Question 1

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

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 2

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 3

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

Accepted Answer

E

Question 4

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?

Accepted Answer

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

Question 5

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

Accepted Answer

Let's start with the calorie limit: 
- 3400 calories per day 
- Each bag of pretzels has 600 calories 
- Each seafood salad has 200 calories

Let's use P to represent the number of bags of pretzels Quincy can eat and S to represent the number of seafood salads he can eat:

- Total calories = 600P + 200S 
- Total spending = 1P + 2S <= 14 (Quincy's daily budget)

Now we need to find the maximum values of P and S that satisfy both constraints.

First, let's look at the spending limit:

1P + 2S <= 14

If we set S = 0, we get:

1P <= 14

P <= 14 (maximum number of pretzel bags Quincy can buy with his entire budget)

So Quincy can buy at most 14 bags of pretzels with his entire budget.

Now let's look at the calorie limit:

600P + 200S <= 3400

Divide both sides by 200:

3P + S <= 17

If we set S = 0, we get:

3P <= 17

P <= 5.666...

But Quincy can't buy a fraction of a bag of pretzels. So he can buy at most 5 bags of pretzels to stay under his calorie limit.

We can also solve for S:

S <= 17 - 3P

If we set P = 4, we get:

S <= 5

So Quincy can also buy up to 5 seafood salads to stay under his calorie limit.

Therefore, the best choice is C: Quincy can consume up to 4 bags of pretzels and 5 seafood salads per day, spending 13 dollars in total and consuming exactly 3400 calories.

Question 6

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 7

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 8

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

When the consumer's income rises, she can afford to purchase more of every good. If the price of one good falls while other prices stay constant, she can now purchase even more of that particular good with her higher income. This increase in purchasing power and ability to consume more of every good makes her better off, indicating that the statement is true.

Question 9

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 and can afford to consume some commodity bundles with 5 units of good 1 and 6 units of good 2, we can set up the following equation:

10 = 5(F1S1 - F101) + 6(F1S1 + F101)

Simplifying, we get:

10 = 11F1S1 + F101

This means that as long as F1S1 and F101 are chosen such that they satisfy this equation, the consumer can afford to consume 5 units of good 1 and 6 units of good 2. Since we have no restrictions on the values of F1S1 and F101, it is physically possible for the consumer to consume such bundles. The price of good 3 is irrelevant to this calculation. Therefore, the answer is A.

Question 10

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

Accepted Answer

When all prices double and income triples, the budget line shifts outward but does not necessarily become steeper since the slope of the budget line, which represents the price ratio of the two goods, remains unchanged.

Question 11

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 -p₂/p₁.

Accepted Answer

The slope of the budget line is -p₁/p₂, representing the rate at which good 2 can be substituted for good 1 while staying within the budget.

Question 12

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 13

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?

Accepted Answer

The answer of Maria spends her entire budget and consumes...

Question 14

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?

Accepted Answer

Let x be the number of uglifruits Maria can buy per day and y be the number of breadfruits she can buy per day.
From the given information, we have the following two equations:
6x + y = Maria's income
11x + 4y = Maria's income

Solving these equations simultaneously, we get:
x = 23
y = 130

Substituting these values in either of the equations, we get:
Maria's income = 6x + y = 6(23) + 130 = 268

Therefore, Maria's income per day is 268 pesos. The closest option is C) 114 pesos.

Question 15

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

Accepted Answer

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

Question 16

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?

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 17

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?

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 18

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 19

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

The ratio of the prices of the two goods allows us to determine the slope of the budget line, which in turn determines how much of each good can be purchased at different levels of income. Therefore, knowing the ratio of prices is sufficient to draw the budget line.

Question 20

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, then the budget line will still have a positive slope because the negative price will be cancelled out by the negative sign of the quantity of that good on the budget line equation.

Quiz 1: Budget Constraint-Part A