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![2) Application of Consumer Theory. Derive and explain the Dual Problem of the Consumer Theory assuming that U (x, y) = xy and
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- 2. Suppose there are two goods in the economy: Food (F) and Composite good (Y), with Pp = 1 and Py = 2. Consider a consumer who has utility function u(F,Y) = InF + In Y and income I = $100. (a) Find the consumer's consumption choice. (b) Suppose, to promote better nutrition, the government institutes a welfare program that gives every consumer with income less than $500 additional $100. Find the consumer's new consumption choice. How much of the government's payment went into purchasing Food? (c) Suppose rather than giving cash, the government gives a voucher that can only be used to purchase (up to) $100 worth of Food. How does this affect the consumer's consumption choice? (d) Which of the two programs is more effective in achieving the government's goal? Explain.1. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects to be found below. (b) u(x1, x2) = x1 + x2. (c) u(x1, x2) = x1x2. (d) u(x1,x2) = min {x1,x2). (e) Rank the substitution effects and the income effects found above by their magnitude. To what extent do they conform to your guess?Other things equal, if the marginal utility from successive units of product Y yields to smaller and smaller amounts of extra satisfaction we would expect that the consumer: Select one: A. will buy additional units of Y if its price increases. B. will buy less units of Y if its price decreases. C. will buy additional units of Y if its price falls. D. will not change the units of Y purchased.
- Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EVFigure#4 Indiflereocetur2. 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?Consumer Theory Daniel spends all his money on only two goods: chocolates (good 1) and milkshakes (good 2). We have information about his purchases, income and prices for 4 weeks: A, B, C and D. For each week, the budget line and the goods bought are shown on the graph below. a) Suppose that Daniel’s preferences are transitive and satisfy "more is better". Shade all the bundles that you are certain are worse for Daniel than bundle A in one colour, and all the bundles that you are certain are better for Daniel than bundle A in a different colour. (You can use different patterns instead of colours.) Indicate which is which. Explain.A consumer consumption bundle contains good X and Y. Suppose the price of good X goes up and a consumer goes on consuming the exact same amount of X as before. Check the correct statement(s).A) Both X and Y are inferior. B) X is an inferior good.C) In the special case where X is Leisure, and Y is "all other goods", X is an inferior good.D) The consumption of Y decreases.E) It is impossible that the consumption of X remains unchanged when the price of × goes up.F) The substitution effect is negative
- 3. Explain the law of diminishing marginal utility with the help of examples and also explain the assumption under which this law is applicable and what the exceptions are where this law does not hold.Question #1. Lisa's level of satisfaction for the consumption of apples at college is given by the following Units Total Utility, TU Marginal Utility, MU MU/$ 0 0 1 20 2 35 3 45 4 50 5 50 6 45 35 a. Fill in the missing MU entries above b. Let apples sell for $0.50 each. Determine Lisa's MU per dollar, MU/$, and fill in the missing entries aboveA consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.
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