Budget Constraints and Taxes: A Graphical Analysis - Prof. Justin Marion, Assignments of Microeconomics

Download Budget Constraints and Taxes: A Graphical Analysis - Prof. Justin Marion and more Assignments Microeconomics in PDF only on Docsity! Problem Set 1 Solution Guide Two goods are consumed by Sam, coffee and cigarettes. Sam has $50 to allocate between these two goods. The price of a cup of coffee is $2 and the price of a pack of cigarette is $5. a. Write down the inequality describing Sam’s budget constraint. Draw the budget line on a graph, taking care to label the slope and intercepts. Shade the area representing the budget set. Let X1 be the amount of cups of coffee; X2 be the amount of packs of cigarettes and P1 be the price of a cup of coffee; P2 be the price of a pack of cigarettes. With the total income of $50, the budget line is shown as below 2 X1+5X2= 50 Solve for X2 X2=10-2/5X1 Slope=-2/5 b. The government, worrying about the health effects of smoking, adds a quantity tax of $1 per pack of cigarettes that must be paid by Sam. Draw Sam’s new budget line on a new graph, indicating the new slope and intercepts. A quantity tax of $1 per pack is equal to increase the price that any consumer receives by $1. So the new price of a pack of cigarettes will be $6. With other condition unchanged, the answer for the change will be: 2X1+(P2+t)X2= 50 2X1+6X2=50 X2=50/6-1/3X1 Slope=-1/3 X1 X2 10 25 c. The cigarette company decides that its consumers are not hooked enough on their product and want to encourage more smoking. For every five packs purchased, they now give away one for free. Draw Sam’s new budget line, again carefully labeling the intercepts. (Ignore the quantity tax.) It is a “buy five get one free” case. The new budget line should be kinked at 5 and 11 packs and go up for one more free pack of cigarettes to 6 and 12 packs as shown in the figure. d. Return to the case without the tax or the free cigarette offer. The government reads recent research touting the athletic performance benefits of coffee and decides to ensure that people are drinking enough caffeine. They impose a lump sum income tax of $10 on each of its citizens and use the tax revenue to give each citizen five cups of coffee. Graph Sam’s new budget line and shade the feasible X1 X2 10 25 5 12 X1 X2 25 50/6 10