Lan's utility function is U = xa y1-a where x denotes her consumption of good X, y denotes her consumption of good Y and a = 0.8. The price of good X is Px = 7, the price of good Y is Py = 14 and Lan's income is M = 338. If each price increases by 2 dollars, how much money must Lan be given to compensate her for the price increase?
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Lan's utility function is
U = xa y1-a
where x denotes her consumption of good X, y denotes her consumption of good Y and a = 0.8.
The
If each price increases by 2 dollars, how much money must Lan be given to compensate her for the price increase?
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- Jane has utility function u(x,y)=x4y5. The price of x is px, the price of y is py, and Jane’s income is W. What is the expression of her consumption of y as a function of prices and income (her optimal consumption is determined by the tangency rule)? Qy(px,py,W)= 9W/5py. Qy(px,py,W)= 5W/9py. Qy(px,py,W)= 4W/3py. Qy(px,py,W)= 5W/4py. Qy(px,py,W)= 4W/5py.Let x be the number of pizza slices and y the number of Cokes. If John’s utility function is u = min{7x, 4x+ 12y}, then if the price of pizza slices is 20 euros and the price of Coke is 40 euros, John will demand ? a- 2 times as pizza slices as Cokes b- 3 times as pizza slices as Cokes c- 6 times as pizza slices as Cokes d- 4 times as pizza slices as Cokes e- 5 times as pizza slices as Cokes f- only CokesSteve's utility for socks (q1) and other goods (q2) is given by U(q1,q2) = 10q10.1 0.1q² 0.9 The price of the composite good is p2=1 and the price of a pair of socks is p1=2. Steve's income is Y=100. Every year, Steve's mom buys him 20 pairs of socks. How many dollars is the equivalent variation of the $40 that his mom spends on socks every year?
- The utility function of a certain consumer is U =(x1,x2)= x11/3 x22/3 , x 1and x 2 is the consumption of two kinds of goods, and the consumer's income is 100. The current prices of the two kinds of goods are P 1 =1 and P 2=2 respectively, ask: 1. If the price of the first commodity increases from 1 to 2, and other factors remain unchanged, what is the total effect of the price increase on the consumption of the first commodity? According to the Slutsky decomposition principle, what are the income effect and substitution effect? 2. Calculate the amount of income compensation that changes the price of the first commodity from 1 to 2, keeping the original effect unchangedAssume that the prices of good X, Y and Z are as follows R5,R1 and R4 respectively, and the Judith has an income of R37 to spend. HOW much of each good will judith consume in order to maximise her utility? What will be her total utility and marginal utility of the last rand spent on each good? Show all the calculationsLea's utility function is U =0.7 ln( x ) + y where x denotes her consumption of good X and y denotes her consumption of good Y. Suppose the government imposes a per-unit tax on good X equal to 5 dollars. The price of good X charged by the sellers of good X is Px = 9 (and does not change due to the tax), the price of good Y is Py = 13 and Lea's income is M = 389. What is Lea's own-price substitution effect of the price increase due to the tax ?
- Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.Suppose Anna’s utility for goods x1 and x2 is represented by the following utility function: U (x1, x2) = x11/2 x21/2 (a) Find Anna’s marginal rate of substitution, MRS12.(b) If the price for good x1 is p1 = 1, the price for good x2 is p2 = 2 and Anna’s available income is m = 12, write down Anna’s budget constraint. (c) For the utility, prices and income given above, find Anna’s optimal consumption choice (Marshallian demand) and her utility level.Assume an individual spends all of the their income on a bundle comprised of good #1 and good #2. In particular, their utility function is given by: U(q1,q2) = q12/3q21/3 Assume the price of good #1 is $1 (p1=1) and the price of good #2 is $3 (p2=3). What must the individual's income be if they maximize their utility by purchasing 10 units of good #1?
- Mrs. Griffiths earns $5000 a week and spend her entire income on dresses and handbags. Since these are the only two items that provide her utility. Furthermore, Mrs. Griffiths insists that for every dress she buys, she must also buy a handbag. Dress is $25 and handbags is $14. i. Suppose the price of a dress increases to $200 and income decreases to $4200. What would be the new marginal rate of substitution that corresponds to the optimal consumption choice? Interpret the marginal rate of substitution.Henry's utility function is u(x,y)=max{x+3y,3x+y}. (a) Suppose Henry's current consumption bundle is (2,1.5), what is his current utility level? If he consumes the bundle (1.5,2), will his utility change from the current utility level?I. A)MRS=1/3, B)MRS=1/4, C)MRS=4/3, D)MRS=12 II. A)Rhea should buy more bread, less milk, B)Rhea should buy more milk, less bread, C) Rhea maximizes her utility at bundle A, so she should not change her consumptions of either good, D) Rhea cannot afford bundle A, so she should buy less of both goods III. A)Rhea's MRS at bundle A is greater than the price ratio (Pb/Pm), B)Changing her bundle moves Rhea to a higher indifference curve, C)The slope of the indifference curve (where bundle A is found) is not equal to the slope of Rhea's budget constraint, D)All of the above statements explain your answer to part II.