1-aAlice only consumes bread (x1) and butter (x2). Her preferences over these goods are represented by u(x1, x2) = x4 x,had an income of m = 12 and faced prices pi = 1 and p2 = 2. Now, Alive lives in Town B, where her income is still m = 12 but prices are pi = 7 and p2 = 1.Alice used to live in Town A. There, sheIf rounding is needed, please round to 3 decimal places.a) When Alice chooses an optimal bundle of bread and butter in Town B, her M RS 2 at that bundle isb) If Alice is exactly as satisfied with her optimal bundle in Town B as she was with her optimal bundle in Town A, this means that a =

MRS is the rate at which consumer is willing to substitute good for each other, keeping the utility…

1-a Alice only consumes bread (x1) and butter (x2). Her preferences over these goods are represented by u(x1, x2) = xx,-". Alice used to live in Town A. There, she had an income of m = 12 and faced prices Pi = 1 and p2 = 2. Now, Alive lives in Town B, where her income is still m = 12 but prices are pi = 7 and p2 = 1. If rounding is needed, please round to 3 decimal places. a) When Alice chooses an optimal bundle of bread and butter in Town B, her M RS1,2 at that bundle is b) If Alice is exactly as satisfied with her optimal bundle in Town B as she was with her optimal bundle in Town A, this means that a =

1-a Alice only consumes bread (x1) and butter (x2). Her preferences over these goods are represented by u(x1, x2) = xx,-". Alice used to live in Town A. There, she had an income of m = 12 and faced prices Pi = 1 and p2 = 2. Now, Alive lives in Town B, where her income is still m = 12 but prices are pi = 7 and p2 = 1. If rounding is needed, please round to 3 decimal places. a) When Alice chooses an optimal bundle of bread and butter in Town B, her M RS1,2 at that bundle is b) If Alice is exactly as satisfied with her optimal bundle in Town B as she was with her optimal bundle in Town A, this means that a =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
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
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1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
A consumer has utility u(x,y,z)= ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pZ = 1 . Optimally sheconsumes 30 units of z. What is her income? How much money does she spend on x?(HINT: MUX =??, MUY =??, MUZ =??and remember the “equivalent bang for the buck” condition)(b) Forget about (a). Suppose you have t = 29 hours in total to spend on 3 projects X, Y and Z to make some money.If you spend x hours on project X, you make 2√? dollars;If you spend y hours on project Y, you make ?√? dollars;If you spend z hours on project Z, you make ?√? dollars;Writing down your “utility function” u(x,y,z) and the constraint, solve the utility maximization problem; what isthe optimal amount of time to spend on x ? on y? on z ?
A consumer has a budget of $3000 in a given period, and wishes to buy two goods, X and Y, so as to maximise his utility. The price of good X is $5 and the price of good Y is $2, and his MRS is given by the formula 2Y/X. How many units of good X will he buy in that period?
2. Consider an individual who not only consumes goods x and y, but also needs a mini- mum amount of x= xo to survive. Her (Stone-Geary) utility function is given by U(x, y) = (x − x)¹/2y¹/2 Let prices be Pa, Py and income is I > Prxo.
Find the change in the amount of good X Jenny buys.
Part 2 beginning with "now assume"
Anne is going to the grocery store to buy some fruit. She can buy either apples or oranges. Let a be the quantity of apples she buys, and let zo be the quantity of oranges she buys. Her utility function is: u(xa, xo) = ln xa + 3 ln xo Anne has y pounds to spend. The price of apples is pa and the price of oranges is po (a) (b) Write down Anne's budget constraint and utility maximization problem, and the Lagrangian associated with this utility maximization problem. Find Anne's Marshallian demand functions for apples and oranges. Find Anne's indirect utility function.
12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.
Consider a consumer with M = $120 to spend (income) and faces prices PX = $15 and PY =$5 for goods X and Y. Her utility function is U(X, Y) = X1/2 + Y1/2.a Carefully. express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the other…