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.

Jennifer's utility function is given by U = x + y, where x = food and y = clothing. If her income = $100, price of x = $10 and price of y= $5, find (graphically) her utility maximizing bundle of x and y. If her utility changes to U = 3x + y, how will her utility-maximizing bundle be affected?

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

Two goods are consumed with respective price p_x and p_y. The utility function is given by u(x,y) = Min {2x + y, 2y} Income is 84
Suppose p_x = 3 and p_y = 2
How do I derive the optimal bundle/utility maximizing problem?

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 the 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 u

Mrs. Wilson buys loaves of bread and quarts of milk each week at prices of $1 and 80 cents, respectively. At present she is buying these two products in amount such that the marginal utilities from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying the utility-maximizing combination of

If Fred is on a set salary and can only eat ham and drink tea. He drinks 4 bottles of tea and eats 10 lbs of ham. The price of tea is $10 per bottle and $4 per lb of ham. The last bottle of tea added 50 units to Fred's utility and the last lb of ham added 40 units. Would you consider that Fred was making a utility-maximizing

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 individualĂ˘??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