Question 1

Goods 1 and 2 are perfect complements and a consumer always consumes them in the ratio of 2 units of good 2 to 1 unit of good 1. If a consumer has an income of $300 and if the price of good 2 changes from $5 to $6, while the price of good 1 stays at $1, then the income effect of the price change

Accepted Answer

The answer of Goods 1 and 2 are perfect complements...

Question 2

Suppose that Agatha has $465 to spend on tickets for her trip. She intends to spend the entire amount $465 on tickets and prefers traveling first class to traveling second class. She needs to travel a total of 1,500 miles. Suppose that the price of first-class tickets is $.40 per mile and the price of second-class tickets is $.10 per mile. How many miles will she travel by second class?

Accepted Answer

The answer of Suppose that Agatha has $465 to spend...

Question 3

The following can be said about the income and substitution effects of a price increase on the demand for a good whose price rose:

Accepted Answer

The income effect is the change in demand resulting from a change in purchasing power due to a change in price, while the substitution effect is the change in demand resulting from a change in the relative price of the good to other goods.

When the price of a good rises, the income effect and substitution effect both work to decrease demand for the good. However, the income effect can be positive or negative, depending on the income elasticity of demand. If the good is a normal good, meaning that as income increases, demand also increases, then the income effect will be negative (a decrease in income leads to a decrease in demand) and the substitution effect will be negative (consumers will switch to buying other goods). However, if the good is an inferior good, meaning that as income increases, demand decreases, then the income effect will be positive (a decrease in income leads to an increase in demand) and the substitution effect will be negative (consumers will switch to buying other, higher-quality goods).

Therefore, while the substitution effect is always negative (as the price of the good increases, consumers will switch to buying other goods), the income effect can be either positive or negative. Thus, choice C is the best answer.

Question 4

Polly consumes crackers and fruit. The price of fruit rose and the price of crackers stayed constant. The income effect on Polly's demand is

Accepted Answer

The income effect measures the change in quantity demanded of a good due to a change in income. In this case, Polly's income hasn't changed, but the price of fruit has. The price increase will make Polly feel poorer, and reduce her overall purchasing power, resulting in a decreased demand for both fruit and crackers. The magnitude of the change in demand for fruit due to the income effect can be found by calculating the change in Polly's purchasing power as a result of the increase in fruit prices and multiplying that by her original consumption of fruit. Option B describes the correct calculation for the income effect in this scenario.

Question 5

Neville from your workbook has a friend named Cedric. Cedric has the same demand function for claret as Neville, namely q = .02m - 2p, where m is income and p is price. Cedric's income is $6,000 and he initially had to pay a price of $40 per bottle of claret. The price of claret rose to $60. The substitution effect of the price change

Accepted Answer

The substitution effect is calculated by keeping utility constant and only considering the change in price. Initially, Cedric's demand is q = 0.02(6000) - 2(40) = 40. After the price increase, the demand at the new price is q = 0.02(6000) - 2(60) = 20. The substitution effect is the change in demand due to the price change alone, which is 40 - 20 = 20. However, the correct calculation for the substitution effect involves finding the hypothetical demand if the price change occurred but income was adjusted to keep utility constant. This typically requires more information or assumptions about utility, but given the options, the closest choice is A, which suggests a reduction by 24.

Question 6

Suppose that bananas are a normal good and Woody is currently consuming 100 bananas at a price of 10 cents each.

Accepted Answer

The answer of Suppose that bananas are a normal good...

Question 7

Charlie consumes apples and bananas. His utility function is U(X_A, X_B) = x_Ax²_B. The price of apples is $1 the price of bananas is $2, and his income is $30 per week. If the price of bananas falls to $1

Accepted Answer

The answer of Charlie consumes apples and bananas. His utility...

Question 8

Ben consumes two goods and his utility function is U(x₁, x₂) = x²₁x⁴₂. The price of good 2 does not change and his income does not change, but the price of good 1 decreases.

Accepted Answer

The price decrease of good 1 will increase the marginal utility per dollar spent on good 1, leading Ben to consume more of good 1 and less of good 2. This is the substitution effect. The income effect is zero since his income did not change. Therefore, the decrease in the demand for good 2 is due to the substitution effect only. This means the demand for good 2 will decrease, while the demand for good 1 will increase due to the substitution effect, leading to an overall shift in Ben's consumption towards good 1.

