Ques 1. Sally consumes two goods, X and Y. Her utility function is given by the expression U=3XY². The marginal utility of X and marginal utility of Y are given by the following equations: MUX-3Y² and MUY=6XY The current market price for X is $10, while the market price for Y is $5. Sally's current income is $500. a) Draw out Sally's budget line. (show the points where it meets the vertical and horizontal axes) b) Determine the X,Y combination which maximizes Sally's utility, given her budget constraint. (Partial units for the quantities are possible.) [Hint: One of the ways to do this is to use the equal marginal principle to find the optimal ratio of X to Y and then use that in the budget equation] c) How much is Sally's utility? d) Now the price of X increases to $15. What is the ratio in which she will consume X and Y ?

7. MRS and utility maximization Suppose your classmate Felix loves to eat dessert-so much so that he allocates his entire weekly budget to apple crisp and pie. The price of one bowl of apple crisp is $1.75, and the price of a piece of coconut crème pie is $7.00. At his current level of consumption, Felix's marginal rate of substitution (MRS) of apple crisp for pie is 5. In other words, Felix is willing to sacrifice five bowls of apple crisp for one piece of pie per week. Does Felix's current consumption bundle maximize his utility? That is, does it make him as well off as possible? If not, how should he change it to maximize his utility? Felix could increase his utility by buying more apple crisp and less pie per week. Felix could increase his utility by buying less apple crisp and more pie per week. Felix's current bundle maximizes his utility, and he should keep it unchanged.

Solve these consumer choice problems: a. Suppose a consumer has a utility function u(x, y) = xy + 7y facing prices p,=S1 and p,=$2 and income I = $10. Draw a diagram and find the consumer's optimal consumption of goods x and y. b. Suppose that you are in a situation where you can afford purchasing 3 units of good x and 4 units of good y. You discover that another affordable bundle of 5 units of good x and 2 units of good y causes you to reach the same level of utility. Assume that your utility function and budget line are both well behaved. Are you maximizing your utility by consuming your original bundle? Why or why not? Propose an alternative, affordable bundle that would yield a higher utility level than either of the original bundles.

4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? = (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income

Sally consumes two goods, X and Y. Her utility function is given by the expression U = 2XY3. The current market price for X is $20, while the market price for Y is $10. Sally's current income is $500. a. Write the equation for Sally's budget constraint. What is the slope of her budget line? b. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint.

Columns 1 through 4 in the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the price of good A is $18, the price of good B is $6, the price of good C is $4, and the price of good D is $24. Ricardo's income is $106. Column 1 Units of A 1 2 3 4 B= 5 6 7 B units. C= 3 units. MU 72 54 45 36 27 18 15 12 Unit A 4 +5 18 Units of B 1 2 3 Column 21 4 5 6 7 8 MU 24 15 12 Unit B 9 7 5 2 1 +0 6 Units of C 1 2 3 Instructions: Enter your answers as whole numbers. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? A = 4 units. 4 5 6 Unit C 7 Column 3 8 MU 15 12 8 7 5 4 3.5 3 Amount of Savings G Units of D 1 24 2 3 4 D-0 units. b. How many dollars will Ricardo choose to save? $ c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule. 5 6 Column 4 7 8…

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Lisa consumes only two goods, pizzas and burritos. In equilibrium, her marginal utility per slice of pizza is 10 and her marginal utility per burrito is 8. Instructions: Enter your answer rounded to two decimal places. If a slice of pizza costs $3, then the price of a burrito must be $

10. Assume an individual's preferences are represented by the following indifference map and he has an income of S400. Which of the following is shown when the price of Good I is $20 and the price of Good 2 increases from $10 to S16? Note: Even though the price of Good 2 is increasing, the steps to determine the income and substitution effects are the same. 50 45 40 35 30 25 20 15 10 10 15 20 25 30 35 40 45 50 Good 1 Good 2 is a normal good. Good 2 is an inferior good, but not a Giffen good. Good 2 does not satisfy the Law of Demand. • Ignoring the Income Effect, the Substitution Effect will cause the individual to consume more of Good I. A. B. 21 C. 3 None of the above statements are true. D. Good 2

Suppose that Jon is purchasing the optimal amounts of apples and oranges. The marginal utility of the last apple is 8 and of the last orange is 6. If the price of an apple is $1, what must be the price of an orange?:"     50 cents.     $1.40.     75 cents.     $1.33.