"Two goods, A and B are perfect substitutes with prices $PA and $PB respectively. The income of an individual is given by $Y. Initially, $PA = $PB. It is claimed that in a particular situation where $I is assumed to remain unchanged and if due to some exogenous factor, SPB < $PA, the budget line will pivot, become flatter and optimal bundle will be a corner solution (0,B*) and no other possibility would exist.

"Two goods, A and B are perfect substitutes with prices $PA and $PB respectively. The income of an individual is given by $Y. Initially, $PA = $PB. It is claimed that in a particular situation where $I is assumed to remain unchanged and if due to some exogenous factor, SPB < $PA, the budget line will pivot, become flatter and optimal bundle will be a corner solution (0,B*) and no other possibility would exist.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter5: Income And Substitution Effects

Section: Chapter Questions

Problem 5.1P

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Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?
Q4. Explain with the aid of well labelled diagram(s) whether this statement is True, False or Uncertain, given the information provided below:“Two goods, A and B are perfect substitutes with prices $PA and $PB respectively. The income of an individual is given by $Y. Initially, $PA = $PB.It is claimed that in a particular situation where $I is assumed to remain unchanged and if due to some exogenous factor, $PB < $PA, the budget line will pivot, become flatter and optimal bundle will be a corner solution (0,B*) and no other possibility would exist.
1 explain With the aid of two well labelled diagram(s) with before and after transitions whether the statement below is True, False or Cannot be determined, given the information provided: Two commodities, P and Q are perfect substitutes with per unit prices of $PP and $PQ respectively. The income of an individual is given by $I. It is also given that initially, $PP = $PQ. Then it can be reasonably claimed that in a specific situation where $I remains unchanged and due to some exogenous factor, $PP < $PQ, then the budget line, which initially was overlapping an indifference curve will pivot, become flatter and resultantly, the optimal bundle will be always be a corner solution at (0,Q*) and no other possibility would exist.
For each of the following statements, define all of the underlined terms. Then, explain why the statement is true or false. a. If a consumer views two goods as perfect substitutes, then their optimal choice will be a corner solution if MRS ≠ MRT. b. The substitution effect from a price increase states that the consumer will always choose a smaller amount of that good to consume. However, the income effect states that consumption can move in either direction. c. Suppose Alf and Bo have convex indifference curves. Alf likes units of "X" more than units of "Y" but Bo likes units of "Y" much more than units of "X." Then, in the optimum, Alf's marginal rate of substitution will be different from Bo's even if they face the same prices. d. Economists assume that preferences are ordinal. This implies that given two utility functions and one is a monotonic transformation of the other, then they represent the same preferences over bundles of goods.
33. Suppose MRSx,y = MUx/MUy = 0.1(a) If the consumer substitutes 10 units of X for one unit of Y, then the utility remainsunchanged(b) Regardless of prices, the consumer will only consume Y(c) If the consumer substitutes 1 unit of Y for 0.1 unit of X, then the utility remainsunchanged(d) Regardless of prices, the consumer will only consume X
For the case of two goods, give an example of a utility function U(x1, x2) that represents the preferences of a consumer who regards the two goods as perfect complements. Next, take the transformation f(U) = U³ of the your example utility function and explain if this newly gener ated function represents the original preferences. Further, provide clear arguments supporting or rejecting the claim that "f(U(x1, x2)) must be strongly increasing in (x1, x2)."
Explain with the aid of well labelled diagram(s) with before and after transitions whether the statement below is True, False or Cannot be determined, given the information provided: “Two commodities, P and Q are perfect substitutes with per unit prices of $PP and $PQ respectively. The income of an individual is given by $I. It is also given that initially, $PP = $PQ. Then it can be reasonably claimed that in a specific situation where $I remains unchanged and due to some exogenous factor, $PP < $PQ, then the budget line, which initially was overlapping an indifference curve will pivot, become flatter and resultantly, the optimal bundle will be always be a corner solution at (0,Q*) and no other possibility would exist.
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a. Is the “more is better” assumption satisfied for both goods? Explain.b. What type of function is this? Explain.c. Provide expressions for the marginal utilities of x and y and does the marginal utility of x increase, remain constant, or diminish as the consumer buysmore units of x? Explain. Does the marginal utility of y increase, remain constant, or diminish as the consumer buysmore units of y? Explain.d. Provide an expression for the marginal rate of substitution of x for y.e. Is MRSx,y diminishing, constant, or increasing as the consumer substitutes more x for y alongan indifference curve? Explain.f. On a graph with x on the horizontal axis and y on the vertical axis, draw the indifferencecurves for U1 and U2 where U2 has a higher value than U1
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Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y). a. Derive his demand functions for x and y. Are they homogeneous in income and prices? b. Assuming I = $60 and px = $1, graph his demand curve for y. c. Repeat part (b) for the case in which px = $2.
Suppose that a consumer has a choicebetween two goods, X and Y. If the price of X is $2 and the priceof Y is $3, how much of X and Y does the consumer purchaseper period, given an income of $17 per period? Use the followinginformation about marginal utility:Units MUX MUY1 10 52 8 43 2 34 2 25 1 2