Consider an individual who considers x1 and x2 to be perfect substitutes at a rate of 2:1 i.e. he gets the same utility from consuming 2 units of x1 as he gets from consuming 1 unit of x2. Let his utility function be given as: U=x1+2x
Furthermore, let the price of x1 be $1 and the price of x2 be $4, while his income is fixed at $20. a) Graph the budget line with x1 on the x axis and x2 on the y-axis. (1 Marks) b) On the same sketch above, graph two indifference curves. (Be careful about the rate of substitution between both x1 and x2 and hence the slopes of the indifference curves). (2 Marks) c) What is the optimal bundle chosen by the consumer? What is her utility at this level? (2 Marks) d) Does the utility maximizing condition, i.e. MRS= MRT hold in this case? Why or why not? (2 Marks) e) How would your answer in part (c) change if the price of x1 increases and becomes $2? (3 Marks)
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Consider an individual who considers x1 and x2 to be perfect substitutes at a rate of 2:1 i.e. he gets the same utility from consuming 2 units of x1 as he gets from consuming 1 unit of x2. Let his utility function be given as: U=x1+2x
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...
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...
Suppose a consumer has quasi-linear utility: u(x1, x2) = 3.01 + x2. The marginal utilities are...
Suppose a consumer has quasi-linear utility: u(x1, x2) = 3.01 + x2. The marginal utilities are MU(X) = 2x7"! and MU2:) = 1. Throughout this problem, assume P2 = 1. (a) Sketch an indifference curve for these preferences (label axes and intercepts). (b) Compute the marginal rate of substitution. (c) Assume w> . Find the optimal bundle (this will be a function of pı and w). Why do we need the assumption w> (d) Sketch the demand function for good...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also,...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
2) If the price of automobiles were to increase substantially, the demand curve for gasoline would most likely A) shift...
2) If the price of automobiles were to increase substantially, the demand curve for gasoline would most likely A) shift leftward. B) shift rightward. C) become flatter. D) become steeper. 3) If the price of automobiles were to decrease substantially, the demand curve for automobiles would most likely A) shift rightward. B) shift leftward. C) remain unchanged. D) become steeper. 4) Suppose a market were currently at equilibrium. A rightward shift of the demand curve would cause A) an increase...
ZOOM Page 2 of 2 D. Consumer Decision Making Total Utility Candy Total Bananas Utility 1...
ZOOM Page 2 of 2 D. Consumer Decision Making Total Utility Candy Total Bananas Utility 1 50 40 2 94 2 76 132 3 106 4 162 4 128 5 182 5 138 1. Candy costs $2, bananas cost S. What is the utility maximizing quantity of candy and bananas to purchase, if you have an $8 budget? 2. I offer you the option to use your $8 to buy 3 pieces of candy and 2 bananas (yay candy!) Why...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1 u(x,y) = 2x+2y C2 u(x,y) = x^3/4y^1/4 C3 u(x,y) = min(x,y) C4 u(x,y) = min(4x,3y) On the appropriate graph, draw each consumer’s indifference curves through the following points: (2,2), (4,4), (6,6) and (8,8), AND label the utility level of each curve. Hint: Each grid should have 4 curves on it representing the same preferences but with different utility levels. 3. In the following parts,...
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...
Suppose a consumer has quasi-linear utility: u(x1, x2) = 3.01 + x2. The marginal utilities are MU(X) = 2x7"! and MU2:) = 1. Throughout this problem, assume P2 = 1. (a) Sketch an indifference curve for these preferences (label axes and intercepts). (b) Compute the marginal rate of substitution. (c) Assume w> . Find the optimal bundle (this will be a function of pı and w). Why do we need the assumption w> (d) Sketch the demand function for good...
ZOOM Page 2 of 2 D. Consumer Decision Making Total Utility Candy Total Bananas Utility 1 50 40 2 94 2 76 132 3 106 4 162 4 128 5 182 5 138 1. Candy costs $2, bananas cost S. What is the utility maximizing quantity of candy and bananas to purchase, if you have an $8 budget? 2. I offer you the option to use your $8 to buy 3 pieces of candy and 2 bananas (yay candy!) Why...
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