Question 1

Maria spends her entire budget and consumes 5 units of x and 6 units of y. The price of x is twice the price of y. Her income doubles and the price of y doubles, but the price of x stays the same. If she continues to buy 6 units of y, what is the largest number of units of x that she can afford?
A) 12
B) 10
C) 14
D) 5
E) There is not enough information to say.

Accepted Answer

B

Question 2

In year 1, the price of good x was $4, the price of good y was $1, and income was $70. In year 2, the price of x was $9, the price of good y was $2, and income was $70. On a graph with x on the horizontal axis and y on the vertical, the new budget line is
A) steeper than the old one and lies below it.
B) steeper than the old one and lies above it.
C) flatter than the old one and lies below it.
D) flatter than the old one and lies above it.
E) None of the above.

Accepted Answer

The new budget line is steeper because the price ratio of good x to good y has increased from 4:1 in year 1 to 9:2 in year 2. It lies below the old one because the same income now buys less of both goods due to the price increases.

Question 3

If all prices double and income triples, then the budget line will become steeper.

Accepted Answer

If all prices double, the slope of the budget line remains the same because the relative prices of the two goods do not change. If income triples, the budget line shifts outward and becomes flatter because the consumer can now afford more of both goods. Therefore, the budget line does not become steeper when prices double and income triples.

Question 4

If there are two goods and if one good has a negative price and the other has a positive price, then the slope of the budget line will be positive.

Accepted Answer

The slope of the budget line is determined by the ratio of the prices of the two goods. If one good has a negative price and the other has a positive price, then the ratio of the prices will be negative. However, since the slope is a measure of the rate at which one good can be exchanged for the other, it will be represented as a positive number. Therefore, the slope of the budget line will be positive.

Question 5

There are 3 goods. The price of good 1 is -1, the price of good 2 is +1, and the price of good 3 is +2. It is physically possible for a consumer to consume any commodity bundle with nonnegative amounts of each good. A consumer who has an income of 10 could afford to consume some commodity bundles that include 5 units of good 1 and 6 units of good 2.

Accepted Answer

Since the consumer has an income of 10, they can afford to spend up to 10 dollars on the three goods. If they were to purchase 5 units of good 1 at a price of -1 each and 6 units of good 2 at a price of +1 each, they would spend (5 x -1) + (6 x 1) = -5 + 6 = 1 dollar. This means they still have 10 - 1 = 9 dollars left in their budget to spend on other goods, including good 3 which is priced at +2. Therefore, it is physically possible for the consumer to consume some commodity bundles that include 5 units of good 1 and 6 units of good 2.

Question 6

Clara spends her entire budget and consumes 5 units of x and 13 units of y. The price of x is twice the price of y. Her income doubles and the price of y doubles, but the price of x stays the same. If she continues to buy 13 units of y, what is the largest number of units of x that she can afford?
A) 10
B) 5
C) 12
D) 14
E) There is not enough information to say.

Accepted Answer

Initially, let the price of y be $P_y$ and the price of x be $P_x = 2P_y$. Clara's initial income is $I$. Her expenditure on y is $13P_y$ and on x is $5(2P_y) = 10P_y$, so her total expenditure (which equals her income) is $13P_y + 10P_y = 23P_y$. Therefore, $I = 23P_y$.When her income doubles and the price of y doubles, her new income is $2I = 2(23P_y) = 46P_y$, and the new price of y is $2P_y$. If she buys 13 units of y at the new price, her expenditure on y is $13(2P_y) = 26P_y$.The remaining income for buying x is $46P_y - 26P_y = 20P_y$. Since the price of x remains $2P_y$, the largest number of units of x she can afford is $20P_y / (2P_y) = 10$.

Question 7

In year 1, the price of good x was $3, the price of good y was $2, and income was $90. In year 2, the price of x was $9, the price of good y was $6, and income was $90. On a graph with x on the horizontal axis and y on the vertical, the new budget line is
A) flatter than the old one and lies below it.
B) flatter than the old one and lies above it.
C) steeper than the old one and lies below it.
D) steeper than the old one and lies above it.
E) None of the above.

