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- Question 7 A consumer has a utility function 100-(x₁-4)4 -(x2-3)4 and a budget constraint of 9x1+3x2 <200. How much of good 2 do they consume?Quantity X TUx MUX MUX/Px Quantity Y TUy MUY MUy/Py 1 75 1 96 135 60 B 72 185 50 3 234 66 4 230 45 A 4 294 60 270 5 348 54 2.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..
- PROBLEM (7) 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 where I = 80, px=10, py= 20..(2) Consider the utility function u(x, y) = Vx+ay. Your budget constraint is P1x+p2y = М. (a) Find the marginal utilities for these goods. (b) Show that these preferences are quasilinicar. (c) Solve the consumer's optimization problem.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.
- Number of Sodas per day Total Utility Marginal Utilit 1 20 35 3 47 12 4 10 Refer to the table, The marginal utility of the second soda per day is L. (Answer should be in the form of numerical characters, e.g. 20) Enter your answer here2. Utility function: U(X,Y)= 2XY* Budget Constraint: 2X +4Y = 80 a. Calculate the utility maximizing amount of X and Y.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 where I = 80, px =10, py = 20.
- 4. Consider the utility function U(r,g) r + Iny. (a) Find the marginal rate of substitution. MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of r and y. How do you interpret these functions? How might a consumer choose between e and y as she tries to increase utility by, for example, consuming more when their income increases?14. Consider the following utility function: U(x, y) = xy+x with MUx = y+1 and MUy = x.As the consumer buys more x, the marginal utility of x:(a) Diminishes(b) Remains constant(c) Increases(Review Question) Sarah consumes both wine ) and cheese (y) and considers them perfect substitutes. She always gets twice as much utility from consuming wine as she does cheese. What equation would represent her utility function? U-(2xy) U=x+2y U=2x+y U=min(x,2y)