Question 9

Charlie's utility function is x_Ax_B. The price of apples used to be $1 per unit and the price of bananas was $2 per unit. His income was $40 per day. If the price of apples increased to $2.25 and the price of bananas fell to $1.25, then in order to be able to just afford his old bundle, Charlie would have to have a daily income of

Accepted Answer

To determine the new income required to afford the old bundle, we calculate the cost of the old bundle at the new prices. Let's assume Charlie used to buy $x$ apples and $y$ bananas. At the old prices, $1x + 2y = 40$. We don't know the exact quantities of apples and bananas, but we know the total cost. At the new prices, the cost of the same quantities would be $2.25x + 1.25y$. To find the new income required, we substitute the old quantities into the new price equation, but since we don't have the quantities, we can't directly calculate this. However, the correct approach involves understanding that the new income must cover the increased cost of apples and the decreased cost of bananas. Given the choices, only one reflects a plausible adjustment in income to cover the increased cost of apples (which has more than doubled) and the decreased cost of bananas. Without the exact quantities, we can't calculate directly, but we can infer that the correct answer must account for a significant increase in income to maintain the same consumption bundle, making A the most plausible choice based on the information provided and the need for a substantial increase in income to afford the old bundle at the new prices.

Question 10

Rob consumes two goods, x and y. He has an allowance of $50 per week and is not endowed with either of the goods. If the price of good x increases and his substitution and income effects change demand in opposite directions,

Accepted Answer

If the price of good x increases and Rob's demand for x decreases, while his demand for y increases, it means that good x is an inferior good. The income effect (less income due to the increased price of x) leads to a decrease in the demand for x, while the substitution effect (x becoming relatively more expensive compared to y) leads to an increase in the demand for y. This scenario is consistent with the law of demand and does not violate the Weak Axiom of Revealed Preference (WARP). Therefore, the correct answer is B.

Question 11

In 2000, Bruce spent his income on two goods, x and y. Between 2000 and 2001, the price of good x rose by 8% and the price of good y rose by 8%. In 2001, Bruce bought the same amount of x as he bought in 2000, but he bought more of good y than he had bought in 2000.

Accepted Answer

If the quantity demanded of good y increases as income increases, then it is a normal good. Since Bruce bought more of good y in 2001 than he did in 2000, despite the increase in its price, it must be a normal good. There is no evidence to suggest that x is an inferior good.

Question 12

Neville from your workbook has a friend named Peregrine. Peregrine has the same demand function for claret as Neville, namely q = .02m - 2p, where m is income and p is price. Peregrine's income is $6,500 and he initially had to pay a price of $50 per bottle of claret. The price of claret rose to $60. The substitution effect of the price change

Accepted Answer

To calculate the substitution effect, we hold real income constant and calculate the change in quantity demanded due to the change in price. 
Initial quantity demanded:
q = 0.02(6500) - 2(50) = 70
New quantity demanded:
q' = 0.02(6500) - 2(60) = 56
The change in quantity demanded due to the price change is: 
ΔqS = q' - q = 56 - 70 = -14
Therefore, the substitution effect of the price change reduced Peregrine's demand by 14 bottles of claret.

Question 13

Charlie's utility function is x_Ax_B. The price of apples used to be $1 per unit and the price of bananas was $2 per unit. His income was $40 per day. If the price of apples increased to $1.50 and the price of bananas fell to $1.75, then in order to be able to just afford his old bundle, Charlie would have to have a daily income of

Accepted Answer

Charlie's initial bundle includes 1 unit of apples and 1 unit of bananas. At the initial prices, this bundle costs $3 ($1 for the apple and $2 for the banana). Charlie's income is $40, so he can afford to purchase 40/3 ≈ 13.33 of these bundles.

If the price of apples increases to $1.50, then the bundle will cost $3.50 ($1.50 for the apple and $2 for the banana). In order to purchase 13.33 of these bundles, Charlie would need 13.33 × $3.50 = $46.67.

If the price of bananas falls to $1.75, then the bundle will cost $2.75 ($1.50 for the apple and $1.75 for the banana). In order to purchase 13.33 of these bundles, Charlie would need 13.33 × $2.75 = $36.67.

Therefore, in order to afford his old bundle at the new prices, Charlie would need a daily income of $46.67, which is answer choice B.

Question 14

Waldo consumes only apples and bananas and bananas are an inferior good for him. The price of apples increases, but there is an increase in his income that keeps him on the same indifference curve as before. (Waldo has convex preferences, and he prefers more to less of either good.)

Accepted Answer

Since bananas are an inferior good for Waldo, their consumption will increase as his income increases but the price of apples is increasing which will make him substitute away from apples towards bananas. Therefore, he will buy more bananas and fewer apples after the change.

Question 15

Herbie consumes two goods and his utility function is U(x₁, x₂) = x³₁x⁴₂. The price of good 2 does not change and his income does not change, but the price of good 1 decreases.

Accepted Answer

According to the utility function, both goods are normal goods, meaning that as income increases, the demand for both goods increase. Since the income does not change, the income effect is zero. The substitution effect dominates, which means that the decrease in the price of good 1 will make it relatively cheaper compared to good 2, and the consumer will substitute good 2 with good 1. Therefore, the demand for good 1 will increase, and the demand for good 2 will decrease.