Accepted Answer

The answer of In year 1, the price of good...

Question 8

Harold lives on Doritos and seafood salads. The price of Doritos is 1 dollar per bag and the price of seafood salads is 2 dollars each. Harold allows himself to spend no more than 11 dollars a day on food. He also restricts his consumption to 6,500 calories per day. There are 1,500 calories in a bag of Doritos and 500 calories in a seafood salad. If he spends his entire money budget each day and consumes no more calories than his calorie limit, he can consume up to
A) 3 bags of Doritos per day but no more.
B) 1 bag of Doritos per day but no more.
C) 4 seafood salads per day but no more.
D) 4 bags of Doritos per day but no more.
E) None of the above.

Accepted Answer

The answer of Harold lives on Doritos and seafood salads....

Question 9

If all prices are doubled and money income is left the same, the budget set does not change because relative prices do not change.

Accepted Answer

Doubling all prices while keeping money income the same reduces the quantity of goods and services that can be purchased, effectively shrinking the budget set, even though relative prices remain unchanged.

Question 10

There are two goods. You know how much of good 1 a consumer can afford if she spends all of her income on good 1. If you knew the ratio of the prices of the two goods, then you could draw the consumer's budget line without any more information.

Accepted Answer

This is correct because with the ratio of prices, you can determine how much of good 2 the consumer can afford based on their budget constraint. The budget line represents all possible combinations of the two goods that the consumer can afford given their income and the prices of the two goods.

Question 11

If there are two goods with positive prices and the price of one good is reduced, while income and other prices remain constant, then the size of the budget set is reduced.

Accepted Answer

The size of the budget set remains constant since income and other prices are constant. However, the relative price of the goods changes and the budget constraint pivots, causing a new optimal consumption bundle to emerge.

Question 12

If there are two goods and the prices of both goods rise, then the budget line must become steeper.

Accepted Answer

The steepness (slope) of the budget line is determined by the relative prices of the two goods, not by their absolute prices. If both prices increase by the same proportion, the slope of the budget line remains unchanged, though the budget line shifts inward due to the reduced purchasing power.

Question 13

A decrease in income pivots the budget line around the bundle initially consumed.

Accepted Answer

A decrease in income causes the budget line to shift inward parallel to its original position, not pivot around the initially consumed bundle.

Question 14

If she spends all of her income on breadfruits and melons, Natalie can just afford 9 breadfruits and 10 melons per day. She could also use her entire budget to buy 3 breadfruits and 12 melons per day. The price of breadfruits is 8 yen each. How much is Natalie's income per day?
A) 313 yen
B) 317 yen
C) 309 yen
D) 303 yen
E) None of the above.

Accepted Answer

First, let's denote the price of a melon as $M$ yen. Given that the price of breadfruits is 8 yen each, we can set up two equations based on the information provided:1. For 9 breadfruits and 10 melons: $9 \times 8 + 10M = \text{Natalie's income}$2. For 3 breadfruits and 12 melons: $3 \times 8 + 12M = \text{Natalie's income}$From equation 1: $72 + 10M = \text{Natalie's income}$From equation 2: $24 + 12M = \text{Natalie's income}$Setting the two expressions for Natalie's income equal to each other gives us:$$72 + 10M = 24 + 12M$$Solving for $M$, we get:$$48 = 2M$$$$M = 24$$Substituting $M = 24$ back into either equation to find Natalie's income, we use equation 1:$$72 + 10 \times 24 = \text{Natalie's income}$$$$72 + 240 = 312$$Therefore, Natalie's income per day is 312 yen, which is not listed among the provided options, making the correct choice "E) None of the above."

Question 15

If she spends her entire budget, Betsy can afford 74 peaches and 9 pineapples. She can also just afford 14 peaches and 21 pineapples. The price of peaches is 17 cents. What is the price of pineapples in cents?
A) 95 cents
B) 5 cents
C) 22 cents
D) 85 cents
E) None of the above.

Accepted Answer

The answer of If she spends her entire budget, Betsy...

Question 16

If good 1 is on the horizontal axis and good 2 is on the vertical axis, then an increase in the price of good 1 will not change the horizontal intercept of the budget line.

