Declining MRSXY implies that: (a) The total utility is decreasing along an indifference curve (b) The consumer’s preferences do not satisfy the more-is-better principle (c) The consumer is willing to give up more and more X for additional Y as the consumption of X increases along an indifference curve (d) The consumer is willing to give up less and less X for additional Y as the consumption of X increases along an indifference curve
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18. Declining MRSXY implies that:
(a) The total utility is decreasing along an indifference curve
(b) The consumer’s preferences do not satisfy the more-is-better principle
(c) The consumer is willing to give up more and more X for additional Y as the consumption of X increases along an indifference curve
(d) The consumer is willing to give up less and less X for additional Y as the consumption
of X increases along an indifference curve
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- Would you expect marginal utility to rise or fall with additional consumption of a good? Why?4. Tim wants to maximise his utility given his utility function of U(A, B) = A²B4. 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 income4. Liam initially has a weekly allowance of €24 to spend on eggs (at €0.40 per egg) and beans (at €0.80 per tin). Liam will only consume 4 eggs with each tin of beans and never changes this proportion. (a) What is the utility maximising amount of eggs and beans that Liam buys each week? (b) Suppose the price of eggs rise to €0.60 per egg but the price of beans falls to €0.60 per tin. At the same time, Liam's weekly allowance rises to €30. How much of each good will Liam now buy? Compare your answer to that in (a) and explain the difference, if there is one. Use a diagram to complement your answer.
- 2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?2. Consider a consumer whose preference relation over the consumption set X = R can be repre- sented by the utility function: u (x1, x2, 13) = A (x1 – T1)ª (x2 – ã2)° (x3 – ã3)" - where A, a, B and y are all strictly positive. (a) Why can you assume A = 1 and a + B+y= 1 without loss of generality? Do so for the rest of the question. (b) Solve the UMP and derive the consumer's Walrasian demand. (c) Find the indirect utility function, the minimum expenditure function, and the Hicksian demand function.3. Assuming a price of X (Px) and a price of Y (Py) are $ 1 each, the individual's income is $ 8 per time period and all of it is spent. The Schedule Utility Marginal for items X and Y for individuals is: Specify : a. How should this individual spend his income in order to maximize total utility? b. What is the total amount of utility received by an individual when it is in equilibrium?
- 4. Let u(z) be a utility function that represents the preferences of a household. We say that the function v(r) is a monotonic transformation of u if f(-) is a strictly increasing function and v(z) = f(u(z)). (a) Show that if v(z) is a monotonic transformation of u, it represents the same preforences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are reprosented by a utility function of the form u(a1, 12) = VEi +#2? What about the function v(z1, r2) = 13z + 13r2? (d) Consider the function u(r1, 2) = VE1#2. What kind of preferences does it represent? Is the function (11, r2) jz a monotonic transformation of 1 u(r1, 12)? Is the function w(r1, 12) u(r1, 12)? = zfr a monotonic transformation of1. A consumer has an income of $3024 to spend each day. The only two goods the consumer is interested in purchasing are goods A and B. The marginal-utility schedules for these two goods are shown in the table below. The price of B does not change and is $378. The marginal utility per dollar from B is also shown in the table. But the price of A varies as shown in the table. The marginal utility per dollar from A when the price of A is $1512 and $756 is shown in the following table. Good A Good B Quantity MU MU/$1512 MU/$756 MU MU/$378 1 24 2 15 3 12 4 8 5 6 6 4 48 32 24 16 8 4 ||||| ||||| |||7. Bob receives utility from days spent traveling on vacation domestically (D) and daysspent traveling in a foreign country (F) as given by the utilityU(D; F) = DFThe price of a day spent traveling domestically is 160 pounds and in a foreigncountry 200 pounds. Bobís annual budget for traveling is 8000 pounds. (a) Find Bobís utility maximising choice of days traveling domestically and of daystravelling in a foreign country. Find also his utility level from consuming thatbundle. Suppose that the price of domestic traveling increases to 250 pounds per day.Denoting his budget for traveling x, (suppose by now that it is unknown) findthe demand for D and F under the new prices as a function of x.
- Lee has calculated her marginal utility from buying pizza slices and soda (shown on the table in the worksheet) and wants to use these data to decide how to rationally spend the money she has. The price of pizza is $2.00 and the price of soda is $2.00 question 9 (a) given these prices and your worksheet calculations, what is the first product lee will buy? (b) would lee ever buy four slides of pizza? Why/why not? question 10Given the data in your worksheet, how many pizza slices and sodas lee should buy to maximize her total utility if she rationally spends her budget of 10.00? question 11 when the price of pizza changes, lee's MU/$P changes. If the price of pizza decreases to $1.50 and her budget decreases to $7.50, how many pzza slices and sodas lee should buy to maximize her total utility?1. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are px and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. = (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px = 10, Py = 5 and m = 100. Suppose that px increases to p how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y > 0). = 15,14. Consider the following utility function: U(x, y) = xy+x with MUx = y+1 and MUy = x.As the consumer buys more x, the marginal utility of x:(a) Diminishes(b) Remains constant(c) Increases