ECO206Y1 Lecture Notes - Lecture 2: University Of Petroleum And Energy Studies, One Economy Corporation, Competitive Equilibrium

65 views1 pages

lemonant197

6 Jul 2016

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

1 true one by one by one economy. There is one consumer who only cares about the amount of goods x she consumes. She has 12 units of labor as endowment, and each unit of labor can be directly converted into one unit of good x: find the competitive equilibrium. 2 cobb douglas one by two by one economy. This is usual consumption leisure choice model in eco208. There is only one good x, but it is possible to treat leisure as the other good y. The utility u (x, y) = x y. Use the production functions fy (l) = 12 l and fx (l) = l2: find the competitive equilibrium. 3 complement one by two by one economy. Consider the same economy in the previous question with u (x, y) = min{x, y} and fx (l) = 2 l: find the competitive equilibrium. 4 another simple two by two by two.

Related Questions

Consider the following economy with production. There is a worker endowed with 1 unit of time, which can be allocated either to leisure or labor. There is a firm with a technology that turns a worker’s labor (the complement of his leisure) into bread. That technology satisfies: b(l)=l^(1/2)

Where l∈[0,1] denotes the worker’s labor and b(l) is the amount of bread produced as a function of labor input. The worker’s utility function from labor supplied and bread consumed is: u(l,b) =αln(b)−l,0< α <2

1. What is the set of Pareto optimal allocations in this economy?

2. Provide prices and an allocation that, together, constitute a competitive equilibrium in this economy.

bluecicada109

Consider the one period model with endogenous labor supply we studied in class, where workers (consumers) are born with one unit of labor effort and no physical endowments. The total population of consumers is one. Furthermore, assume that workers have the following lifetime utility function: U(c, l) = ln c + ln l Production takes place by a representative firm that has access to a production technology of the Cobb-Douglas form: Y = AK Î± L 1âÎ± and as usual profits are rebated back to consumers and P = 1. Unlike the model discussed in class, the firm pays (w + Ï ) for every unit of labor time used, Ï > 0 is a unit tax imposed by the government (or some type of regulation). In this manner, the firm pays ÏL to the government and wL to workers. Finally, the government does no collect taxes from workers but only from employers as mentioned above. Government revenue is used to finance spending, G where G does not directly affect the economy. The governmentâs budget constraint is such that: ÏL = G

A. Write down the individualâs problem of utility maximization. Be sure to derive the budget constraint for the problem. Provide economic interpretation for this model.

PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = x^ay^b (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + y^b (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are p_x and p_y respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, p_x = 10 and p_y = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, s_x, is defined as

(p_x x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.

aquamarinescorpion997

ECO206Y1 Lecture Notes - Lecture 2: University Of Petroleum And Energy Studies, One Economy Corporation, Competitive Equilibrium

Document Summary

Get access

Related textbook solutions

Principles of Economics

Principles of Macroeconomics

Principles of Microeconomics

Related Documents

ECO206Y1 Lecture Notes - Lecture 1: Pareto Efficiency, Exchange Economy, Competitive Equilibrium

ECO206Y1 Lecture Notes - Lecture 3: Bargaining Problem, Social Welfare Function, Externality

ECO206Y1 Study Guide - Midterm Guide: Ordinary Income, Slutsky Equation, Lump Sum

Related Questions