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2. A different firm has this daily production function. Assume that capital is fixed at 8...
the second question
In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4) Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing (Round responses to two decimal places.) The MPK at 5 units of capital is 156.12 The MP at 6 units of capital is 144.02 The MP at 50 units of labor is 8.84 The MP...
Find all the first and second-partial derivatives for the utility function, U -50x 5y 0.2 (a) Give a verbal description of each derivative. (b) Are the marginal functions increasing or decreasing. Use the derivatives to justify your answer b. Given the function Q- Al'KB, explain the terms: constant returns to scale; increasing returns to scale; decreasing returns to scale. Show that the production function, Q -100L0.3K0.5, exhibits decreasing returns to scale and diminishing returns to labour Show that the production...
The production function 9 = k1.270.5 exhibits: a. increasing returns to scale but no diminishing marginal productivities. b. decreasing returns to scale. C. increasing returns to scale and diminishing marginal product for / only. d. increasing returns to scale and diminishing marginal products for both k and I.
The production function q = k0.620.5 exhibits: a. increasing returns to scale and diminishing marginal products for both k and 1. b. increasing returns to scale and diminishing marginal product for 1 only. c. increasing returns to scale but no diminishing marginal productivities. d. decreasing returns to scale.
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution. Then answer the following for each: does this production function exhibit diminishing marginal product of labour? Does this production function exhibit diminishing marginal product of capital? Does this production function exhibit constant, decreasing, or increasing returns to scale? Show all your work.(a) \(Q=L+K\)(b) \(Q=2 L^{2}+K^{2}\)(c) \(Q=L^{1 / 2} K^{1 / 2}\)
Consider the production function below. ?? ?(?, ?) = ?? + ?? a) Find the demand for labor and capital b) Draw the demand curve for labor c) Does the production function exhibit diminishing marginal returns of labor? d) Is the production function exhibiting increasing, constant or decreasing returns to scale?
2. Consider a firm with the following production function: Q = 3K2/3L2/3 2a. Calculate the marginal product of labor. Show all work. 2b. Is the marginal product of labor increasing, decreasing or constant? Explain how you know. 2c. Calculate the output elasticity of labor. Show all work. 2d. Does the production process for this firm exhibit increasing returns to scale, decreasing returns to scale or constant returns to scale? Explain how you know.
Consider the following production function: Q = 55⋅K2/3L4/3 A. Determine whether this production function has increasing, decreasing, or constant returns to scale. Explain and show your work. B. Does this production function obey the law of diminishing marginal product in labor? Explain and show your work.
2. Suppose the firm has the one variable production function Q=L?. Assume that the wage rate is w= 20 and that the firm has fixed costs of 10. Finally, assume that the firm is a price taker and the market price is 2. a) Show that this production function exhibits increasing returns to scale. Show that the marginal product of labor is increasing. Illustrate the production function. Is it convex, concave or neither? b) Find the variable and total cost...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...