Consider a consumer who consumes only two goods, x and y. His utility over these two goods  is given by U (x, y) = x + y. The budget constraint of the consumer is given by 3x + 6y = 300, where 3 is the price of good x, 6 is the price of good y, and 300 is the total income of the consumer.

(a) Find the optimal quantities of good x and y that the consumer is going to consume. In your answer, reference the Marginal Rate of Substitution between goods x and y. Show the solution in a graph.

(b) Now assume that the price of good x increases to 6. Find the new optimal consumption bundle and comment on  it.

(c) Find the income and substitution effects associated with the increase in the price of x. Explain your findings.