Question 1

John purchases two goods, x and y.Good x is an inferior good for some range of income.There must be another range of income for which good x is a normal good.

Accepted Answer

This statement is true. An inferior good is a good for which demand decreases as income increases, while a normal good is a good for which demand increases as income increases. Therefore, there must be a range of income where good x is a normal good since the demand for it would increase as income increases.

Question 2

Walt considers x and y to be perfect substitutes.They originally cost $10 and $9 respectively.His income is $720.One day the price of x drops to $8.

Accepted Answer

The substitution effect will lead Walt to buy more of the cheaper good, x, when its price drops, increasing the quantity of x by 90.

Question 3

A Giffen good must be an inferior good.

Accepted Answer

A Giffen good is a special type of inferior good for which demand actually increases as price increases.

Question 4

When the price of a good rises and income remains constant, there is a substitution effect on demand but there cannot be an income effect.

Accepted Answer

When the price of a good rises and income remains constant, there is not only a substitution effect (where consumers may substitute the more expensive good for a cheaper alternative) but also an income effect. The income effect occurs because the consumer's purchasing power decreases with the price increase, effectively making them feel poorer, which can lead to a decrease in the quantity demanded of the now more expensive good.

Question 5

Suppose a consumer has strictly convex preferences and her Engel curve for a good is a vertical line for some range of income.In that same income range, her demand curve for the good slopes down.

Accepted Answer

If the Engel curve is a vertical line for some range of income, it means that the consumer is willing to spend the same amount on the good regardless of changes in income. Since the preferences are strictly convex, the demand curve must slope down in that income range, as the consumer would want to purchase less of the good as price increases. This is consistent with the law of demand.

Question 6

In the case of homothetic preferences, the entire change in demand from a price change is due to the substitution effect.

Accepted Answer

In the case of homothetic preferences, both income and substitution effects influence the change in demand following a price change, but the income effect is proportional across income levels, maintaining constant expenditure shares.

Question 7

The compensated demand function refers to the demand function of someone who is adequately paid for what he or she sells.

Accepted Answer

The compensated demand function refers to the demand function of someone who is adequately compensated or compensated based on a certain wage rate. It is not specific to someone who sells a product, but rather for any worker who is paid a wage.

Question 8

A consumer has the utility function U(x, y)= x + 2y^1/2.The price of good x is 2 and the price of good y is 1.The consumer's income is 20.If the price of good y rises to 2, then entire change in demand for y is due to the substitution effect.

Accepted Answer

To determine whether the entire change in demand for y is due to the substitution effect, we can use the Slutsky equation:
∆xy = ∆x + (∂x/∂p)y * (p1/p2)
Where ∆xy is the total change in demand for y, ∆x is the substitution effect, (∂x/∂p)y is the income effect, and (p1/p2) is the ratio of the new and old prices.
Since the problem tells us that the price of y has risen to 2, and all other variables are constant, we can use this equation to solve for the substitution effect:
∆xy = ∆x + (∂x/∂p)y * (1/2)
We know that the income of the consumer is 20, and the prices of x and y are 2 and 1 respectively. Plugging these values into the utility function, we can solve for the demand functions for x and y:
x = 5 - 2y
y = 10 - 5√(2-x/5)
Using these demand functions, we can solve for the substitution effect:
∆x = (∂x/∂p)y * (p2 / p1) * ∆p
Since the price of y has risen from 1 to 2, and the price of x is constant, we have:
∆x = (∂x/∂p)y * (1/2) * (-1)
Taking the derivative of the demand function for x with respect to the price of y, we get:
(∂x/∂p)y = -2/5
Substituting in the values, we get:
∆x = (2/5) * (1/2) * (-1) = -1/5
Thus, the substitution effect is ∆x = -1/5.
Since the total change in demand for y is equal to the substitution effect (as given in the problem), and the income effect is zero, we can conclude that the entire change in demand for y is due to the substitution effect. Therefore, the answer is A.

Question 9

An increase in the price of a Giffen good makes the people who consume that good better off.

Accepted Answer

Giffen goods are inferior goods for which demand increases as the price increases, due to the income effect of the price increase outweighing the substitution effect. However, this does not make people better off; it simply means they end up buying more of the inferior good because they can no longer afford better alternatives.

Question 10

If two goods x and y are perfect complements, then if the price of x falls, the entire change in the demand for x is due to the income effect.

Accepted Answer

If goods x and y are perfect complements, then they are consumed in fixed proportions, regardless of their relative prices. Therefore, a change in the price of x will not affect the quantity demanded of x unless it becomes more affordable relative to the price of y. As a result, any change in the quantity demanded of x must be due to a change in income (i.e., the income effect).

