Q(K,L) = AKL² – BL³ where K represents…
A: Given: The production function of a firm- Q (K, L) = AKL2 - BL3 A company has- 1200 units of capital…
Q: Assume the production function is given by: f(x1, x2) = (2x9.253.5)3. What is the absolute value of…
A: Production refers to the process of using inputs to make useful output. The functional relationship…
Q: Consider the following production functions F(L,K)=LK^3 F(L,K)=L+3K (a) Discuss if each marginal…
A: (a) MPL = ∂Q/∂L = K3 So, MPL is independent of L and is constant. MPK = ∂Q/∂K = 3LK2 So, as K…
Q: For the production function Q = L² +0.5K², returns to scale: O is constant O Can be increasing,…
A: Return to Scale:Return to scale refers to the effect on output or production when all inputs are…
Q: Suppose the production function for a firm is given by: q=4L0.5K0.25, If the firm currently has 20…
A: The production function describes the correlation between inputs and outputs(q) in the production…
Q: If the production function is F(K, L) = AKL¹-a then the Marginal Rate of Technical substitution does…
A: Production function: The marginal rate of technical substitution between input L and K is the rate…
Q: Consider the case of a firm which produces q units of a single output using two inputs, labour (L)…
A: An isoquant refers to that combinations of inputs which provide same level of output . Slope of an…
Q: Suppose Honda operates a car engine manufacturing plant in Canada and one in Mexico. Suppose further…
A: Given,The production function of Honda's car engine manufacturing unit in Canada is The production…
Q: • Consider a production function f(r1, 12) = min{r1, 12}: When r1 < r2, please calculate the…
A: the marginal product or marginal physical productivity of an input is the change in output resulting…
Q: d) Given that Rock star’s cost function is TC(Q) = 1000 + 50Q². Determine the marginal cost and…
A: According to the question, given that the total cost of production is given by TC(Q) = 1000 + 50Q^2…
Q: Given the production function of F(K,L) = sqrtKL If the short run has a fixed K of 5 units, which…
A: Here the production function of F(K,L)=KL the short run fixed capital k=5 units so, F(K,L)=KL=5L…
Q: A firm faces the production function: q=10L^0.32 K^0.56 (a) What kind of returns to scale does…
A:
Q: *Find the elasticity of scale and the elasticity of substitution for the CES production function…
A: Let the production function be: Q = x1ρ+x2ρ1ρ
Q: For a production function that exhibits diminishing marginal product: From Lourdes N to Everyone:…
A: The study and analysis of commercial barriers impacting businesses using abstract economic concepts…
Q: Problem 1: A firm has the following production function: f(L, M) = min{L, 3M) where L is the number…
A: Returns to scale is an economic concept that explains how the scale of production or the size of a…
Q: For the production function y = 2x1 + 3x2, What is the Technical Rate of Substitution? (Remember the…
A: The marginal rate of technological substitution (MRTS) is an economic theory that defines the rate…
Q: Assume the production function is given by: f(x1, x2) = (2x9.253.r5)³. What is the absolute value of…
A: A production function is a mathematical relationship between the physical output of a production…
Q: Write the technical rate of substitution expression for f(x1, x2) = (x1 - 1)0.25 x20.5
A: The marginal rate of technical substitution (MRTS) is an concept that explains the rate by which one…
Q: The production function has the following form q= K + 2L where q is output, K is capital input and L…
A: Answer: Given, Production function: q=K+2Lw=5v=2q=6 units The following condition must satisfy to…
Q: For the production function Q = 16L + 0.2K, returns to scale: O is decreasing can be increasing,…
A: Production function states the relationship between the input and output of goods in production by a…
Q: (a) For the cost function C(w₁, W2, y) 2y ww, calculate the Allen elasticity of substitution between…
A: The purpose of this question is to determine if the market is in its long-run equilibrium, consider…
Q: Suppose that a firm's estimated production Q = K3/4L1/4 What is the marginal rate of technical…
A: Marginal rate of technical substitution refers to the ratio of marginal product of labour and…
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: The Constant Elasticity of Substitution (CES) production function is a flexible way to describe how…
A: (A)Given, that the question states that the firm's objective is to maximise the present discounted…
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
- Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.Suppose a production function is given by the equation Q = LVK. 1. Graph the isoquants corresponding to Q = 10, and Q = 20. 2. MP = √K and MP = 0.5(L/VK). Find the Marginal Rate of Technical Substitution LK (MRTSLK). Do these isoquants exhibit diminishing marginal rates of technical substitution? (Does the slope get flatter as L increases?) 3. The cost of labor is w = $5 per labor hour and the cost of capital is r = $15 per machine hour. What is the equation of the $1500 iso-cost curve?Juan 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?
- Q2) Consider the following production function TPL = 12L2 – 0.8L3 Determine the marginal product function(MPL) Determine the average product function (APL) Find the value of L that maximizes TPL Find the value of L that maximizes APL Find the value of L that maximizes MPLConsider the following production function: f (A, B) = gamma multiply A^alpha multiply B^Beta. where A and B are the inputs and alpha, Beta, gamma are in the set (0,1). Let wA and wB the price of the two inputs. Assume wA, wB > 0. Is the production function separable?Does the production function exhibit constant returns of scale?Compute the cost function and the conditional input demand function.How do these three functions react to a change in wA? Suppose the price of both inputs double, what happens to the conditional input demand function? And to the cost function? Suppose the desired level of output double, what happens to the conditional input demand function? And to the cost function?…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?
- Consider the production function q=√L+8K^(3). Starting from the input combination (3,6), does the production function exhibit increasing, constant or decreasing returns to scale if inputs double?Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True FalseThe marginal product of labour is diminishing when: The marginal product of labour is larger than the average product of labour. The production function is convex. The production function is concave. The second derivative of the production function is negative.
- The Cobb-Douglas production function for a particular product is N(x,y) = 80x0.6.0.4, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40 and each unit of capital costs $60. Answer the questions (A) and (B) below. (A) If $150,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $50,000 is budgeted for the production of the product. C (A) If $150,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. Production will be maximized when using units of labor and units of capital.How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether β is larger than, smaller than, or equal to one?You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L^2 – 0.5L^3 where L is variable input labor, Q is output of Cars assembled a. Find the ranges of the three stages of production. b. Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above. c. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L^.30K^.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant.…