1. Suppose two different bundles of goods cost the same amount of income M. How does this relate to a budget line? Furthermore, suppose there are only two goods, x and y and that the price of x is $4 and the price of y is $2. If the income of the consumer is $20, find two bundles that are affordable and have the same total expenditure. Illustrate this in a graph.

1. Suppose a consumer has income $25 and can spend it in two goods x and y. The price of y is $2 and the price of x is dependent on how many units of x purchased. More specifically, suppose the price of x is px=2x. For example, if the consumer buys one unit of x then the price per unite is px=2 1 = 2 andif the consumer buys two units of x then the price per unit is px = 22 = 4 per unit. Determine the equation for the budget constraint. Illustrate this on a graph

1. Suppose there are two goods the consumer can buy with income M and facing prices px and py. If Income and both prices double, what happens to the budge line? Why? Show this mathematically.

1. Consider a consumer with utility function u(x,y) = xy. Is the bundle (1,1) better than the bundle (0.5,2)? Suppose a consumer now wants to maintain a utility level of 4. What are the bundles of (x,y) that will achieve this objective?

1. Consider a relation R= " is at least as old as." Does this relation satisfy the three axioms if consumer theory