Assume a firm has the following short-run production function:\[ q(L) = L + 2L^2 - \frac{1}{3}L^3 \]Given the production function above, answer the following two questions:A) If this firm is going to maximize profits in the short-run by producing a strictly positive level of output $( q > 0 )$, what is the lowest level of labor $( L )$ they would employ?Minimum level of labor = [ ]B) Now suppose the firm must pay each unit of labor $( L )$ a wage of $10 $( w = 10 )$. If this firm is maximizing their profits in the short-run by hiring 4 units of labor $( L = 4 )$, what must be the price $( p )$ that they can charge for each unit of output they produce?Price = [ ] dollars

The change in q(output) due to the change in l(labor) is measured by MPL(marginal product of labor).…

Assume a firm has the following short-run production function: ) they would employ? ), what is the lowest level of labor ( q(L) = L + 2L² 3 Given the production function above, answer the following two questions: A) If this firm is going to maximize profits in the short-run by producing a strictly positive level of output ( Minimum level of labor = ) a wage of $10 ( ), what must be the price ( 9>0 Price = L B) Now suppose the firm must pay each unit a labor ( dollars L - w = 10 3 ). If this firm is maximizing their profits in the short-run by hiring 4 units of labor ( L = 4 L Р ) that they can charge for each unit of output they produce?

Assume a firm has the following short-run production function: ) they would employ? ), what is the lowest level of labor ( q(L) = L + 2L² 3 Given the production function above, answer the following two questions: A) If this firm is going to maximize profits in the short-run by producing a strictly positive level of output ( Minimum level of labor = ) a wage of $10 ( ), what must be the price ( 9>0 Price = L B) Now suppose the firm must pay each unit a labor ( dollars L - w = 10 3 ). If this firm is maximizing their profits in the short-run by hiring 4 units of labor ( L = 4 L Р ) that they can charge for each unit of output they produce?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…
Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for production. The price of product is $p. The production function is Q (K; L) = 4L^1/4 K^1/4 . Assume that the hourly wage of workers is fixed at $w and the price per machine is $r Write out the optimal inputs quantities, L and K, as a function of parameters, p, w, and r
A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.
Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?
1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No Yes
Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
Assume that the production function for competitive firm is given by F(L)=9L1/3, where L is the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?
The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?
Solve this question on paper.
If a firm has the the production function F(K, L) = min(3K, 4L) What is its contingent demand for labor, Le(w, v, q)? q 4w+3v q (b) 3w+4v (c) 1/31 (d) 1/1 (e) W when w 4v 3
A firm's production function is f(x₁, x₂) = (min{x₁,5x2})¹/². If the price of the first factor is w₁ = 20, then the = 5 and the price of the second factor is w2 supply function is given by y = 9p y = min{5p, 8p} y=p/18 Oy=pmax{w₁, 5w₂}² y = p min{w₁, 5w₂}²