8. If a firm has a production function of the form: Q = L0.5 K2, what can we conclude? (a) The firm has a quasi-concave production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (b) The firm has a quasi-concave production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. (c) The firm has a convex production function and will experience increasing marginal returns to labour and increasing marginal returns to capital. (d) The firm has a convex production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (e) The firm has a linear production function and will experience decreasing marginal

8. If a firm has a production function of the form: Q = L0.5 K2, what can we conclude? (a) The firm has a quasi-concave production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (b) The firm has a quasi-concave production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. (c) The firm has a convex production function and will experience increasing marginal returns to labour and increasing marginal returns to capital. (d) The firm has a convex production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (e) The firm has a linear production function and will experience decreasing marginal

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.14P

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If a firm has a production function of the form: Q = LK³, what can we conclude? The firm has convex production function and will experience constant marginal returns to labour and increasing marginal returns to capital. The firm has a linear production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. The firm has a quasi-concave production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. The firm has a convex production function and will experience increasing marginal returns to labour and increasing marginal returns to capital. The firm has a quasi-concave production function and will experience constant marginal returns to labour and increasing marginal returns to capital.
8. Consider a representative firm that faces a constant returns to scale production function Y = zF(K, Nd), where Y is output of consumption goods, z is TFP, K is physical capital, and Nª is labour input. The amount of capital is assumed to be given and fixed. The production function exhibits a positive marginal product of labour, as well as diminishing returns to labour. The firm seeks to maximize profits. (a) Explain what the profit maximizing condition for the firm is and show the profit maximizing labor demand on the graph with total revenue and total variable cost curves. On another graph show the firm's demand for labour curve and the profit maximizing labor input. (b) Suppose that the government now imposes an output tax Ty < 1 per unit of con- sumption good produced. What is the effect of this tax on the firm's demand for labor? Explain.
1. Suppose firms use two inputs, capital, K, and labour L to produce output. Their production functions are written as a function of K and L: F(K, L). For each of the following production functions, determine i) whether the production function exhibits increasing, decreasing, or constant returns to scale, and ii) if both inputs double, by what factor (how many times) output will increase. (a) F(K,L) = 5K² +3L² (b) F(K,L) = 8K0.4 0.3 (c) F (K, L) = K² (2K³ – L³)
4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
Suppose that firms face the following production function: Q = 10 + L+K+ 2L/2K1/2, This production function exhibits information that is not enough to determine Returns to Scale Constant Returns to Scale Decreasing Returns to Scale Increasing Returns to Scale
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Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α
2. Which of the following production functions with inputs K, L, and H exhibits Constant Returns to Scale (CRS)? (Assume Ā > 0 is a constant) a) Y = AK/2L/2 b) Y = ĀK/2L/3H/4 c) Y = ĀK/2 – L/H d) Y = ĀKL/2H\/2
(2) The general Cobb-Douglas production function for two inputs is given by q = f(k,I) = Ak“1® where 0 0, f; > 0, fx 0 (b) Show that (the elasticity of output with respect to capital) e = a and (the elasticity of output with respect to labor) e = B
A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a) What is the average product of labor, APL, when the level of capital is fixed at 36 units and the firm uses 16 units of labor? (b) What is the marginal product of labor, MPL, when capital is fixed at 36 units? (c) Suppose capital is fixed at 36 units. If the firm can sell its output at a price of $100 per unit of output and can hire labor at $40 per unit of labor, how many units of labor should the firm hire in order to maximize profits?
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 False