Consider the utilityfunction u(x1,x2) = 2lnx1+lnx2. Initially, the prices are p1 = $2 and p2 =...
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Consider the utilityfunction u(x1,x2) = 2lnx1+lnx2. Initially, the prices are p1 = $2 and p2 = $1 per unit. The consumer has an income of $18. Then, the price of good x1 increases to p'1 = $3 per unit.
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State the consumer's maximization problem and use this problem to derive his demand functions for the two goods.
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Determine whether the two goods are ordinary or Giffen.
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Determine whether the demand functions for the two goods are elastic, inelastic or unit elastic.
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Calculate the income elasticities for the two goods. Are they normal? Are they luxuries or necessaries? Justify your answers.
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Find his optimal consumption bundle and his utility level (round your answers to two decimal places) before and after the price change.
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Calculate the compensating variation and equivalent variation of the price change (round your answers to two decimal places). What is the relationship between compensating variation and equivalent variation?
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Homework Answers
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Consider the utilityfunction u(x1,x2) = 2lnx1+lnx2. Initially,
the prices are p1 = $2 and p2 =...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where I and y are the two goods she consumes. The price of good r is p ,. The price of good y is Py. Her income is m. (a) Write her maximization problem and find her demand functions for the two goods. Is it always possible to have an interior solution? Justify your answer. (b) Are the two goods ordinary or giffen? Are the...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find the initial optimal bundle. ii. If the prices change to (6, 2), find the new optimal bundle. Show this in your graph in (i). iii. How much of the change in demand for x1 is due to the substitution effect? How much due to...
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect...
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect utility function v(p, w). (b) Find the Hicksian demand function h(p, u) and the expenditure function e(p, u). (c) For the remainder of the problem, suppose α = 4 and w = 5. If p = (2,1), what is5 the optimal bundle? What is the utility of that bundle? [Leave your answer in terms of fractions and exponents] (d) Suppose the price of good...
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect...
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect utility function v(p, w). (b) Find the Hicksian demand function h(p, u) and the expenditure function e(p, u). (c) For the remainder of the problem, suppose α = 4 and w = 5. If p = (2,1), what is5 the optimal bundle? What is the utility of that bundle? [Leave your answer in terms of fractions and exponents] (d) Suppose the price of good...
Consider two goods, good 1 and good 2. The consumer’s utility function is given by U(x1,x2)=V(x1)+x2....
Consider two goods, good 1 and good 2. The consumer’s utility function is given by U(x1,x2)=V(x1)+x2. Derive the ordinary demand function of good 1. When the market price of good 1 is given P1=P1' , derive the consumer’s surplus. If the price is changed to P1=P1", prove that the change measured by consumer’s surplus is the same as the Compensating variation. Also prove that it is the same as Equivalent variation.
Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of...
Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of good 1 and good 2 are p1 = P2 = 4. The consumer's income is m = 120. (a) Find the consumer's preferred bundle. (b) Draw the consumer's budget line. (c) On the same graph, indicate the consumer's preferred bundle and draw the indifference curve through it. (d) Now suppose that the consumer gets a discount on good 1: each unit beyond the 4th...
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...
a. U(r, 2)xfr + a)°(x2 + b)1-a d. U(,)( h. U(, 2) 1. For each of...
a. U(r, 2)xfr + a)°(x2 + b)1-a d. U(,)( h. U(, 2) 1. For each of the utility functions above, find the consumer's opti mal consumption bundle when prices of goods 1 and 2 are pi and P2, and the consumer has an income m 2. For each of the utility functions above, find the consumer's opti mal consumption bundle when prices of goods 1 and 2 are pi and P2, and the consumer has an endowment (e1, e2) of...
please show all math work EXERCISE 3 Consider a consumer who consumes two goods and has...
please show all math work
EXERCISE 3 Consider a consumer who consumes two goods and has utility function u(x1, x2) = x2 + VX1. Income is m, the price of good 2 is 1, and the price of good 1 changes from p to (1+t)p. Compute the compensating variation, the equivalent variation, and the change in consumer's surplus for a change in the price of good 1, holding income and the price of good 2 fixed.
Intermediate Microeconomics. Please show work for each section. Thank you. EXERCISE 3 Consider a consumer who...
Intermediate Microeconomics. Please show work for each section.
Thank you.
EXERCISE 3 Consider a consumer who consumes two goods and has utility function U(X1, X2) = x2 + VX1. Income is m, the price of good 2 is 1, and the price of good 1 changes from p to (1+t)p. Compute the compensating variation, the equivalent variation, and the change in consumer's surplus for a change in the price of good 1, holding income and the price of good 2...
Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of good 1 and good 2 are p1 = P2 = 4. The consumer's income is m = 120. (a) Find the consumer's preferred bundle. (b) Draw the consumer's budget line. (c) On the same graph, indicate the consumer's preferred bundle and draw the indifference curve through it. (d) Now suppose that the consumer gets a discount on good 1: each unit beyond the 4th...
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...
a. U(r, 2)xfr + a)°(x2 + b)1-a d. U(,)( h. U(, 2) 1. For each of the utility functions above, find the consumer's opti mal consumption bundle when prices of goods 1 and 2 are pi and P2, and the consumer has an income m 2. For each of the utility functions above, find the consumer's opti mal consumption bundle when prices of goods 1 and 2 are pi and P2, and the consumer has an endowment (e1, e2) of...
please show all math work
EXERCISE 3 Consider a consumer who consumes two goods and has utility function u(x1, x2) = x2 + VX1. Income is m, the price of good 2 is 1, and the price of good 1 changes from p to (1+t)p. Compute the compensating variation, the equivalent variation, and the change in consumer's surplus for a change in the price of good 1, holding income and the price of good 2 fixed.
Intermediate Microeconomics. Please show work for each section.
Thank you.
EXERCISE 3 Consider a consumer who consumes two goods and has utility function U(X1, X2) = x2 + VX1. Income is m, the price of good 2 is 1, and the price of good 1 changes from p to (1+t)p. Compute the compensating variation, the equivalent variation, and the change in consumer's surplus for a change in the price of good 1, holding income and the price of good 2...
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