in question (c), optimal choice between original budget line and new budget line is (180,160), and in solution, where that point's MRS=1. why?

Consider a consumer who purchases two goods: X and Y. Her preferences can be described by the utility function: U(X,Y) = x9Y8. Her income is $1200, the price per unit of X is $4, and the price per unit of Y is $3. (a) Is this consumer's preference homothetic? Explain. (b) Find out the optimal choice of the consumer. (c) Now suppose that the consumer is issued 2500 ration points and must pay 5 points for each unit of X and 10 points for each unit of Y. These ration points must be paid in addition to the dollar prices indicated. Draw the consumer's new budget set. Recall that the budget set consists of consumption bundles that the consumer can afford. Calculate the new amounts of X and Y she will purchase. Will she be better off, worse off, or equally well off, compared with the solution in (b)? Explain the relation between her MRSx,y at the optimal bundle and the two price ratios (there are two price ratios: one is the dollar price ratio, the other is the ratio implied by the relative ration points). Consider a consumer who purchases two goods: X and Y. Her preferences can be described by the utility function: U(X,Y) = x9Y8. Her income is $1200, the price per unit of X is $4, and the price per unit of Y is $3. (a) Is this consumer's preference homothetic? Explain. (b) Find out the optimal choice of the consumer. (c) Now suppose that the consumer is issued 2500 ration points and must pay 5 points for each unit of X and 10 points for each unit of Y. These ration points must be paid in addition to the dollar prices indicated. Draw the consumer's new budget set. Recall that the budget set consists of consumption bundles that the consumer can afford. Calculate the new amounts of X and Y she will purchase. Will she be better off, worse off, or equally well off, compared with the solution in (b)? Explain the relation between her MRSx,y at the optimal bundle and the two price ratios (there are two price ratios: one is the dollar price ratio, the other is the ratio implied by the relative ration points)