Question 11

Cindy consumes goods x and y.Her demand for x is given by x(p_x, m)= 0.05m =5.15p_x.Now her income is $419, the price of x is $3, and the price of y is $1.If the price of x rises to $4 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS, then

Accepted Answer

Using the formula for the price effect on demand: Price effect = DI + DS We first need to calculate the initial demand for x: x(p_x, m) = 0.05m/(5.15p_x) Substituting the values given, we get: x(3, 419) = 0.05(419)/(5.15(3)) ≈ 4.09 Now, when the price of x changes to $4, we have: x(4, 419) = 0.05(419)/(5.15(4)) ≈ 3.07 The income effect can be calculated by holding the real income constant and assuming the price change is the only factor affecting demand. DI = x(p1, m)/x(p0, m) - 1 Substituting the values given, we get: DI = 3.07/4.09 - 1 ≈ -0.25 or -0.28 (rounded to two decimal places) To calculate the substitution effect, we need to adjust the consumer's income to keep her on the same indifference curve relative to the price change. New income = old income - (price change)x(initial quantity purchased) New income = 419 - (4 - 3)(4.09) = 413.76 Now we can calculate the new quantity purchased for x at the new price and with the new income: x(4, 413.76) = 0.05(413.76)/(5.15(4)) ≈ 3.08 DS = x(p1, m1)/x(p1, m0) - 1 Substituting the values given, we get: DS = 3.08/3.07 - 1 ≈ 0.33 or 0.34 (rounded to two decimal places) Therefore, the answer is (B) DI F1F1F1S1F1F1F10 F1F1F1S1F1F1F100.28 and DS F1F1F1S1F1F1F10 F1F1F1S1F1F1F104.88.

Question 12

If a good is an inferior good, then an increase in its price will increase the demand for it.

Accepted Answer

If a good is an inferior good, it means that as the consumer's income increases, the demand for that good decreases. Therefore, if the price of an inferior good increases, it would further decrease the demand for it.

Question 13

Cindy consumes goods x and y.Her demand for x is given by x(p_x, m)= 0.04m -4.24p_x.Now her income is $322, the price of x is $2, and the price of y is $1.If the price of x rises to $3 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS, then

Accepted Answer

The answer of Cindy consumes goods x and y.Her demand...

Question 14

Jessica's preferences for peanut butter and jelly are represented by the utility function U(p, j)= min{2p, 5j}.If prices and income change, but her old consumption bundle lies somewhere on her new budget line, she will not change her consumption.

Accepted Answer

If Jessica's old consumption bundle lies somewhere on the new budget line, it means that she can still afford to buy the same combination of peanut butter and jelly as before. Since her preferences are represented by a utility function, she will continue to consume the same combination to maximize her utility. Therefore, she will not change her consumption.

Question 15

Jimmy's utility function is U(a, b)= ab, where a is his consumption of apples and b is his consumption of bananas.If prices and income change in such a way that Jimmy's old consumption lies on his new budget line, then Jimmy will not change his consumption bundle.

Accepted Answer

Jimmy's utility function suggests he has perfect substitutes preferences (linear utility function), meaning he will consume only the good that gives him the highest utility per dollar spent. If prices or income change, even if his old consumption bundle lies on the new budget line, he may adjust his consumption to focus on the good that now offers more utility per dollar, assuming the price change affects the relative prices of apples and bananas.

Question 16

If the Engel curve slopes up, then the demand curve slopes down.

Accepted Answer

The Engel curve depicts the relationship between the quantity consumed of a good and household income. If the Engel curve slopes up, it indicates that as income increases, the quantity consumed of the good also increases. This suggests that the good is a normal good. As the demand for a normal good increases with increased income, the demand curve for the good slopes down. Therefore, if the Engel curve slopes up, the demand curve must slope down.

Question 17

Ivan spends his entire income on two goods.One of them is a Giffen good.If the price of the Giffen good rises, demand for the other good must fall.

Accepted Answer

For a Giffen good, as the price increases, the income effect dominates the substitution effect leading to a higher quantity demanded for the Giffen good. This often leads to a decrease in the demand for the other good, as Ivan's income may not be sufficient to purchase both goods at the new higher price of the Giffen good. Therefore, the statement is true.

Question 18

The Slutsky substitution effect measures the movement between two points on the same indifference curve.

Accepted Answer

The Slutsky substitution effect measures the movement between two different indifference curves, while holding utility constant.

Question 19

The Hicks version of the substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indifference curve as before the price change.

Accepted Answer

This is the correct definition of the Hicksian substitution effect.

Question 20

A rational consumer prefers more of good x to less.If the price of good x rises and the prices of all other goods remain constant, then the consumer must necessarily demand less of x.

Accepted Answer

While it might be expected that a consumer would demand less of a good as its price increases, this is not necessarily the case due to the income and substitution effects. The substitution effect might lead the consumer to buy less of the more expensive good and more of a substitute. However, the income effect, which reflects the change in the consumer's purchasing power, could lead to different outcomes depending on whether the good is normal or inferior. For an inferior good, an increase in price, effectively reducing real income, could lead to an increase in demand for the good if the income effect outweighs the substitution effect.

Quiz 7: Slutsky Equation-Part A