Ann and Bob have the same income level and face the same prices of goods x and y. The price of x is 4 and the price of y is 8.

(a) At the current consumption level, Ann's MRS is equal to 1. In order to improve her situation, should Ann increase or decrease her consumption of x?

(b) At the current consumption level, Bob's MRS is equal to 0.5. Is Bob's current consumption bundle optimal or suboptimal?

(c) Suppose that, after adjusting their consumption levels, both Ann and Bob choose their optimal levels of x and y. Ann chooses x = 5 and Bob chooses x = 4. True or false: Ann and Bob have the same MRS at their current consumption levels.

(d) Continuing with the assumptions of the previous question. True or false: If Ann exchanges 1 unit of x for 2 units of y, then both Ann and Bob become better off.

(e) Bob's income increased and his consumption of x changed from 4 to 4.5. True or false: x is an inferior good for Bob.

(f) Suppose Bob's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Bob's consumption of x decreased from x = 4 to x = 3. True or false: The income effect of the price increase is necessarily negative.

(g) Suppose Ann's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Ann's consumption of x increased from x = 5 to x = 6. True or false: Ann's behavior necessarily contradicts economic theory.

(h) Suppose Ann's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Ann's consumption of x increased from x = 5 to x = 6. True or false: The income effect of the price change on Ann's consumption of x must be positive.

(i) True or false: Since Ann and Bob have the same income level, they also must have the same level of consumer surplus.