Accepted Answer

An increase in the price of good 1 will decrease the quantity of good 1 that can be purchased if all income is spent on good 1, thus shifting the horizontal intercept of the budget line to the left.

Question 17

A consumer prefers more to less of every good. Her income rises, and the price of one of the goods falls while other prices stay constant. These changes must have made her better off.

Accepted Answer

An increase in income allows the consumer to purchase more of all goods, which makes her better off. If the price of one good falls, she can now afford even more of that good, and may still afford the same amount of other goods. Therefore, she is consuming more overall and is better off.

Question 18

If good 1 is measured on the horizontal axis and good 2 is measured on the vertical axis and if the price of good 1 is p₁ and the price of good 2 is p₂, then the slope of the budget line is - .

Accepted Answer

The answer of If good 1 is measured on the...

Question 19

Quincy lives on pretzels and seafood salads. The price of pretzels is 1 dollar per bag and the price of seafood salads is 2 dollars each. Quincy allows himself to spend no more than 14 dollars a day on food. He also restricts his consumption to 3,400 calories per day. There are 600 calories in a bag of pretzels and 200 calories in a seafood salad. If he spends his entire money budget each day and consumes no more calories than his calorie limit, he can consume up to
A) 2 bags of pretzels per day but no more.
B) 5 seafood salads per day but no more.
C) 4 bags of pretzels per day but no more.
D) 5 bags of pretzels per day but no more.
E) None of the above.

Accepted Answer

Let's first set up some equations to represent Quincy's restrictions. Let x be the number of bags of pretzels he buys and y be the number of seafood salads he buys.

1. Cost restriction:

1x + 2y <= 14

This is because he can spend at most 14 dollars, and pretzels cost 1 dollar per bag and seafood salads cost 2 dollars each.

2. Calorie restriction:

600x + 200y <= 3400

This is because pretzels have 600 calories per bag and seafood salads have 200 calories each, and he can consume at most 3400 calories.

Now we can graph these two inequalities on the coordinate plane.

1. Cost restriction:

If we set x=0, then 2y<=14 and y<=7. So the y-intercept is (0,7). If we set y=0, then 1x<=14 and x<=14. So the x-intercept is (14,0). Plotting these two points and drawing a line through them gives us:

y = (-1/2)x + 7

This line represents all possible combinations of pretzels and seafood salads that cost at most 14 dollars.

2. Calorie restriction:

If we set x=0, then 200y<=3400 and y<=17. So the y-intercept is (0,17). If we set y=0, then 600x<=3400 and x<=5.67 (which we round down to 5). So the x-intercept is (5,0). Plotting these two points and drawing a line through them gives us:

x = (3400/600)y

This line represents all possible combinations of pretzels and seafood salads that have at most 3400 calories.

Now we need to find the intersection point of these two lines, which represents the point where both restrictions are satisfied.

y = (-1/2)x + 7

x = (3400/600)y

Therefore,

x = (3400/600)(-1/2)x + (3400/600)(7)

x = (-17/12)x + (119/12)

x = 7

Substituting x=7 into the second equation gives us:

y = (3400/600)(7) = 39

So the intersection point is (7,39).

This means that Quincy can buy up to 7 bags of pretzels and 39 seafood salads, as long as he spends no more than 14 dollars and consumes no more than 3400 calories. However, we need to check if this is physically possible.

7 bags of pretzels have 7 x 600 = 4200 calories.

39 seafood salads have 39 x 200 = 7800 calories.

So in total, Quincy would be consuming 4200 + 7800 = 12000 calories, which is well below his limit of 3400 calories.

Therefore, Quincy can buy up to 7 bags of pretzels and 39 seafood salads, but no more. However, since he cannot buy a fractional number of pretzel bags, the practical answer is that he can buy up to 4 bags of pretzels and 19 seafood salads, which cost a total of 14 dollars and have a total of 3400 calories.

