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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 Prx+Pyy = B.Application of Consumer Theory. Derive and explain the Dual Problem of the Consumer Theory assuming that and Pxx+Pyy=Bb. A consumer purchases two goods, the amounts of which are x and y. Her marginal utility of consuming good x is Ux , while that of consuming good ? is Uy. If the two marginal utility functions are given by Ux = y2 + 2xy and Uy = 4xy + 3x2 − 3 and the consumer is known to stay on the same utility curve, find the total utility function of this consumer buying the two goods
- 1. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are px and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. = (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px = 10, Py = 5 and m = 100. Suppose that px increases to p how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y > 0). = 15,U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.1) Explain the following: i. UTILITY ii. UTILITY FUNCTION iii. LAW OF DIMINISHING MARGINAL UTILITY. iv. Given a consumer has a money budget M = 360 and utility function U(X, Y)=X^(3/4)Y^(1/4). If she consumes two goods x and y with prices given by Px=10 and Py=30. Find the QUANTITIES of X and Y that MAXIMIZE her utility.
- 3. Susan has the following utility function U(x,y) = xy, where x represents food and y represents other goods. Susan has £20 (budget m) to spend on these two goods. Suppose that the initial price of x (Px) is £1 per unit, and that of y (Py) is £1 per unit. Note that MUx=y and MUy=x. (i) How many units of x and y will Susan purchase? Assuming that Px varies and m and Py stay constant at the values £20 and £2, respectively, what is the individual demand function for x? (ii) What are the characteristics of the individual demand function for x? What is its aggregate counterpart, and what is its economic importance?At the current combination of X and Y the consumer's MU-7 and MU, 4. If Px=3 and Py=2, is the consumer maximizing their satisfaction? If not, explain in detail what the consumer should do, and illustrate.PROBLEM (5) A consumer with I dollars budget has the utility u(x,y) = x(y+1) over amounts of cake (x) and ice cream (y) she consumes. The prices are px , py respectively. (a) Derive her demand for cake (x), as a function of prices px , py and her budget I.(b) Looking at the demand function in (a), is cake a normal good or an inferior good? Are cake and ice cream complements or substitutes?(c) Calculate the (i) (own) price, (ii) income, (iii) cross- price elasticity of demand for cake at the point whereI = 80, px =10, py = 20..
- Explain the principles, concepts, and theories underlying individual consumers’ behaviour with respect to utility maximization.What condition should be met in order for the consumer to maximize satisfaction in the consumption of good X and good Y? Provide the calculation that satisfies the equilibrium condition.Explain one difference and one example between the Cardinal utility and ordinal utility!
