Consider two consumers, each having income of $300 that can be used to purchase two goods: X and Y. The price per unit of X is $5, and the price per unit of Y is $4. Ms. A’s preferences can be described by the utility function: U = (X^2)Y and her marginal rate of substitution is given by MRS X,Y = 2Y/X. Mr. B’s preferences can be described by the utility function: U = X(Y+100) and his marginal rate of substitution is given by MRS X,Y = (Y+100)/X. Calculate the amounts of X and Y each of these consumers will purchase if each is trying to make her- or himself as well off as possible.

Amy consumes x and y and her preferences can be represented by the following utility function U(x,y) = 4x + y. 1. Are Amy's preferences transitive? 2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. 6- 3. Can you use (2) to answer whether Amy's preferences are strictly monotonic? 4. What is MRS.y ? Is MRSx.y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? 5. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1. 6. Are Amy's preferences convex? Are they strictly convex? Explain

Alice receives an allowance of 500 dollars that she spends on buying snacks (S) and tea (T). The price of each snack is 10 dollars and the price of each tea is 5 dollars. Her utility is given by: U (S, T) = 2S³/4 +T3/4 (a) Find her marginal rate of substitution (MRS) between S and T. (b) Write Alice's budget constraint. (c) Find Alice's optimal consumption and the optimal A. (d) What is her new consumption if the price of tea becomes 10 dollars? Note: numeric solutions for questions (c) and (d) are not integers.

Bob views apples and oranges as perfect substitutes in his consumption, and MRS = 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is €2 per pound, the price of oranges is €3 per pound, and Bob's budget is $24 per week. What is Bob's utility maximizing choice between these two goods? A. 12 pounds of apples and no oranges B. 8 pounds of oranges and no apples C. 4 pounds of oranges and 6 pounds of apples D. 12 pounds of oranges and no apples Fiona uses her entire budget to purchase food and clothing. The price of food is €1 per unit and the price of clothing is €2 per unit. Fiona's marginal utility from food is 2 and her marginal utility from clothing is 6. She currently spends all her money on food and clothing. Her objective is to maximise her utility. Which of the following statements is correct? Fiona should buy more food and more clothing. A. B. C. D. E. Fiona is currently maximsing her utility and should continue to consume her current…