Question 20

If she spends all of her income on uglifruits and breadfruits, Maria can just afford 11 uglifruits and 4 breadfruits per day. She could also use her entire budget to buy 3 uglifruits and 8 breadfruits per day. The price of uglifruits is 6 pesos each. How much is Maria's income per day?
A) 115 pesos
B) 105 pesos
C) 114 pesos
D) 119 pesos
E) None of the above.

Accepted Answer

Let the income of Maria be I and the price of breadfruit be B.

From the given information, we can form two equations:

11U + 4B = I  --- (1)

3U + 8B = I   --- (2)

Where U is the price of uglifruits (6 pesos each).

We can solve these equations by eliminating I:

11U + 4B = 3U + 8B

8U = 4B

2U = B

Substituting this value in equation (1):

11U + 4(2U) = I

19U = I

If Maria spends all her income on buying 11 uglifruits and 4 breadfruits, she spends:

11U + 4(2U) = 19U

If she spends all her income on buying 3 uglifruits and 8 breadfruits, she spends:

3U + 8(2U) = 19U

So, either way Maria spends 19U pesos each day.

Using the price of uglifruits (6 pesos each), Maria's income per day is:

19U = 19(6) = 114 pesos.

Therefore, the answer is C (114 pesos).

Quiz 1: Budget Constraint

Maria spends her entire budget and consumes 5 units of x and 6 units of y. The price of x is twice the price of y. Her income doubles and the price of y doubles, but the price of x stays the same. If she continues to buy 6 units of y, what is the largest number of units of x that she can afford?

In year 1, the price of good x was $4, the price of good y was $1, and income was $70. In year 2, the price of x was $9, the price of good y was $2, and income was $70. On a graph with x on the horizontal axis and y on the vertical, the new budget line is

If all prices double and income triples, then the budget line will become steeper.

If there are two goods and if one good has a negative price and the other has a positive price, then the slope of the budget line will be positive.

Clara spends her entire budget and consumes 5 units of x and 13 units of y. The price of x is twice the price of y. Her income doubles and the price of y doubles, but the price of x stays the same. If she continues to buy 13 units of y, what is the largest number of units of x that she can afford?

In year 1, the price of good x was $3, the price of good y was $2, and income was $90. In year 2, the price of x was $9, the price of good y was $6, and income was $90. On a graph with x on the horizontal axis and y on the vertical, the new budget line is

If all prices are doubled and money income is left the same, the budget set does not change because relative prices do not change.

There are two goods. You know how much of good 1 a consumer can afford if she spends all of her income on good 1. If you knew the ratio of the prices of the two goods, then you could draw the consumer's budget line without any more information.

If there are two goods with positive prices and the price of one good is reduced, while income and other prices remain constant, then the size of the budget set is reduced.

If there are two goods and the prices of both goods rise, then the budget line must become steeper.

A decrease in income pivots the budget line around the bundle initially consumed.

If she spends all of her income on breadfruits and melons, Natalie can just afford 9 breadfruits and 10 melons per day. She could also use her entire budget to buy 3 breadfruits and 12 melons per day. The price of breadfruits is 8 yen each. How much is Natalie's income per day?

If she spends her entire budget, Betsy can afford 74 peaches and 9 pineapples. She can also just afford 14 peaches and 21 pineapples. The price of peaches is 17 cents. What is the price of pineapples in cents?

If good 1 is on the horizontal axis and good 2 is on the vertical axis, then an increase in the price of good 1 will not change the horizontal intercept of the budget line.

A consumer prefers more to less of every good. Her income rises, and the price of one of the goods falls while other prices stay constant. These changes must have made her better off.

If good 1 is measured on the horizontal axis and good 2 is measured on the vertical axis and if the price of good 1 is p1 and the price of good 2 is p2, then the slope of the budget line is - .

If she spends all of her income on uglifruits and breadfruits, Maria can just afford 11 uglifruits and 4 breadfruits per day. She could also use her entire budget to buy 3 uglifruits and 8 breadfruits per day. The price of uglifruits is 6 pesos each. How much is Maria's income per day?

If good 1 is measured on the horizontal axis and good 2 is measured on the vertical axis and if the price of good 1 is p₁ and the price of good 2 is p₂, then the slope of the budget line is - .