6 BUDGET CONSTRAINT (Ch. 2) ale Laurel can afford if she spends all of her money on ale. Since ale costs 1 dollar a bottle, her income in dollars is equal to the largest number of bottles she can afford. Alternatively, you can reason as follows. Since the bundles(20, 5) and(10, 10)cost the same, it must be that giving up 10 bottles of ale makes her able to afford an extra 5 loaves of bread. So bread costs twice as much as ale. The price of ale is I dollar, so the price of bread is 2 dollars. The bundle(20, 5) costs as much as her income Therefore her income must be20×1+5×2=30 When you have completed this workout, we hope that you will be able to do the following Write an equation for the budget line and draw the budget set on a graph when you are given prices and income or when you are given two points on the budget line Graph the effects of changes in prices and income on budget sets Understand the concept of numeraire and know what happens to the budget set when income and all prices are multiplied by the same positive amount Know what the budget set looks like if one or more of the prices · See that the idea of a“ budget set” can be applied to constrained choices where there are other constraints on what you can have, in addition to a constraint on money expenditure
6 BUDGET CONSTRAINT (Ch. 2) ale Laurel can afford if she spends all of her money on ale. Since ale costs 1 dollar a bottle, her income in dollars is equal to the largest number of bottles she can afford. Alternatively, you can reason as follows. Since the bundles (20, 5) and (10, 10) cost the same, it must be that giving up 10 bottles of ale makes her able to afford an extra 5 loaves of bread. So bread costs twice as much as ale. The price of ale is 1 dollar, so the price of bread is 2 dollars. The bundle (20, 5) costs as much as her income. Therefore her income must be 20 × 1+5 × 2 = 30. When you have completed this workout, we hope that you will be able to do the following: • Write an equation for the budget line and draw the budget set on a graph when you are given prices and income or when you are given two points on the budget line. • Graph the effects of changes in prices and income on budget sets. • Understand the concept of numeraire and know what happens to the budget set when income and all prices are multiplied by the same positive amount. • Know what the budget set looks like if one or more of the prices is negative. • See that the idea of a “budget set” can be applied to constrained choices where there are other constraints on what you can have, in addition to a constraint on money expenditure
NAME 2.1(0) You have an income of $40 to spend on two commodities. Com- modity 1 costs $10 per unit, and commodity 2 costs $5 per unit (a)Write down your budget equation. 10C1+5.T2=40 (b)If you spent all your income on commodity 1, how much could you buy? (c) If you spent all of your income on commodity 2, how much could you buy? 8 Use blue ink to draw your budget line in the graph below Blue li Red -Black shading acki 2 0 2 8 (d) Suppose that the price of commodity 1 falls to $5 while everything else stays the same. Write down your new budget equation. 5C1+5 40. On the graph above, use red ink to draw your new budget line (e) Suppose that the amount you are allowed to spend falls to $30, while the prices of both commodities remain at $5. Write down your budget quation. 5 1 +522= 30. Use black ink to draw this budget ()On your diagram, use blue ink to shade in the area representing com- modity bundles that you can afford with the budget in Part(e) but could not afford to buy with the budget in Part(a). Use black ink or pencil to shade in the area representing commodity bundles that you could afford with the budget in Part (a) but cannot afford with the budget in Part 2.2(0)On the graph below, draw a budget line for each case
NAME 7 2.1 (0) You have an income of $40 to spend on two commodities. Commodity 1 costs $10 per unit, and commodity 2 costs $5 per unit. (a) Write down your budget equation. 10x1 + 5x2 = 40. (b) If you spent all your income on commodity 1, how much could you buy? 4. (c) If you spent all of your income on commodity 2, how much could you buy? 8. Use blue ink to draw your budget line in the graph below. 0 246 8 2 4 6 x1 x2 8 Blue Line Red Line Black Line Black Shading Blue Shading (d) Suppose that the price of commodity 1 falls to $5 while everything else stays the same. Write down your new budget equation. 5x1+5x2 = 40. On the graph above, use red ink to draw your new budget line. (e) Suppose that the amount you are allowed to spend falls to $30, while the prices of both commodities remain at $5. Write down your budget equation. 5x1 + 5x2 = 30. Use black ink to draw this budget line. (f) On your diagram, use blue ink to shade in the area representing commodity bundles that you can afford with the budget in Part (e) but could not afford to buy with the budget in Part (a). Use black ink or pencil to shade in the area representing commodity bundles that you could afford with the budget in Part (a) but cannot afford with the budget in Part (e). 2.2 (0) On the graph below, draw a budget line for each case
8 BUDGET CONSTRAINT (Ch. 2) (a)pi= l, P2= 1, m= 15.(Use blue ink. (b)pi= 1, P2= 2, m= 20.(Use red ink. 1, 10.(Use black ink. d)pi p2, m= 15p1.(Use pencil or black ink. Hint: How much of good 1 could you afford if you spend your entire budget on good 1?) 5 Black line FRed Li 10 2.3(0) Your budget is such that if you spend your entire income, you can afford either 4 units of good a and 6 units of good y or 12 units of a d 2 units of y (a) Mark these two consumption bundles and draw the budget line in the 16
8 BUDGET CONSTRAINT (Ch. 2) (a) p1 = 1, p2 = 1, m = 15. (Use blue ink.) (b) p1 = 1, p2 = 2, m = 20. (Use red ink.) (c) p1 = 0, p2 = 1, m = 10. (Use black ink.) (d) p1 = p2, m = 15p1. (Use pencil or black ink. Hint: How much of good 1 could you afford if you spend your entire budget on good 1?) 0 5 10 15 20 5 10 15 x1 x2 20 Blue Line Red Line Black Line 2.3 (0) Your budget is such that if you spend your entire income, you can afford either 4 units of good x and 6 units of good y or 12 units of x and 2 units of y. (a) Mark these two consumption bundles and draw the budget line in the graph below. 0 4 8 12 16 4 8 12 x y 16
