22. If the cost of buying 10 units of good 1 is less than 1/2w, a consumer buys 10 units of good 1 and spends her remaining wealth on good 2. Otherwise she spends half of her wealth on each good. The utility function is
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- Suppose that a typical consumer’s utility function is characterized by the following relation between good X and good Y. The consumer’s consumption decision is influence by the price of the respective goods, which requires him 2 birr for each unit of X and 3 birr for each unit of Y and the resource available to him is 160 birr. A construct the budget constraint of this typical consumer Find the optimal consumption of X and YSuppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 309. A consumer has the utility function u(x,y) = =x+6y and the price of x is $1 and the price of y is $5. If the consumer's income is $40, what bundle of goods will maximize her utility? x = 20, y = 4 x=40, y = 0 x = 0, y = 8 x= 10, y = 6 A a. b. c. d.
- Total utility O diminished as the quantity of a good increases increases as long as more goods are acquired increases as long as marginal utility increases O increases as long as marginal utility is positive diminishes as consumption of some good rises4.An individual consumes products X and Y and spends $30 per time period. The prices of the two goods are $3 per unit for X and $3 per unit for Y. The consumer in this case has a utility function expressed as: U(X.Y) = 0.5XY How much X should this individual consume, given that he is maximizing the utility? ( A) 4.17 ( B) 5 (C)6 D) 6.25Amadea spends all her income on pizza,chocolate milk, and music streams. The price of pizza is $4 per slice and price ofchocolate milk $2 per bottle. At Amadea's current consumption level, her marginalutility for pizza is 50 units per slice and for music 100 units per stream. Assuming thatAmadea is a utility maximizer, how much is (a)her current marginal utility for a bottleof chocolate milk, and (b) the price of streams she buys. Show your work. [Hint: Ch 6:Utility-maximizing formula)
- 25 Columns 1 through 4 in the following 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 prices of A, B, C, and D are, respectively, $9, $3, $2, and $6 and that Ricardo has an income of $71. Column 1 Column 2 Column 3 Column 4 Column 5 Units of Good A Units of Units of Units of MU MU MU MU Good B Good C Good D Number of Dollars Saved MU 1 72 1 24 1 15 1 36 1 5 2 54 2 15 2 12 2 30 2 4 3 45 3 12 3 8 3 24 3 3 4 36 4 9 4 7 4 18 4 2 5 27 5 7 5 5 5 13 5 1 6 18 6 5 6 4 6 7 6 0.50 7 15 7 2 7 3.5 7 4 7 0.25 8 12 8 1 8 3 8 2 8 0.13 Instructions: Enter your answers as a whole number. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? 4 units of A 3 units of B units of C units of D b. How many dollars will Ricardo choose to save?By definition, a budget constraint shows the consumption bundles that a consumer can afford. Assume that a college student spends her income on Mc-cheese and CD's. The price of one box of Mc-cheese is $1.00 and the price of one CD is $10.0 . If she has $90 of income, she could choose to consume : a- 10 boxes and 9 CDs b- 30 boxes and 7 CDs c- 25 boxes and 6 CDs d- 25 boxes and 8CDS2. Vibha consumes three goods X, (shirts), X, (food in pounds), and X, (shelter in square feet). Vibha's utility function is given by: U (X,, X, X,) = 5ln Xt 3ln X + 2ln X, where In (x) or log. (x) is the natural logarithm. Vibha's weekly income is $100. Let the price of X, = P, = $10, the price of X, = P, = $2, and the price of X, = P; = $4. What is the equation for Vibha's budget constraint? а. b. |How many shirts, pounds of food, and square feet of shelter, will Vibha consume, as a rational consumer?
- 5. Suppose the representative consumer has the (quasilinear) utility function: U(x, y) = ax + In(v) where x,y are consumption goods. Denominated in US dollars, the prices of x and y Pi and pz, respectively. (a) What does the term quasilinear mean? Is consumption of x independent of y? (b) Assume the consumer has a budget of C dollars at his/her disposal. What is the maximum utility the consumer may achieve with this budget? (c) What is the minimum expenditure if the consumer wants to derive U,units of utility?The table shows the total utility (TU) that James receives from consuming different amounts of two goods X and Y, per month. Quantity TUx MUx MUx/Px TUy MUy MUy/Py 0 0 0 0 0 0 0 1 50 50 16.67 75 75 25.00 2 88 38 12.67 117 42 14.00 3 121 33 11.00 153 36 12.00 4 150 29 9.67 181 28 9.33 5 175 25 8.33 206 25 8.33 6 196 21 7.00 225 19 6.33 7 214 18 6.00 243 18 6.00 8 229 15 5.00 260 17 5.67 9 241 12 4.00 276 16 5.33 d.How much total utility will James experience by buying the utility-maximizing combination? e.Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize his utility now?UTIITY (Units of utility) 10 Suppose your friend Deborah offers you the following bet: She will flip a coin and pay you $2,000 if it lands heads up and collect $2,000 from you if it lands tails up. Currently, your level of wealth is $6,000. The graph shows your utility function from wealth. Use the graph to answer the following questions. 100 90 80 B 70 A 60 50 40 30 20 10 WEALTH (Thousands of dollars)