Question 16

Goods 1 and 2 are perfect complements and a consumer always consumes them in the ratio of 2 units of good 2 to 1 unit of good 1. If a consumer has an income of $120 and if the price of good 2 changes from $3 to $4, while the price of good 1 stays at $1, then the income effect of the price change

Accepted Answer

The answer of Goods 1 and 2 are perfect complements...

Question 17

Charlie's utility function is x_Ax_B. The price of apples used to be $1, the price of bananas used to be $2, and his income used to be $40. If the price of apples increased to $5 and the price of bananas stayed constant, the substitution effect on Charlie's apple consumption would reduce his consumption by

Accepted Answer

To calculate the substitution effect, we need to hold Charlie's utility constant and find the new optimal bundle of goods with the new price ratio.

Initial prices: pa=$1, pb=$2
Initial income: M=$40
Initial optimal bundle: (xa=8, xb=6)

New prices: pa=$5, pb=$2
New income: M=$40
New optimal bundle: (xa=4, xb=6)

Substitution effect: Δxa = xa(new) - xa(initial) = 4 - 8 = -4

Therefore, Charlie's apple consumption would reduce by 4 apples due to the substitution effect. The correct answer is option C.

Question 18

When the price of x rises, Marvin responds by changing his demand for x. The substitution effect is the part of this change that represents his change in demand

Accepted Answer

The answer of When the price of x rises, Marvin...

Question 19

Ernest's income elasticity of demand for natural gas is 0.4. His price elasticity of demand for natural gas is -0.3, and he spends 10% of his income on natural gas. What is his substitution price elasticity?

Accepted Answer

The substitution price elasticity can be calculated using the formula: substitution elasticity = price elasticity - (income elasticity * budget share). Substituting the given values: -0.3 - (0.4 * 0.1) = -0.3 - 0.04 = -0.34.

Question 20

Charlie's utility function is x_Ax_B. The price of apples used to be $1, the price of bananas used to be $2, and his income used to be $40. If the price of apples increased to $6 and the price of bananas stayed constant, the substitution effect on Charlie's apple consumption would reduce his consumption by

Accepted Answer

To find the substitution effect on Charlie's apple consumption, we need to look at how his utility changes due to the price change assuming that he still has the same level of utility. With the new prices, Charlie's marginal rate of substitution (MRS) between apples and bananas becomes:

MRS = (MU of Apples) / (MU of Bananas)
MRS = (dS1U1B1/dxS1U1B0) / (dS1U1B0/dxS1U1B1)
MRS = (1/(2(xS1U1B0)^2)) / (1/(6(xS1U1B0)^2))
MRS = 3/2

To see how Charlie's apple consumption changes, we can look at how the new MRS compares to the MRS at the initial prices:

MRS_old = (MU of Apples) / (MU of Bananas)
MRS_old = (dS1U1B1/dxS1U1B0) / (dS1U1B0/dxS1U1B1)
MRS_old = (1/(2(xS1U1B0)^2)) / (1/(2(xS1U1B0)^2))
MRS_old = 1

Since the new MRS is greater than the old MRS, this means that Charlie wants to consume relatively more bananas and less apples than before. Using the new prices and utility function, we can find Charlie's optimal bundle. Let xA be the new quantity of apples and xB be the new quantity of bananas:

MU of Apples / Price of Apples = MU of Bananas / Price of Bananas
dS1U1B1/dxA / 6 = dS1U1B0/dxB / 2

Simplifying this equation and substituting the expression for MRS, we get:

3(xS1U1B0)^2 dS1U1B1/dxA = (xS1U1B0)^2 dS1U1B0/dxB
3 dS1U1B1/dxA = dS1U1B0/dxB

Similarly, using the budget constraint:

Price of Apples x Quantity of Apples + Price of Bananas x Quantity of Bananas = Income
6xA + 2xB = 40

We can substitute xB = (40 - 6xA)/2 into the expression for MRS to get:

3 dS1U1B1/dxA = dS1U1B0/dx(40 - 6xA)/2
3 dS1U1B1/dxA = -3(xS1U1B0)^2/(40 - 6xA)^2

Solving for xA using these two equations, we get xA = 10 and xB = 15. Therefore, the change in Charlie's apple consumption is:

Delta xA = xA_new - xA_old = 10 - 40/1 = -30

This means that Charlie reduces his apple consumption by 30 units (not 30 apples since we don't know the size of an apple unit in this context). To convert this to the number of apples, we need to divide by the new price of apples:

Delta Apples = Delta xA / Price of Apples_new = -30 / 6 = -5

Therefore, Charlie reduces his apple consumption by 5 apples due to the price change. The closest answer choice is (C) 8.33 apples, but this is not the correct answer since it assumes that the decrease in apple consumption is proportional to the decrease in apple affordability (i.e., the percentage increase in the price of apples). However, the decrease in apple consumption is affected by both the increase in price and the change in MRS, which may not be proportional.

Quiz 7: Slutsky Equation