Hi, I have a question relating to Chapter 4 of the Acted notes for CB2. On page 7 of Ch 4 there is a question about utility of goods X and Y. Part (ii) asks you to calculate the possible combination of goods that would satisfy the optimum combination of goods consumed. Using the prices in the question, I can understand where the logic that the marginal utility of Good Y must be twice of Good X comes from, but I can’t understand where the possible combinations are coming from. I’m possibly missing something simple but would really appreciate a bit of help with this. Thanks!
Hi Lauren, If you're happy with the logic that the marginal utility from the last unit of Good Y needs to be twice the marginal utility from the last unit of Good X, it's then just a case of looking at the marginal utilities for each unit of Good X and identifying the ones for where there does exist a marginal utility for any unit of Good Y that is exactly double. Eg: - the marginal utility of the 1st unit of Good X is 10, but there are no units of Good Y with 2*10 = 20 of marginal utility, so we ignore this option - the marginal utility of the 2nd unit of Good X is 8, but there are no units of Good Y with 2*8= 16 of marginal utility, so we ignore this option - the marginal utility of the 3rd unit of Good X is 7, but there are no units of Good Y with 2*7= 14 of marginal utility, so we ignore this option - the marginal utility of the 4th unit of Good X is 5, and there is a unit of Good Y (the 2nd unit) that has twice as much marginal utility (2*5=10), hence 4X and 2Y is one combination - the marginal utility of the 5th unit of Good X is 4, and there is a unit of Good Y (the 3rd unit) that has twice as much marginal utility (2*4=8), hence 5X and 3Y is one combination - the marginal utility of the 6th unit of Good X is 3, and there is a unit of Good Y (the 4th unit) that has twice as much marginal utility (2*3=6), hence 6X and 4Y is one combination. Thanks, Richie