(b)What is the ratio of the price of x to the price of y? 1/2 (c) If you spent all of your income on a, how much a could you buy? 16 (d)If you spent all of your income on y, how mu ou bu 8 (e)Write a budget equation that gives you this budget line, where the 1.x+2y=1 I) Write another budget equation that gives you the same budget line, but where the price of r is 3. 3 +6y= 48 2.4(1) Murphy was consuming 100 units of X and 50 units of Y. The price of X rose from 2 to 3. The price of Y remained at 4 (a) How much would Murphy's income have to rise so that he can still exactly afford 100 units of X and 50 units of Y? $100 2.5(1) If Amy spent her entire allowance, she could afford 8 candy bars nd 8 comic books a week. She could also just afford 10 candy bars and 4 comic books a week. The price of a candy bar is 50 cents. Draw her budget line in the box below. What is Amy's weekly allowance? $6 Comic books 16 8 81216 Candy bars
NAME 9 (b) What is the ratio of the price of x to the price of y? 1/2. (c) If you spent all of your income on x, how much x could you buy? 16. (d) If you spent all of your income on y, how much y could you buy? 8. (e) Write a budget equation that gives you this budget line, where the price of x is 1. x + 2y = 16. (f) Write another budget equation that gives you the same budget line, but where the price of x is 3. 3x + 6y = 48. 2.4 (1) Murphy was consuming 100 units of X and 50 units of Y . The price of X rose from 2 to 3. The price of Y remained at 4. (a) How much would Murphy’s income have to rise so that he can still exactly afford 100 units of X and 50 units of Y ? $100. 2.5 (1) If Amy spent her entire allowance, she could afford 8 candy bars and 8 comic books a week. She could also just afford 10 candy bars and 4 comic books a week. The price of a candy bar is 50 cents. Draw her budget line in the box below. What is Amy’s weekly allowance? $6. 0 8 16 24 32 8 16 24 Candy bars Comic books 32 12
10 BUDGET CONSTRAINT (CI 2.6(0) In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Prices have been remark- ably stable for the last 50 years or so. Potatoes cost 2 crowns per sack meatballs cost 4 crowns per crock, and jam costs 6 crowns per jar (a) Write down a budget equation for a citizen named Gunnar who has an income of 360 crowns per year. Let P stand for the number of sacks of potatoes, M for the number of crocks of meatballs, and for the number of jars of jam consumed by Gunnar in a year. 2P+4M+6J (b) The citizens of this country are in general very clever people, but they are not good at multiplying by 2. This made shopping for potatoes excru- ciatingly difficult for many citizens. Therefore it was decided to introduce a new unit of currency, such that potatoes would be the numeraire. A sack of potatoes costs one unit of the new currency while the same rel- ative prices apply as in the past. In terms of the new currency, what is the price of meatballs? 2 crowns (c) In terms of the new currency, what is the price of jam? 3 crowns d)What would Gunnar's income in the new currency have to be for him to be exactly able to afford the same commodity bundles that he could afford before the change? 180 crowns (e)Write down Gunnar's new budget equation. P+2M+3J 180. Is Gunnar's budget set any different than it was before the change? N 2.7(0 Edmund Stench consumes two commodities, namely garbage and punk rock video cassettes. He doesnt actually eat the former but keeps it in his backyard where it is eaten by billy goats and assorted vermin The reason that he accepts the garbage is that people pay him $2 per sack for taking it. Edmund can accept as much garbage as he wishes at $6 e price. He has no other source of income. Video cassettes cost him (a) If Edmund accepts zero sacks of garbage, how many video cassettes can he buy?
10 BUDGET CONSTRAINT (Ch. 2) 2.6 (0) In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Prices have been remarkably stable for the last 50 years or so. Potatoes cost 2 crowns per sack, meatballs cost 4 crowns per crock, and jam costs 6 crowns per jar. (a) Write down a budget equation for a citizen named Gunnar who has an income of 360 crowns per year. Let P stand for the number of sacks of potatoes, M for the number of crocks of meatballs, and J for the number of jars of jam consumed by Gunnar in a year. 2P + 4M + 6J = 360. (b) The citizens of this country are in general very clever people, but they are not good at multiplying by 2. This made shopping for potatoes excruciatingly difficult for many citizens. Therefore it was decided to introduce a new unit of currency, such that potatoes would be the numeraire. A sack of potatoes costs one unit of the new currency while the same relative prices apply as in the past. In terms of the new currency, what is the price of meatballs? 2 crowns. (c) In terms of the new currency, what is the price of jam? 3 crowns. (d) What would Gunnar’s income in the new currency have to be for him to be exactly able to afford the same commodity bundles that he could afford before the change? 180 crowns. (e) Write down Gunnar’s new budget equation. P + 2M + 3J = 180. Is Gunnar’s budget set any different than it was before the change? No. 2.7 (0) Edmund Stench consumes two commodities, namely garbage and punk rock video cassettes. He doesn’t actually eat the former but keeps it in his backyard where it is eaten by billy goats and assorted vermin. The reason that he accepts the garbage is that people pay him $2 per sack for taking it. Edmund can accept as much garbage as he wishes at that price. He has no other source of income. Video cassettes cost him $6 each. (a) If Edmund accepts zero sacks of garbage, how many video cassettes can he buy? 0