7. A consumer spends all income on only two goods, it and y. His preference is represented by the utility function: (x, y) = xy, where MUr = y, MU}; = x. The consumer's income is $10001 the price of good x is $10 and the price of good y is $5. a. What is the expression of the marginal rate of substitution (MRS)? b. What is the slope of the budget line? c. What are the optimal amounts of consumption of goods x and y? Show your steps. d. If the consumer's income rises to $1200 while the prices of both goods do not change, how does that affect the optimal amount of consumption of goods x and y? e. Based on your answer in the part d., are goods it and y normal good or inferior good? f. Suppose the consumer's income is still $1000, but the price of good y increases to $10. (i) Find the new optimal amounts of consumption of goods x and y. Show your steps. (ii) Graphically show the changes on an indifference-curve diagram, show also the substitution effect and income effect on your diagram