The preferences of a consumer are represented by the utility function

u(x; y) = x + y:

The price of a unit of good x is 2, the price of a unit of good y is p, and the

income of the consumer is M. Moreover, the consumer is given a lump-sum

subsidy of S that can only be used to purchase good y. Suppose that p 6= 2.

1. Dene the utility maximization problem of the consumer.

2. Find the optimal amounts of x and y as functions of p, M and S.