Q1) For quasilinear preferences between goods X and Y, show, using Hicks method, how Income effect is divided into substitution and Price effect. Assume Y is toothpaste and X is a composite of other goods.
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- Suppose a consumer consumes only two goods, x1 and x2 and both goods are normal goods. 8 points (a) Explain with the help of a diagram the Slutsky substitution effect and the income effect when the price of good, x1 increases. (b) Explain with the help of a diagram, how the Hicks Substitution effect is different from the Slutsky Substitution effect.Ma1. Please give only typed answer. Assume the following expendiexpenditure function. (a) Interpret this function. In particular, what will happen to the optimal expenditure, if the consumer wanted to maintain a high level of utility? (b) Calculate Hicks demand for good 2. (c) Suppose that p1 = 1, p2 = 1 and that U = 28. Calculate and interpret the variation compensation if the price of good 2 increases by $1.a good is normal, then an increase in the price of the good will lead to which of the following to be true for this good? (Assume that there are only two goods, the individual's preferences lead to well-behaved preferences with strictly convex indifference curves and an interior solution for all budgets). Let SE = substitution effect, IE = income effect) (a) The magnitude of the IE for this good must be larger than the magnitude of the SE (b) The magnitude of the SE for this good must be larger than the magnitude of the IE (c) The good could be a Giffen good d) The good must be an ordinary good ( (e) None of the above
- Q1: (I)Asma eats only apples and almonds. Her level of income is $36, Price of apple (Pa) is $2 per kg and price of almond (Pl) is $6 per kg. The preferences of Asma are represented by the following utility function Utility U= 10*Qa + 40*Ql where Qa and Ql are Asam’s consumption of Apples and almonds. (a) which kind of preferences Asma has? (b) Find Utility per dollar spent on apple and almond (c) Find Marginal rate of substitution and interpret it (d) Find utility maximizing values of apples and almond and show graphicallyhe Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 601. 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?
- Suppose a consumer purchases food X and clothing Y. The utility function of the consumeris given by: U(X,Y ) = XY + 5Y and the budget /income/ of the consumer is 200 ETB. Andalso the price of food is X P and the price of clothing is Y P . Then drive the equation ofconsumer’s demand function for food and clothing.(1) For each of the three Indifference Curve Maps, what can you infer about the relationship of the goods? What about its substitutability? Provide an example pair of goods for each a) Ug U2 a) Uz QxO Economic Applications of Differential Equations An individual preference scale for two goods x and y is defined by the marginal rate of - a)? +(y- b)? is one form of utility substitution of y for x, R = y- b Show that u =(x function.
- lets us assume ,aleeza consumption basket consist os two goods ,X1 and X2.three preferences statements from a-c are given below .develope MRS and graph the indifference curves that matches the given information; a) aleeza consider X1 and X2 as perfect substitutes with one unit of X1 equivalent to four un its of X2. b) aleeza consume three units of x2 with every unit of X1 c) aleeza likes good X1 ands neither likes nor dislikes good X2.3. Cevdet'sutility function is U(F, C) = FC + F where F is for food and C is for clothes. Income of the consumer is 20 liras and price of clothes (Pc) is 4 liras. a) b) c) d) Derive the demand function for food. Calculate Income Effect and Substitution Effect when price of food (PF) rises from 1 lira to 4 liras. Calculate and explain compensating variation (CV). Calculate and explain equivalent variation (EV).3- Assuming that the equation F(U, x, X2 = f(x1, x2,, ... Xn): ******* **** ,xn) = 0 implicitly defines a utilityfunction U 073 a) Find the expressions for 60, 6U and 6x4 " 3 6x2 6xn 6x2 6xn b) Interpret their respective economic meanings. c) Now. assume the utility function is U(x, y) = y√x. Does the consumer believe that more is better for each good? Do the consumer's preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?
