Budget constraint

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Economics for Management Studies
Gordon Cleveland

110o0n PrVfeseorrlund Answers Problem Set 1 Ch.2 BudgetConstraint Problem 1:Mr. Slick has $30 to spend on Evian and PowerBars. The price of a Powerbar is $3, and the price of a bottle of Evian is $1. a) Draw a picture of Mr. Slick’s budget line (measure Evian on the horizontal axis and PowerBars on the vertical axis): PowerBar 18 14 10 6 2 2 6 10 14 18 22 26 30 34 Evian b) How many PowerBars can he afford if he buys 6 bottles of Evian? You can either read it off the graph or look at the budget line. LeP x denote the number of PowerBars: 3*x P+ 1*6 = 30. Solve it, P =8. c) What is the largest number of PowerBars he can afford? Once again you can either look at the vertical intercept in the graph above of use the budgetline. Let consumption of Evian be 0. Then 3 xP= 30 Ö x =P10. d) What is the slope of the budget line? (Be sure to include the sign) Let b be the slope, then b = -Ep/ P = - 1/3. e) Explain in plain English what this slope measures. It measures the number of Powerbars the market requires that he gives up to purchase one bottle of Evian. f) Using the price and income above write an equation for Mr. Slick’s budget constraint (denote Evian by x E and PowerBars by x aPd use the prices given above). 1*x E+ 3* xP≤ 30 g) Rearrange the equation of the budget line such that xPas a function of xE, i.e.Px = f Ex ) 1* xE+ 3* x P 30 3 xP= 30 - x E x = ଷ଴ି௑ಶ = 10 – ⅓ x P ଷ E h) Illustrate on your graph how the budget line from question a) changes when the price of Evian increases to $3 per bottle. i) Illustrate on your graph above how the budget line from question a) changes when his income decreases to $12. PowerBar 18 14 10 6 h 2 i 2 6 10 14 18 22 26 30 34 Evian Problem 2: Martha is preparing for exams in economics and sociology. She has time to read 40 pages in economics and 30 pages in sociology. In the same amount of time she could also read 30 pages of economics and 60 pages in sociology. a) Assuming that the number of pages per hour she can read of either subject does not depend on how she allocated her time, how mange pages of sociology could she read if she decided to spend all of her time on sociology and none on economics? (Show your work) By the statement above we know that the slope b of her budget line will be constant. Let xE be the number of pages she reads in economics and x S be the number of pages she reads in sociology. Let the slope of the budgetline b denote the number of pages in sociolog
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