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2. Suppose there are two goods, labeled x, y. A consumer has a budget of w = 220. Suppose the following two consumption bundles: (x = 4, y = 10), (x = 6, y = 4) all cost the consumer 220.

(a) What’s the price ratio between the two goods? Namely what’s py px ? Show how you obtain this result.

(b) What’s the price level for good x? What’s the price level for good y?

(c) Write out the algebraic expression for this consumer’s budget line

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Related questions

A consumer with the utility function U(X, Y) = [X – 10] Y^(1/2) with an income of $100 to spend on good X (with price $1) and good Y (with price $15).

1 Express this consumer’s utility maximization problem, using the particulars of this problem.

2 Give two conditions that the consumer’s optimal bundle will satisfy, again using the particulars of this problem.

3 Find the two conditions for the consumer’s optimal bundle. Neatly show your work.

4 Find the demand function for good X for a consumer with the given utility function. In other words, resolve this problem only now leaving the prices and income as variables: pX, pY, and m. Neatly show your work.

Suppose that there are two goods (X and Y). The price of X is $2 per unitu, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8Y^.2

Consumer A has an income of $100, and Consumer B has an income of $300.

1. Derive the marginal utlities of goods X and Y for consumer A


2. Derive the marginal utilities of goods X and Y for consumer B


3. Set consumer A's MRS equal to the price ratio. Then use the budget constraint to solve for her optimal bundle


4. Set consumer B's MRS equal to the price ratio. Then use the budget contraint to solve for his optimal consumption bundle.


5. Calculate the MRS for each consumer at their optimal consumption bundles.


6. Suppose that there is another conusmer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's MRS at her optimal consumption bundle? Why?


Consider an individual making choices over two goods, x and y with prices px and py, and who has income:

Suppose that, as a result of changes in the individual'­s economic circumstances, the budget line rotates outward, with the vertical (good y) intercept remaining unchanged but the horizontal (good x) intercept shifting to the right. Explain how this could have happened if the price of good x did not change?

If the individual'­s utility function is u(x; y) = x 2 + 4y 2 , are these preferences convex? Are they monotonic? Explain.

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