For each product X and Y, you have data given and you need to calculate the data that is not there so you can calculate maximum utility per dollar spent.

For each quantity (Q) you need total utility (TU), marginal utility (MU), and marginal utility over the price (MU/P). After you have these numbers in a table, go one by one to decide how to choose between consuming X and Y, given the prices, budget and marginal utility numbers provided.

Once you know how many X's you will buy at the first price, then change the price and see you many you will buy. Given 2 prices and 2 quantities demanded at those prices, if you plot them on a graph and connect the two point, you have a straight line demand curve.

Problem Set Utility Theory and the Theory of Demand Product X Product Y Total Income =$12 Price X=$2 Price Y=$1 a. Fill in the columns b. How many x and how many y would the rational consumer purchase? c. Prove your answer using the Equal Marginal Utility Principle d. Select three different combinations of x and y that are different from your answer to (B). and prove that the total utility from those combinations does not equal the utility maximizing combination that you show. e) Suppose the price of Product x decreases to $1. Answer b,c,d from above again. f) Derive the demand curve for Product x