Question: An individual has the utility function, U(X, Y) = 0.5log(X) + log(Y). Let her income be I > 0 and the prices of goods X

An individual has the utility function, U(X, Y) = 0.5log(X) + log(Y). Let her income be I > 0 and the prices of goods X and Y be Px > and Py > 0.

(a) Determine whether her utility function exhibits increasing, diminishing, or constant marginal rate of substitution.

(b) Prove that her expenditure function is homogenous of degree 1 in prices.

(c) Suppose the price of X increased by 20% but the price of Y decreased by 50%. By what percentage and in which direction should her income change to make her as well off as she was before the change in prices? [Note: DON'T choose numbers for Px and Py].

Step by Step Solution

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!

Economics of Public Expenditures Problem 4: Coase Theorem. A rusty old railroad shoots sparks when used by trains. The sparks occasionally start res in a nearby eld of wheat, destroying a farmer's...

I'm having a hard time with this question, thanks for helping. An individual has the utility function u = min (x, y). His income is $ 12. Initially, the prices were px = 4 and py = 1, and the...

Slutsky.Consider a consumer with utility function U ( x , y ) = 2 xy . Her income is I = 1 5 , andprices are given by px = 2 , and py = 3 . Address the following questions:a ) Find the demand...

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...

Solve this problem on paper, as usual, but you will also submit the numerical answer from part (a) in the space at the bottom of the question. Suppose Cody has utility function U (x, y) = avi + By...

Hi tutor. Kindly help me solve these I1 Exercise 2. Let f: R" + R be a real-valued function on R", and Xo = E R a In point. (a) If f is differentiable at Xo, explain what it means to say that the...

Suppose that a small economy's production possibility frontier for oil (X) and food (Y) is given by the equation X2 + Y2 = 3200. a) Sketch this PPF in a diagram. Write down an expression for the...

Intermediate Microeconomics PROBLEM 2: Theory of Demand Randy chooses between two goods, x and y , with prices p x and p y , respectively. He has an income I and his preferences are represented by...

Mira chooses between two goods, x and y, with prices p x and p y , respectively. She has an income I and her preferences are represented by the utility function U (x, y) =x + y. Assuming that an...

Under what circumstances might inventory turnover be too high? That is, what possible negative consequences might occur?

Draw a scatter diagram of the interest rate and the unemployment rate. Describe the relationship.

Problem 8 - 1 4 Stock Valuation [ LO 1 ] Avacado Farms just paid a dividend of $ 3 . 5 5 on its stock. The growth rate in dividends is expected to be a constant 6 percent per year indefinitely....

Problem 3: Find the PV of a bi-annual perpetuity in which you receive $1000 each odd year starting at t=9 (i.e., at t=7, 9, 11, ..) if EAR is 9%

8. Property developers who build shopping malls like to have them anchored with the outlets of one or more famous national retail chains, like Target or Nordstrom. Having such anchors is obviously...

4. In an oligopoly, each firms share of the total market is typically determined by: LO14.4 a. Scarcity and competition. b. Kinked-demand curves and payoff matrices. c. Homogeneous products and...

5. Some analysts consider oligopolies to be potentially less efficient than monopoly firms because at least monopoly firms tend to be regulated. Arguments in favor of a more benign view of...