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True or False:
(a) If a consumer spends her entire income, then she has a strictly monotone utility function.
(b)The condition that ‘the marginal rates of substitution equal the ratio of prices’ is necessary but not sufficient for a given bundle to be a Walrasian demand.
(c) If U, V: R2 → R are such that U is a strictly increasing transformation of V then U and V must represent the same preferences.
(d) If the substitution effect is negative (in response to a price increase) then we know the Walrasian demand for the good in question (in response to the same price increase) will also be negative.
(e) A consumer’s utility is continuous and strictly monotone and when prices are given by p and income is I her Walrasian demand yields a utility of 7. Then, any bundle that yields a utility of at least 8 must cost more than I.
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- Please answer all (a) to (e), whether they are True or False:(a) If a consumer spends her entire income, then she has a strictly monotone utility function.(b) The condition that ‘the marginal rates of substitution equal the ratio of prices’ is necessary but not sufficient for a given bundle to be a Walrasian demand.(c) If U, V: R2 → R are such that U is a strictly increasing transformation of V then U and V must represent the same preferences.(d) If the substitution effect is negative (in response to a price increase) then we know the Walrasian demand for the good in question (in response to the same price increase) will also be negative.(e) A consumer’s utility is continuous and strictly monotone and when prices are given by p and income is I her Walrasian demand yields a utility of 7. Then, any bundle that yields a utility of at least 8 must cost more than IPlease answer all (a) - (e), whether they are True or False: (a) If a consumer spends her entire income, then she has a strictly monotone utility function. (b)The condition that ‘the marginal rates of substitution equal the ratio of prices’ is necessary but not sufficient for a given bundle to be a Walrasian demand. (c) If U, V: R2 → R are such that U is a strictly increasing transformation of V then U and V must represent the same preferences. (d) If the substitution effect is negative (in response to a price increase) then we know the Walrasian demand for the good in question (in response to the same price increase) will also be negative. (e) A consumer’s utility is continuous and strictly monotone and when prices are given by p and income is I her Walrasian demand yields a utility of 7. Then, any bundle that yields a utility of at least 8 must cost more than I.If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.
- (a) A good is a luxury if it has a budget elasticity larger than 1, (i.e., good k is a luxury if εk ≡∂qk/∂m *m/qk> 1). Show that when a good is a luxury, then if a consumer’s total budget rises, theywill raise the share of their budget they allocate to the good. (b) Suppose m is the total budget a consumer has available to spend on three electronic products,a laptop, a phone and a tablet. Can all three of these goods simultaneously be luxuries? Whyor why not?1/2 1/2 2. Cynthia has preferences represented by the utility function u(x) = x¹/² + x¹/² (a) Calculate Cynthia's marginal rate of substitution. (b) Calculate Cynthia's Marshallian Demand functions x(p, 1) and x(p,1). (c) Does Cynthia consider either of these goods to be Inferior Goods? (d) Show that Cynthia's demands generate an indirect utility function V(p,1)=√√IP₁P2 (e) Solve for Cynthia's expenditure function.(a) A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less, with diminishing MRS) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her new optimal X consumption? (b) Forget about (a). A consumer with I=$240 budget is shopping for apples (x) and oranges (y). Apples cost $1 each up until 60 units; thereafter each apple costs $2. Similarly, oranges cost $1 each up until 60 units, and thereafter $2 each. Draw the graph of feasible set of bundles for the consumer with relevant points and numbers (shade the feasible area), no explanation needed. (c)(HARD!) In (b), calculate the optimal bundle assuming the consumer’s utility function is u(x,y) = x5y.
- A consumer has the following utility function: U (x, y) = (x + a) (y + b) Prices of the two goods x and y respectively are px and py and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m is high enough so that both x and y are strictly positive in equilibrium. (a) Solve the consumer’s optimization problem and express the demand for the two goods in terms of prices and income. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Suppose an individual has the following utility function: U(X,Y)= min{X, 2Y}, and they choose marshallian demands gx,gy. Suppose you have an increase in px. Which of the following is true about the change in demand for good X, gx? (a) No substitution effect, because they only consume one of the goods. (b) No substitution effect, because they always consume the goods in fixed proportion. (c) No income effect, because they only consume one of the goods. (d) No income effect, because they always consume the goods in fixed proportion. Which of the following production functions exhibits constant returns to scale? (a) f(k,l) = 0.310.7 (b) f(k, l) = kl (c) f(k, 1) = ln(k)+ln(1) (d) f(k, l) In(k) + In(1) =(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.
- (c) If the preferences are concave, will the consumer ever consume both of the goods together?A utility function is given by the equation U = 20xe¬0.1x, where x is the number of glasses of wine consumed. (a) Show that this utility function has a maximum value and calculate the maximum utility. (b) Describe how marginal utility changes for glasses of wine consumed after the maximum utility is reached. Do you consider this reasonable? Give an explanation.The consumer’s utility function is u(x1, x2) = 2√x1 + √(x2/4) (a) Determine the equilibrium condition for MRS21 and prices p1, p2. (b) Express the general form of D1(p1, p2, m), D2(p1, p2, m). (c) Calculate the desired amounts x1, x2 for p1 = 8, p2 = 2, m = 80. (d) Express the general form of income elasticity for commodity x1. Please show working step by step for b,c,d with final values of solution like in a