Homework Answers
To check for WARP, we will plot budget lines for all three cases and mark the bundle chosen by the consumer in all three cases.
It
is clear that these choices violate WARP. When the consumer was
choosing under second set of prices, the consumer chose a bundle
which was available with first set of prices and was not chosen.
Hence, the consumer preferred the bundle (1,2) over (2,1) under the
first set of prices and preferred (2,1) over (1,2) under the second
set of prices, which is a violation of WARP.
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Consider the following hypothetical consumption data of a consumer, Alice. 2. X2 X1 P2 Observation P1...
The utility function of the consumer is u(x1, x2) = VX1 + X2. a) Let P1...
The utility function of the consumer is u(x1, x2) = VX1 + X2. a) Let P1 = 2,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p. = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1,P2 = 4 and m = 4. Compared to point b), by how much would the consumer...
A consumer is observed to purchase X1 = 20, X2 = 10 at prices P1 =...
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1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s...
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s optimal consumption of good 1. (Hint: you can use the 5 step method or one of the demand functions derived in class to find the answer). 2.) Using the information from question 1, find Liz’s optimal consumption of good 2 3.) Lyndsay has utility given by u(x2,x1)=min{x1/3,x2/7}. If P1=$1, P2=$1, and I=$10, find Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief utility)....
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
8.3 Unanswered Consider u(x1, x2) = x95x95, I = 300,P1 = 25,p2 = 1. If Pidecreases...
8.3 Unanswered Consider u(x1, x2) = x95x95, I = 300,P1 = 25,p2 = 1. If Pidecreases from $25 to $9, what is the equivalent variation? Enter a number only, round to two decimals. If money needs to be taken away from the consumer include a negative sign. Type your response 8.4 Unanswered Consider u(x1, x2) = x9.5x2:5,1 = 300,P1 = 4,p2 = 1. If Piincreases from $4 to $9, what is the compensating variation? Enter a number only, round to...
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 +...
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 + x2. a) Let pı = 2 ,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p1 = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1, p2 = 4 and m = 4. Compared to point b),...
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes...
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given. > 1. What is special about P2 1) Find the demand functions for and x2 assuming these demand functions? Are both goods normal? Are these tastes homothetic? 2) Now find the demand functions for x1 and x2 assuming-<1. You probably P2 assumed the opposite above, so now will you find something different. Explain 3) Graph...
how did they dervice that to get 1/x1=p1/p2 income goes entirely to the consumption of good 2. If quasilinear,...
how did they dervice that to get 1/x1=p1/p2
income goes entirely to the consumption of good 2. If quasilinear, we sometimes say that there is a "zero income e income doesn't Thus the Engel curve for good 1 is a vertical line the demand for good 1 remains constant. For example, let us calculate the demand functions for t as yo u(x1, 2)= In a1+x2. Applying the first-order condition gives P1 P2
Consideru(x1, x2) = 2x0.5 + x2,1 = 200,p1 = 1,P2 = 4. If P2 increases from...
Consideru(x1, x2) = 2x0.5 + x2,1 = 200,p1 = 1,P2 = 4. If P2 increases from $4 to $8, what is the compensating variation? Enter a number only, round to two decimals. If money needs to be taken away from the consumer include a negative sign.
The utility function of the consumer is u(x1, x2) = VX1 + X2. a) Let P1 = 2,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p. = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1,P2 = 4 and m = 4. Compared to point b), by how much would the consumer...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
8.3 Unanswered Consider u(x1, x2) = x95x95, I = 300,P1 = 25,p2 = 1. If Pidecreases from $25 to $9, what is the equivalent variation? Enter a number only, round to two decimals. If money needs to be taken away from the consumer include a negative sign. Type your response 8.4 Unanswered Consider u(x1, x2) = x9.5x2:5,1 = 300,P1 = 4,p2 = 1. If Piincreases from $4 to $9, what is the compensating variation? Enter a number only, round to...
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 + x2. a) Let pı = 2 ,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p1 = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1, p2 = 4 and m = 4. Compared to point b),...
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given. > 1. What is special about P2 1) Find the demand functions for and x2 assuming these demand functions? Are both goods normal? Are these tastes homothetic? 2) Now find the demand functions for x1 and x2 assuming-<1. You probably P2 assumed the opposite above, so now will you find something different. Explain 3) Graph...
how did they dervice that to get 1/x1=p1/p2
income goes entirely to the consumption of good 2. If quasilinear, we sometimes say that there is a "zero income e income doesn't Thus the Engel curve for good 1 is a vertical line the demand for good 1 remains constant. For example, let us calculate the demand functions for t as yo u(x1, 2)= In a1+x2. Applying the first-order condition gives P1 P2
Consideru(x1, x2) = 2x0.5 + x2,1 = 200,p1 = 1,P2 = 4. If P2 increases from $4 to $8, what is the compensating variation? Enter a number only, round to two decimals. If money needs to be taken away from the consumer include a negative sign.
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