Given a utility function U(X,Y) = Xa y(1-a), with price Px and Py, and income I, Statement 1: The income elasticity of demand for good Y, is equal to -1/a. Statement 2: The budget share of spending on good X will always be constant no matter what the price is.
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- Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y). a. Derive his demand functions for x and y. Are they homogeneous in income and prices? b. Assuming I = $60 and px = $1, graph his demand curve for y. c. Repeat part (b) for the case in which px = $2.David's utility function for good X and Y is given by U (X,Y) =X2y3. Where px,py and I are the price of good X, price of good Y and consumer income respectively. E). Suppose david faces a new utility such as U(X, Y)=25x0.2 Y0.75 for consuming commodity X and Y, redo question b and c. Derive the demand function for good X and Y What combination of X and Y maximizes the consumer at I=100,px=4,and py=5 F). Suppose david faces another new utility function such as U (X, Y) =15xy2 for consuming commodity X and Y,redo question b and c Derive the demand function for good X and Y What combination of X and Y maximizes the consumer at I=100,px=4,and py=5I need asnwers of f,g Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?
- Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…Draw the following scenario: Assume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ? 1to ? 2, and that she perceives jewelry as a Giffen good in the price range from ? 2to ? 4. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph. The graph may be something like this:Assume a piece of jewelry, and 3 consecutive drops in its price, from ??1 to ??2, from ??2 to ??3 and from ??3 to ??4. Alia’s preferences are such that her demand is relatively elastic between ??1 and ??2, relatively inelastic between ??2 and ??3, and that she perceives that piece of jewelry as a Giffen good between prices ??3 and ??4. How would her priceconsumption curve look like in an indifference curves framework with well-behaved preferences? Clearly label your graph.
- PROBLEM 2 – Uncompensated and Compensated Demand Functions, Price Elasticities of Demand, and Expenditure Functions Susi enjoys her favorite drink (D) and food (F) which she always spends her monthly income on those goods. Her average allocated income spent on drink and food is Rp 3 million, and the current prices of drink and food are Rp 30k and Rp 90k, respectively. Suppose her happiness by consuming those goods can be capture by the utility function as follows: *see image* a. What are her uncompensated (Marshallian) demand functions for drink and food, and calculate how many drinks and food that she currently consumes? Draw and describe how her demand curves for drink and food are shifted by changes in her income or the price of the other good. (hint: Use Lagrangian method). b. If the price of drink increases to Rp 50k, calculate the price elasticity of demand for drink. c. What is her the expenditure function for drink and food? Use the expenditure function to compute the…Given an individual’s current consumption patterns, we know that the person is consuming in such a manner that he is maximizing his satisfaction. Given a decrease in the price of one of the goods he normally purchases, what will happen to the consumer’s total satisfaction and to the marginal utilities connected with the consumption of this particular good. a) His overall satisfaction will increase, but his satisfaction from the last unit consumed of the good with a decreased price will decrease. b) His overall satisfaction will decrease and his satisfaction from the last unit consumed of the good with a decreased price will decrease. c) His overall satisfaction will increase and his satisfaction from the last unit consumed of the good with a decreased price will increase. d) His overall satisfaction will decrease and his satisfaction from the last unit consumed of the good with a decreased price will increase. e) We cannot tell about the changes in his total utility or his marginal…Assume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ?1 to ?2, and that she perceives jewelry as a Giffen good in the price range from ?2 to ?3. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph.
- I need asnwers of e,f,g Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?Please no written by hand solutions Bunter’s preferences over a bundle consisting of x1 units of good 1 and x2 units of good 2 are represented by the utility function U (x1, x2) = 2√x1 + √x2. Bunter faces prices p1 = 4, p2 = p, and he has an income of I = 16. 1. Is Bunter’s utility function quasi-concave? 2. Find Bunter’s demand function for good 1 and good 2 as a function of the price p. 3. What is Bunter’s marginal utility for income? 4. Suppose the price of good 2 increases from p2 = 2 to p2 = 3. What is the income and substitution effect of this price change? If the government wanted to maintain Bunter’s original utility by giving him a cash subsidy, how much should it be? 5. Suppose that, as in part (4), the government wanted to maintain Bunter’s utility after the price increase. However, the government does not know Bunter’s preferences. As a consequence, to compensate for the price increase, the government decides to give a cash subsidy just sufficient so that Bunter…I need asnwers of d,e,f. Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?