A firm produces its product using only labor. Its production function is Q= 20L -L, where Qis the number of units of output produced and Lis the number of labor hours used.The firm purchases labor in a competitive labor market at the going wage rate of w = $12 per hour. The firm sells its output in a competitive market at the market price of P= $5.To maximize profit, the firm should usehours of labor and produceunits of output. (Enter your responses rounded to two decimal places.)

Given information- Production function- The wage rate is equal to $12/hour. And the market price is…

Answered: A firm produces its product using only…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Maximizing profit with isoprofit curvesSuppose that you are starting up a lawn-raking business. All of your workers are required to supply their own rakes, so the only cost to you is hiring labor at an hourly rate. Suppose that the market price of raking someone's yard is $24 per lawn and the hourly wage is $18 per hour. The following graph shows the production function (PF) for your business.
Suppose a firm uses a single input to produce a single output according to a production function f(x) = 10√x where x is the number of units of input. The output initially sells for £120 per unit. The input costs £20 per unit. A change in the market causes the product price to increase from £120 per unit to £200 per unit, all else equal. How does this change in product price affect the firm's profit maximizing level of profits? a. Profits increase by £16,000 Ob. Profits do not change Profits increase by £8,000 d. None of the other answers is correct Profits increase by £9,000 f. Profits increase by £18,000 g. Profits increase by £50,000 h. Profits increase by £32,000 C. e.
A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. The production function is given by: Q=60L-2L^2+180K-3K^2, where Q is total output. Determine the firm's optimal combination of capital (K) and labor (L)?
B. Suppose that your production process is characterized by the production function x = f(e) = 100 In ( + 1). For purposes of this problem, assume w > 1 and p > 0.01. a. Set up your profit-maximization problem. b. Derive the labor demand function. C. The labor demand curve is the inverse of the labor demand function with p held fixed. Can you demonstrate what happens to this labor demand curve when p changes? d. Derive the output supply function. e. The supply curve is the inverse of the supply function with w held fixed. What happens to this supply curve as w changes? (Hint: Recall that In x = y implies e' = x, where e ≈ 2.7183 is the base of the natural log.) f. Suppose p = 2 and w profit will you make? = 10. What is your profit-maximizing production plan, and how much
Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K¹/2 [1/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.
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
XYZ Co. operates in a competitive market. Its production function is q = L^α K^β . The firm takes the wage, rental rate and price as given. a) Derive the firm's conditional labor and capital demand functions. b) How does the firm react to an increase in the wage rate? c) Derive the firm's cost function.
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.
Lesson 8 - Costs Question 8
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Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short run. Calculate the factor demand function Given the product price (P) is 6 and the price of factor 1 (w1) is 12, calculate the optimum amount of factor 1. Show your results on a graph.
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

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