Question: George has a Cobb-Douglas utility function: U(x, y) = xa y1a where 0 < a < 1. The budget constraint is pxx + pyy =

George has a Cobb-Douglas utility function: U(x, y) = xa y1–a where 0 < a < 1. The budget constraint is pxx + pyy = I.

a. Using marginal utilities, find the formula for the MRS (= – dy/dx). Draw a typical IC.

b. Give the equation for the tangency condition and use it to express y as a function of x.

c. Using your answer in b and the budget constraint, show that the demand functions for x and y (i.e., the expressions for the optimal quantities) are: x^d = aI/px and y^d = (1–a)I/py.

Step by Step Solution

★★★★★

3.54 Rating (144 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Economics Questions!

Beyond the examples in Fig. 14.13, there are other models that can be linearized using transformations. For example, y = 04xe Linearize this model and use it to estimate o4 and B based on the...

A monopoly has a Cobb Douglas production function per hour Q (K, L) = K^1/3 L^1/3. The cost of capital (rent) is $27 per hour and the cost of labor (wage) is $8 per hour. Moreover, this firm has a...

Create an anonymous function for 10e -2x and use it to plot the function over the range 0 x 2.

George has a Cobb-Douglas utility function: U(x, y) = xa y1a where 0 < a < 1. The budget constraint is pxx + pyy = I. a. Using marginal utilities, find the formula for the MRS (= dy/dx). Draw...

UNIVERSITY OF WISCONSIN-MADISON DEPARTMENT OF ECONOMICS ECONOMICS 301 - 002 FALL 2021 Problem Set #2 (to be submitted online by 11:59 p.m. CDT Friday, October 15) 1 . A utility maximizing consumer...

b. Derive an expression for this consumer's income consumption curve. Derive an expression for this consumer's price consumption curve for PX . Comment on their similaIities or differences. i. This...

man2 Exercise #1. Annas preferences over consumption bundles (x1,x2) are summarized by the utility function U (x1,x2) = x1 (x2 + 1)2. (a) Derive an algebraic expression for the marginal utility MU1...

Please answer all questions with explanations Consumer Choice Model 1. Elizabeth has the following utility function for goods X and Y: U =X Y. Her income is $300 per unit of time, the price of X...

All the questions Exercise #1. A firm produces output using the technology y = 7 1.000 where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and y denotes the yearly...

2 a) Given utility function U (C; R) = min (C; 2R); daily endowment of time 24h, price and wage pc= w = 1; nd optimal choice of C; relaxation time R and labor supply L. (three numbers, use secrets of...

When a sound is contaminated by another sound near, we say that the sound has

1/19/2017 Principles of Operations Management: Sustainability and Supply Chain Management, Global Edition PRINTED BY: abdelkader.mazouz@aau.ac.ae. Printing is for personal, private use only. No part...

Devise three unique parametric expressions for a circle with a radius of \' r . \' These expressions should originate from the point ( 0 , - r ) and must meet the following conditions: ( a ) Complete...

QUESTION 5 [30 marks] Case Study: Innovation Offshoring: Asia's Emerging Role in Global Innovation Networks Source: www.eastwestcenter.org Most analysts agree that critical ingredients for economic...

1. Gwerrero 24 Aviation 31 Mid-Term Exam 10/18/22 onus (1 Point): Describe the primary means by which adverse yaw is reduced on the Cessna-150/152 and how works: Show all of your work and Pro Bonus...

2. List the Young's modulus, Yield strength(or breaking strength for brittle material), and failure strain for a)steel, b)aluminum alloy,c) glass, d) rubber, and e)Nylon. For strength and failure...

Question 21 and 20. I would appreciate if anyone could tell me, what is the right answer for them, please? 20. [4 points] Rewrite the following method as a generic method public int countIt (int...

During the year land was revalued and the surplus reported as Revaluation surplus; and an asset costing 80,000, written down to 38,000, was sold for 40,000. Identify the cost of any non-current...

Let us consider a more general version of the voluntary public goods game described in the previous question. This game has N players, each of whom can contribute either $10 or nothing to the public...

The table below reports the inflation rate and the annual rate of return on treasury bills in several countries for the years 1984 and 1985. Inflation Rate and Interest Rate for Selected Countries...

This is an example of the game of Chicken. Two teenagers in souped-up cars drive toward each other at great speed. The first one to swerve out of the road is chicken. The best thing that can happen...

A $5000, 5.75% coupon bond has 16 years remaining until maturity. Calculate the bond discount if the required return in the bond market is 6.5% compounded semiannually.

Bond C and Bond D both have a face value of $1000, and each carries a 4.2% coupon. Bond C matures in 3 years and Bond B matures in 23 years. If the prevailing required rate of return in the bond...

Refer to the Why Divide by n - 1 applet. The first applet on the page randomly selects sample of n = 3 from a population in which the standard deviation is = 29.2. a. A sample consisting of n = 3...