Julie consumes two goods, food and clothing, and always has a positive marginal utility for each good. Her income is 24. Initially, the price of food is 2 and the price of clothing is 2. After new government policies are implemented, the price of food falls to 1 and the price of clothing rises to 4. Suppose, under the initial budget constraint, her optimal choice is 10 units of food and 2 units of clothing.
a) After the prices change, can you predict whether her utility will be higher, lower, or the same as under the initial prices?
b) Does your answer require that there be a diminishing marginal rate of substitution of food for clothing? Explain.