[Nonlinear Budget Constraints] Suppose thatSimone has preferences that are representedby the utility function U(x, y) = V(xy), and shehas an income I = 20.(a) Suppose that px = 1 and py = 2. What isSimone's MRSX,y? What is her optimalbundle?%3D(b) Suppose now that Simone is subject torationing. What is her optimal bundle whenthe maximum amount of x she can purchaseis 15? When it's 10? When it's 5?(c) Suppose that the store where Simone doesher shopping has a sale going on, where the xis half-off, up to 4 units. Algebraically, px = 0.5for x < 4, but px = 1 for x > 4. That is, the priceper unit, up to four units of x is 1, but thenincreases to 2. The price of good y is py = 2.What is her new optimal bundle? (Note: itmay be helpful to plot the budget set. Whatare the possibilities for what a solution wouldlook like for this budget set?)

Answered: [Nonlinear Budget Constraints] Suppose…

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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9. A consumer has the utility function u(x,y) = =x+6y and the price of x is $1 and the price of y is $5. If the consumer's income is $40, what bundle of goods will maximize her utility? x = 20, y = 4 x=40, y = 0 x = 0, y = 8 x= 10, y = 6 A a. b. c. d.
3. [30+10] A consumer who consumes two goods and has the following utility function: U(x₁, x₂) = log(x₁ + 1) + log(x2 + 1), where ₁ and ₂ denote the monthly consumption of two goods. The consumer maximizes her utility subject to the following constraints: P₁x1 + P₂x2 ≤m, x₁ ≥ 0, X₂ ≥ 0, where p₁ > 0, p2 > 0 and m > 0. [Hint: Note that log f(x) = f(df (2).] 1_df f(x) dx (a) Write down the Kuhn-Tucker conditions for a point (x₁, x2) to solve the problem, and find all points that satisfy the conditions. Do any of those points solve the problem? (b) Show the above results by drawing indifference curves and budget set on the x₁x2 plane.
. (Figure 4.13) What rotated the budget constraint? Quantity of good Y 10 9 8 7 6 5 N WAS 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Quantity of good X an increase in the price of good X a decrease in income an increase in the price of good Y a decrease in the price of good Y
-3 For the utility function: U = X+Y⁰¹5, is there constant, increasing or diminishing marginal utility in x? a. Increasing b. Constant c. Decreasing d. There are no returns to marginal utility
Root beer Candy bars Quantity Total Marginal Quantity Total Marginal utility utility utility utility 0 0 0 0 0 0 1 60 60 1 80 80 2 110 50 2 150 70 3 150 40 3 200 50 4 180 30 4 230 30 5 200 20 5 240 10 6 210 10 6 240 0 Reference: Ref 6-9 (Table) Using the information in the table, assume the consumer has a weekly budget of $3, the price of a root beer is $1 and the price per candy bar is $0.50. The consumer maximizes utility by: purchasing three root beers. purchasing two root beers and two candy bars. purchasing six candy bars. purchasing four candy bars and one root beer.
Subpart 7 only
2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Amy's preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Amy spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 45 hours (and thus has 55 hours of leisure) and earns $250 per week. Use the grey point (star symbol) to indicate Amy's initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. CONSUMPTION (Dollars per week) 1000 900 800 700 600 500 400 300 200 100 0 0 + 10 20 30 40 50 60 70 80 LEISURE (Hours per week) 90 U3 100 110 Initial bundle + $200 Unemployment Benefits Equivalent Bundle, $100 Unemployment Benefits Equivalent Bundle ?
28 - Which of the following statements is true about the point where the budget line cuts the horizontal axis? a) Returns the slope of the budget line. B) It shows the marginal utility of the good on the horizontal axis. C) When all of the income is spent on the good on the horizontal axis, it shows the amount that can be bought from this good. D) It shows the rate of substitution between goods. TO) It represents the bundle of goods that makes the marginal utility of income zero.
part 3 4 5 Suppose Joan has a fixed income of 1000 and spends the entire income on commodity X and Y. The prices of commodity X and Y are 5 and 10 respectively.(i) Derive the consumer’s budget equation and sketch the line of this equation plotting Y on the vertical axis and X on the horizontal axis.(ii) What is the slope of the budget line (i) and what does it mean?(iii) Assuming income and price of X remain the same, show the effect of a 50 percent reduction in the price of Y on the consumer’s budget line.(iv) Show the effect of a 100 percent increase in income and a 50 percent reduction in prices on the consumer’s budget line.(v) If Joan’s U = X2Y2find the optimal bundle of X and Y that maximises Joan’s utility.
11. (Originally #7 on Homework #3) Consider a consumer with the following information: At the optimal consumption bundle this consumer consumes 3 boxes of apples and 3 boxes of oranges. If the Marginal Rate of Substitution of Apples for Oranges is 6 at the optimal consumption bundle (MRSA0= 6), and the price of a box of Oranges is $1.80, what is the price of a box of Apples? Show how you found your answer.
Principles of Economics 1 | S1 21/22 Time left 0:5) When the price of one good increases and the price of the other good and income are held constant, the budget line Select one: shifts parallel to the original budget line so that the new budget line is farther from the origin O b. shifts parallel to the original budget line so that the new budget line is closer to the origin rotates so that the intercept is farther from the origin on the axis representing the good that has experienced an increase in price O a. O c. O d. rotates so that the intercept is closer to the origin on the axis representing the good that has experienced an increase in price Next page

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