The utility funetion is u(s1, 12) = ef£2: > 0. The good 1 is a numeraire. Price of 2 is p. Income is 10. a) Show that the indifference curve are strongly convex and increasing. b) Find the Marshallian demands and the indirect utility fumction.
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- It is the property of indifference curve that no two ICs can intersect each other because: a. same combination of two goods cannot give different level of satisfaction. b. of diminishing MRS. c. consumer preferences are transitive. d. MRS will not equal with MRT.Suppose the consumer solves the following UMP: max (x1)^2 + (x2)^2 , s.t. p1x1 + p2x2 ≤ w where p1,p2 > 0. a) Plot the indifference curves b) Find the Marshallian demand functions. Show graphically the utility maximizing choices.Determine the optimum demand for goods 1 and 2 for consumers who have the utility function u(x)=x1x2. Show that the solution will be the same whether using the slope approach (i.e the slope of the indifference curve is the same as the slope of the budget line) or using the Lagrange approach.
- Utility Maximization A consumer faces income constraints and has CES preferences of the following form: U(x, y) =x y Find the consumer’s demand for x as a function of prices and incomeThe marginal rate of substitution (MRS) can be defined as: Select one or more: a. The amount of one good that the consumer is willing to trade for one unit of the other. b. The ratio of the amounts of two goods. c. The change in the consumer’s utility when one good is substituted for another. d. The absolute value of the slope of the indifference curve.Indifference curves are convex to the origin because of: A) the assumption that more is preferred to less. B) transitivity of consumer preferences. C the assumption of completeness. D) the assumption of a diminishing marginal rate of substitution. E) none of the above
- Consider the relative slopes of the indifference curves for two individuals with respect to the same two goods, xylophones (on the X-axis) and yams (on the Y-axis). The individual with the relatively steeper indifference curves: a) is indifferent between yams and xylophones. b)has a weaker preference for yams. c)has a stronger preference for yams. d)has inconsistent preferences.Assuming a linear budget constraint, consider the following utility maximization problem:U (x1, x2) = 2x10.5 + 4x20.5 1. Compute the Marshallian demand functions for goods 1 and good 2.2. Find the compensated demand function.3. Derive the expenditure function and verify that h (p, u) = ∇pe (p, u)4. Derive the indirect utility function and verify Roy's IdentitA consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Equivalent variation and compensation variation are equivalent ways of evaluating welfare. Discuss
- If bananas are on the x-axis and apples are on the y-axis, then the marginal rate of substitution is (select all that apply): MUa/MUbMUa/MUb MUb/MUaMUb/MUa the absolute value of the slope of the indifference curve that goes through the current consumption bundle.the absolute value of the slope of the indifference curve that goes through the current consumption bundle. the number of apples the consumer is willing to give up to get an additional banana.the number of apples the consumer is willing to give up to get an additional banana. the number of bananas the consumer is willing to give up to get an additional apple.Suppose Coffee and Tea have a perfect substitute indifference curve, with Coffee on the X-axisand Tea on the Y-Axis. We are also given that for the person, MRS = 10 and MRS < Px/Py.Graphically show and explain the optimal choice of the person. Show the necessarymathematical work to accompany your answer.An individual has an income of 240 and finds his satisfaction by consuming goods x1 for 2$ and x2 for 3$. It is known that the individual utility function is as follows U (x1, x2) = x1²x2³ Determine the value of x1 and x2 for maximum individual satisfaction and calculate the value of utility.
