Question: Suppose that a consumer's utility function for two goods ( X and Y ) is U(X,Y)=10X^0.5+2Y The price of good X is $5 per unit

Suppose that a consumer's utility function for two goods (X and Y) is U(X,Y)=10X^0.5+2Y

The price of good X is $5 per unit and the price of good Y is $10 per unit. Suppose that the consumer must have 80 units of utility and wants to achieve this level of utility with the lowest possible expenditure.

a.HOW TO make a statement of the constrained optimization problem.

b.Use a Lagrangian to solve the expenditure-minimization problem.

c.Plot the utility (at U(X,Y) = 80) and budget constraint for this problem at the optimum.

Check your answer by solving the same problem as a utility maximization problem.

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!

Suppose that a consumers utility function for two goods (X and Y) is U(X,Y) = 10X0.5 + 2Y The price of good X is $5 per unit and the price of good Y is $10 per unit. Suppose that the consumer must...

3. Suppose a consumer has the following utility function from two goods, x and y:U(x,y)=x0.25y0.75. (a) Suppose the price of goodx is 10 and the price of goody is 15 . What is the utility-maximizing...

E x pl ainan s w ers f or t h ese q u es t i o n s : Answer all: Problem set 1: Preferences and Utility Exercise 1: Suppose the utility function for two goods, X and Y, has the Cobb-Douglas form...

3. Suppose a consumer has the following utility function from two goods, x and y: U(x, y) = x0.25 0.75 (a) Suppose the price of good x is 10 and the price of good y is 15. What is the...

Suppose the utility function for two goods, X and Y, has the Cobb-Douglas utility form: U(X; Y ) = pXY a. Graph the U = 10 indierence curve associated with this utility function. b. If X = 5; what...

The Calculus of Utility Maximization and Expenditure Minimization End of Appendix Problem Suppose that a consumer's utility function for two goods, X and Y , is U ( X , Y ) = 1 0 8 0 . 5 + 2 Y The...

3. \{This problem is based on the exercise that I did in class to explain the income and substitution effects of a price rise and the COLA (cost of living adjustment for social security) application....

5. Suppose that a consumers utility function for two goods (X and Y) is U(X,Y) = 10X 0.5 + 2Y The price of good X is $5 per unit and the price of good Y is $10 per unit. Suppose that the consumer...

Suppose that a consumer's utility function for two goods, X and Y , is U ( X , Y ) = 1 0 8 0 . 5 + 2 Y The price of good X is $ 5 per unit and the price of good Y is $ 1 0 per unit. Suppose that the...

Wilson Wonders bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10 percent. The bonds sell at a price of $850....

What are the two main types of diagrams in UML?

2 Copy and complete this list of powers of 3. Power 3 Number 33 31 32 33 34 35 36 3 27 37 38 2187

what are the strategies for deciding which form of business is ((Alphabet eyes new frontiers -harvard business school 9-717-418 case))?please explain thanks 1.capital what is the best source of start...

3. Choose a social incident in your local area. (a) List three points that you believe are the cause of the social incident and develop a model that shows a linear relationship. (b) What is the...

Peoples understanding of what is being said

5. Develop a circular model, with positive and negative feedback loops, showing the relationships between the following critical variables: The population of a city Industrialization Relocation ...