1. Derive the indirect utility function as a function of px, py and M, where px and py
are respectively the prices of the two goods x and y, and where M is the consumer's
income.

2. Now calculate the level consumption of both goods and the level of utility achieved
by this consumer if prices and income are as follows: px = 2; py = 3 ;M = 9

3. Now set up the dual of this problem: minimize expenditure subject to the level of
utility that you calculated in part 2 and with prices px and py. Find the expression
for the expenditure function.

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Let

1. Derive the indirect utility function as a function of px, py and M, where px and py
are respectively the prices of the two goods x and y, ...

Solution Summary

Solution provides detailed explanation of how to find utility-maximizing demand for goods given a specific utility function. It also shows how to calculate the expenditure function. While a specific functional form for utility function is used , the steps are detailed enough for a student comfortable with basic calculus to repeat the steps for a different utility function.

1. Using Indifference Curve and Budget Line analysis, graphically demonstrate the equilibrium of a consumer who is maximizing utility. Briefly explain.
2. Using Indifference Curve and Budget Line analysis, graphically demonstrate how you can derive a demand curve. Briefly explain.
Note: In the above questions, assume a bun

You are choosing between two goods, X and Y, and your marginal utility from each is as shown below. if your income is $9 and the price of X and Y are $2 and $1, respectively,
Units of X Marginal Utility for X
1 10

1) consider a consumer with the following utility function U=f(x,y)=4xy
a) derive demand functions for both commodities.
b) Px=2, Py=2.5, I=40, find the utility maximizing consumption combination.
2) A firm produces two commodities, Q1 and Q2, in pure competition. P1=15 and P2=18. C=2Q1^2 + 2Q1Q2 + 3Q2^2
a) form the prof

5. Use consumer theory (i.e. indifference curves and budget constraints), where the usual assumptions apply, to illustrate the following:
Assume the individualâ??s utility is an increasing function of medical goods (m) and all other goods (X). That is,
Utility =U (m,x) where delta u/delta m >0, delta u/delta x >0 , and

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern Florida. To meet monthly demandfor electricity in these counties, which is represented by the inverse demand function, P = 1000 - 5 Q, the utility company has set up two electric generating facilities: Q â? kilowat

Bridget has a limited income and consumes only wine and cheese; her current consumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is $10 per bottle, and the price of cheese is $4 per pound. The last bottle of wine added 50 units to Bridget's utility, while the last pound of cheese added 40 units.

For this problem, assume that Joe has $80 to spend on books and movies each month and that both goods must be purchased whole (no fractional units). Movies cost $8 each and books cost $20 each. Joe's preferences for movies and books are summarized by the following information:
MOVIES

In your own words, explain the law of demand through the income and substitution effects, using a price increase as a point of departure for your discussion.
Explain the law of demand in terms of diminishing marginal utility.

Let M(U)a = z = 10 - x and M(U)b = z = 21 - 2y, where z is marginal utility per dollar measured in utils, x is the amount spent on product A, and y is the amount spent on product B.
Assume that the consumer has $10 to spend on A and B -- that is, x + y = 10.
How is the $10 best allocated between A and B?
How much utilit