Consider an economy with 2 firms and a mass 1 of labor input that can be...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider an economy with 2 firms and a mass 1 of labor input that can be allocated to either firm (that is, labor supply is 1 unit for every possible level of the wage rate. This assumption - perfectly inelastic labor supply is a popular one when you want to focus on labor demand. All the qualitative conclusions from the problem will still hold if you assume an upward sloping labor supply curve.). Each firm i=1,2 produces using the production function Y = An (note the use of lowercase letters for firm-specific choices of factor inputs). Assume A₁ > A₂ (you'll need this assumption in (c)). 1. A Planning Problem. Suppose a hypothetical benevolent social planner wants to maximize total output for this economy by choosing how much labor each firm gets. This planner solves the following problem: max An+Ana 11.2 subject to n₁ + n₂ = 1. Solve the planner's problem and find the optimal choices of n₁, 7₂ (hint: it's more direct if you substitute for n₂ using the constraint and solve the unconstrained maximization problem for 7₁, and then solve for n₂=1-₁.). Call these n. n. Calculate the ratio n/n as a function of A₁, A2 only. We'll use this ratio in part (c). 2. A Decentralization of the Planning Problem. Now let's consider how the market economy would allocate resources if it were allowed to function freely. Suppose labor must be hired at a wage w. Each firm i = 1,2 solves the problem max An n₂ 1-0 ww (a) Solve for firm is optimal labor input as a function of w. A, only. (b) Calculate the total demand for labor at the wage rate w. (e) Use Market Clearing in the labor market to obtain the equilibrium wage u as a function of A₁, A₂, a only. Recall that the total mass of labor input is 1. (d) Substitute the market clearing wage back into each firm's labor demand curve to get the equilibrium inputs of labor for each firm ni, ng. How do these compare with ni, n? Provide some intuition for why the market and the planning solution are related in the specific way you find. Consider an economy with 2 firms and a mass 1 of labor input that can be allocated to either firm (that is, labor supply is 1 unit for every possible level of the wage rate. This assumption - perfectly inelastic labor supply is a popular one when you want to focus on labor demand. All the qualitative conclusions from the problem will still hold if you assume an upward sloping labor supply curve.). Each firm i=1,2 produces using the production function Y = An (note the use of lowercase letters for firm-specific choices of factor inputs). Assume A₁ > A₂ (you'll need this assumption in (c)). 1. A Planning Problem. Suppose a hypothetical benevolent social planner wants to maximize total output for this economy by choosing how much labor each firm gets. This planner solves the following problem: max An+Ana 11.2 subject to n₁ + n₂ = 1. Solve the planner's problem and find the optimal choices of n₁, 7₂ (hint: it's more direct if you substitute for n₂ using the constraint and solve the unconstrained maximization problem for 7₁, and then solve for n₂=1-₁.). Call these n. n. Calculate the ratio n/n as a function of A₁, A2 only. We'll use this ratio in part (c). 2. A Decentralization of the Planning Problem. Now let's consider how the market economy would allocate resources if it were allowed to function freely. Suppose labor must be hired at a wage w. Each firm i = 1,2 solves the problem max An n₂ 1-0 ww (a) Solve for firm is optimal labor input as a function of w. A, only. (b) Calculate the total demand for labor at the wage rate w. (e) Use Market Clearing in the labor market to obtain the equilibrium wage u as a function of A₁, A₂, a only. Recall that the total mass of labor input is 1. (d) Substitute the market clearing wage back into each firm's labor demand curve to get the equilibrium inputs of labor for each firm ni, ng. How do these compare with ni, n? Provide some intuition for why the market and the planning solution are related in the specific way you find.
Expert Answer:
Answer rating: 100% (QA)
Question 1 Suppose a hypothetical benevolent social planner wants to maximise total output for this economy by choosing how much labor each firm gets ... View the full answer
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
Students also viewed these economics questions
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
which one is the corresponding Maxwell relationship derived from dH=TdS+VdP a. b, dP ()s - ($)P ()s--(%)r Od. 6P
-
1. Determine the amounts of the missing items, identifying them by letter. Enter all amounts as positive numbers. On Company Off Company 47,440 Letter a. b. C. d. e. f. LA LA tA tA $ 420,320 436,870...
-
Calculate UTX's market value-added (MVA) for each year 2010-2012.
-
From Pillar to Post Starting from a pillar, you run 200 m east (the + x-direction) at an average speed of 5.0 m/s, and then run 280 m west at an average speed of 4.0 m/s to a post. Calculate (a) Your...
-
Pisa Pizza, a seller of frozen pizza, is considering introducing a healthier version of its pizza that will be low in cholesterol and contain no trans fats. The firm expects that sales of the new...
-
What steps to take in planning the litigation?
-
a. Discuss the concept of pyramiding as it applies to this investment situation. b. What is the present margin position (in percent) of Ravi's account? c. Ravi buys the 1,000 shares of RS through his...
-
Terry Barnes, a 35-year-old mother of three young children, visits the healthcare clinic. She reports experiencing increasing bilateral joint pain, especially in her hands, wrists, and knees. She...
-
Calculate the following four reliability coefficients using the Pearson product-moment correlation formula, correlate the scores to determine the reliability coefficient (xx). Show your work. 3....
-
The following circuit consists of 7 identical components with 2 inputs "a" and "b", and 2 outputs "c" and "d". The maximum propagation time from inputs "a" or "b" to outputs "c" or "d" is equal to...
-
How do CIs relate to the specification tree?
-
Cite various Solution Space tools that enable a homeowner to leverage their time, resources, and skills to maintain their lawn.
-
What is AFP?
-
What is IV&V and how is it applied?
-
Describe the Agile Development Model, its characteristics, and shortcomings.
-
Using T accounts, post the following journal entries to the general ledger and calculate ending balances. (Post entries in the order of journal entries presented in the question.) Date Sept. 2 4 10...
-
What are the key dimensions of critical thinking 2. Watch the NBC Learn video on Diet Scams. What types of claims are made in this video Are they valid Elaborate on your responses. Discuss this video...
-
Local Differences in Property Taxes: Since property taxes are set locally in the U.S., they differ across communitieswith different communities therefore facing different taxes on housing capital....
-
Social Security payments to the elderly are adjusted every year in the following way: The government has in the past determined some average bundle of goods consumed by an average elderly person....
-
Consider again the example of grade insurance. Suppose students know whether they are typically A, B,C, D or F students, with A students having a 75% chance of getting an A and a 25%chance of getting...
-
How closely related do you believe language and thought to be? During the production of Chapter 3 in this book, the authors and editors debated whether we should use the word "autistics" or the...
-
When did human language originate?
-
How do children learn language?
Study smarter with the SolutionInn App