The budget line implies that if Susan spent all her income on clothing she would be able to purchase OB units of it. If on the other hand, Susan spent all her income on food, she would be able to purchase OA units of food. If she allocates her income on both goods then all combinations of food and clothing she can attain are those on or within the line AB. Thus the triangle OAB defines the combinations of food and clothing attainable by Susan, given her income and the prices of food and clothing.
Assuming that Susan is rational, and the law of diminishing marginal utility holds for both goods, and she has continuous and complete preferences, her preferences can be depicted by downward sloping convex indifference curves. Susan’s objective is to attain the highest possible indifference curve within the reach of her budget set. This is shown in figure 2. Figure 2: the utility maximising choice in Adelaide As shown above in figure 2, given her budget constraint, Susan’s utility maximizing choice in Adelaide is point E. She consumes OC of food and OD of clothing and this generates the level of utility denoted by the indifference curve IC1. Linda is aware that in Melbourne the prices of both goods are higher and that food is relatively more expensive than clothing compared to the situation in Adelaide. Therefore, with her present income (that she earns by working in Adelaide) Susan will be able to by lesser of both food and clothing. Additionally, because food is relatively more expensive, not only she will be able to buy less of food if she invests all her income in food compared to the amount of food she would be able to buy in Adelaide, the reduction in the amount of food she can buy will be more than the reduction in the amount of clothing she will be able to buy. What this implies is that i) her budget line will shrink inwards and ii) it will be relatively more flat compared to her budget line in Adelaide. This is depicted in figure 3. Figure 3: FG - Susan's budget line in Melbourne if her income remains equal to her Adelaide income In the diagram above, FG is Susan’s budget line in Melbourne if her income remains unchanged. Observe that not only can she buy fewer amounts of either products, the reduction in her capacity to purchase clothing had she chosen to invest all her income in clothing, depicted by the amount GB in the figure above, is less than the reduction in the amount of food she can buy if she invests all her income in food, AF. This is implied by the fact that food is relatively more expensive than clothing in Melbourne. Figure 4: Susan's new budget set relative to her old preferred bundle and utility level. Therefore, as reflected in figure 4, Susan can no longer access the utility level denoted by the indifference curve IC1 and nor can she afford the commodity bundle she preferred when she was in Adelaide. Therefore her real income will fall if she has to move to Melbourne but her income is still as it was back in Adelaide. Linda, if she has to make sure Susan accepts the offer, will have to pay her enough to ensure that her real income is at least as high as it is presently in Adelaide. There are two possible ways of achieving this. I. If Susan is paid an income so that she can purchase a commodity bundle that places her again at the utility level IC1. This implies paying her an income over her present Adelaide income that will allow her to access her old indifference curve IC1. This would be what is termed as the Hicksian compensation. The idea is that Susan will be back at her old real income level if she has access to her old utility level. Figure 5: The Hicksian Compensation - PQ