A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1 - a units turn out to be defective, where 1 > 1 - only a fraction a of purchased units of input 1 actually contributes to producing output y. Let x₁ and x₂ be the quantities that are not defective and can be employed towar production. If rounding is needed, please round your answers to 3 decimal places. Suppose the firm's production function is such that x₁ and x₂ are perfect substitutes: each unit of output can be made with either one unit of x₁ or units of x₂. Suppose W₂ = 9. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a > Suppose the firm's production function is such that x₁ and x₂ are perfect complements: the firm needs 1 unit of x₁ and 4 units of x₂ to make each unit of output. Find the producing 3 units of output when w₁ = W₂ = 1 and a = 0.7.

A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1 - a units turn out to be defective, where 1 > 1 - only a fraction a of purchased units of input 1 actually contributes to producing output y. Let x₁ and x₂ be the quantities that are not defective and can be employed towar production. If rounding is needed, please round your answers to 3 decimal places. Suppose the firm's production function is such that x₁ and x₂ are perfect substitutes: each unit of output can be made with either one unit of x₁ or units of x₂. Suppose W₂ = 9. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a > Suppose the firm's production function is such that x₁ and x₂ are perfect complements: the firm needs 1 unit of x₁ and 4 units of x₂ to make each unit of output. Find the producing 3 units of output when w₁ = W₂ = 1 and a = 0.7.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.7P

See similar textbooks

Similar questions

b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L and K can vary with production. Compute the input demand functions as a function of Q. (4 Points) c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. At what prices of textile will the producer shut down production. (3 Points) d Now suppose Q = 10LK. The market prices of inputs are as in subpart (b) above. Compute the input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)
Suppose that a firm’s production technology is described by theproduction function f(x1, x2) = (x1)^2x2, where x1 denotes the quantity ofinput 1 and x2 denotes the quantity of input 2. Let the price of input 1 be$1 and the price of input 2 be $4.a. Derive the conditional input demand functions for bothinputs.b. Derive the firm’s cost function
Given the production function y 1/x05, if Price of output is P and price of input X is V and fixed cost is FC, what is the expression for marginal cost (MC) as a function of Y? O MC = Vy0.5 O MC = -2Vy-3 O MC = Vy-0.5 O MC = y/V
A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.
Problem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…
1. The total cost of producing a quantity q is C(q). The average cost a(q) is given in figure below. The following rule is used by economists to determine the marginal cost C'(q0), for any qo: Construct the tangent line ti to a(q) at qo. Let t, be the line with the same vertical intercept as t, but with twice the slope of t, . Then C'(q0), is the vertical distance shown in figure below. Explain why this rule works. $/unit a(q) t2 t1 C'(qo)
1. Pekan Nenas has 20 competitive pineapple orchards, all of which sell pineapples at the world price of RM2 per pineapple. The following equations describe the production function and the marginal product of labor in each orchard: where Q is the number of pineapples produced in a day, L is the number of workers, and MPL is the marginal product of labor. (a) (b) (c) Q = 100L - L² MPL = 100 - 2L, (d) What is each orchard's labor demand as a function of the daily wage W? What is the market's labor demand? Pekan Nenas has 200 workers who supply their labor inelastically. Solve for the wage W. How many workers does each orchard hire? How much profit does each orchard owner make? Calculate what happens to the income of workers and orchard owners if the world price doubles to RM4 per pineapple. Now suppose that the price is back at RM2 per pineapple but a flood destroys half the orchards. Calculate how the flood affects the income of each worker and of each remaining orchard owner. What…
2. A firm combines two inputs 21 and 22 to produce an output y. The prices of the two inputs are wi and w2, while the price of output is p. To produce an amount of output equal to y, the firm spends the following amount (which depends on the input prices): () () 248 + . Is it possible that the firm is minimizing cost when producing q? Explain C (w₁, W2, y) = (y) ats 48 A (w₁) ars. (W₂) a+s . If the answer to the previous question is positive, can you compute the conditional input demand functions? • How do your previous answers change if w₁ and we simultaneously double?
Q.No.3. Consider the production function: (3) Y = 0.75X + 0.0042X2 – 0.000023X3 (a) At what level of X, the output will be maximum? (b) If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?
dien There are two factors in a production function y = x 113 x₂¹1³. The market price of each unit ofy is p=3, and the factor prices are w₁=1 and W₂=2 for x₁ and X₂ respectively. variable (a). Calculate your cost function as a function of y if X, and x₂ are both barible factors. (b). Now derive the functions of average and marginal cost and plot them against quantity (C). Solve for your optional output of y. Calculate the ratio of two factors (X₁/X₂) (d). In the short run the fixed factor is set at X₂=1. What is the new optimal output level now?
The table below presents the output and input levels: K L Q 2 2 1 100 2 2 200 2 3 250 2 4 270 Also assume that the per unit cost of capital is $10. Since the firm has two units of capital, the firm's total fixed cost is $20. Also assume that the cost of each unit of labor is $50. What is the marginal cost when four units of labor (L) are employed?
If a perfectly competitive firm which produces two commodities, has the cost function C = 2Q² + 2Q³ where Q1 and Q2 denote the production level of commodity 1 and commodity 2 respectively. (Note: There are 3 questions in the test regarding the information given above) Which of the following is Hessian determinant of the above problem O a. H|=-16 O b. H|=14 Oc. H|=16 O d. H=-14