Question 1

Kinks in budget constraints always produce non-convexities in choice sets.

Accepted Answer

Kinks in budget constraints do not necessarily produce non-convexities in choice sets; they simply indicate points where the slope of the budget constraint changes, often due to piecewise linear budget constraints or changes in prices or income. Non-convexities in choice sets typically arise from other factors, such as indivisibilities or externalities, not merely from kinks in the budget constraint.

Question 2

Suppose that choice sets are convex.State assumptions about tastes that are necessary and sufficient to guarantee that the solution to the consumer optimization problem is a unique interior solution.(Explain)

Accepted Answer

To rule out corner solutions, it is necessary and sufficient to assume that all goods are essential. To rule out multiple interior solutions, it is necessary and sufficient to assume that tastes are (strictly) convex. While these assumptions are not necessary for the solution to be a unique interior solution, they are necessary to guarantee that the solution to be unique and in the interior.

Question 3

If all goods are essential, a consumer will optimize at an interior solution.

Accepted Answer

If all goods are essential, then the consumer will not be able to satisfy all of their wants with the given budget. As a result, the consumer will have to choose a combination of goods that provides the most satisfaction, given the budget constraint. This will lead to an interior solution, where the consumer is consuming some of each good.

Question 4

When the price of peaches went up, people bought fewer peaches and more strawberries.This is an indication that tastes have changed as a result of the price increase.

Accepted Answer

This is an indication of the substitution effect, where consumers switch to a cheaper alternative (strawberries) when the price of a good (peaches) increases, not a change in tastes.

Question 5

Which of the following is correct about a consumer's optimization problem:
A)In order for a consumer to not be optimizing at a corner solution, it is necessary for us to assume that all goods are essential.
B)In order for a consumer to not be optimizing at a corner solution, it is sufficient for us to assume that all goods are essential.
C)In order for a consumer to not be optimizing at a corner solution, it is necessary and sufficient for us to assume that all goods are essential.
D)None of the above.

Accepted Answer

In order for a consumer to not be optimizing at a corner solution, it is sufficient for us to assume that all goods are essential. This is because if all goods are essential, then the consumer will always want to consume some of each good, and will never want to consume zero of any good. This means that the consumer will always be on the interior of the budget constraint, and will never be at a corner solution.

Question 6

Explain how we can estimate the shape of a person's indifference map by observing choices under different economic circumstances.Explain also why we will not be able to identify any non-convexities in tastes from our observations.

Accepted Answer

The answer of Explain how we can estimate the shape...

Question 7

Suppose that choice sets are convex.State assumptions about tastes that are necessary and sufficient to guarantee that the first order conditions are necessary and sufficient for identifying a true optimum.

Accepted Answer

The answer of Suppose that choice sets are convex.State assumptions...

Question 8

Suppose you solve a consumer's constrained 2-good optimization problem for a given economic environment --- and your answer contains a negative consumption level of good 2.Which of the following is a valid conclusion on your part:
A)The true optimum has the consumer consume none of good 1.
B)The true optimum has the consumer consume none of good 2.
C)There are multiple "true" optimal consumption bundles.
D)The consumer will sell good 2.
E)None of the above.

Accepted Answer

Consumption levels of goods cannot be negative. Therefore, the answer that makes the most sense is that the true optimum has the consumer consume none of good 2. This will ensure that consumption levels are non-negative.

Question 9

If not all goods are essential, a consumer will end up optimizing at a corner solution.

Accepted Answer

If not all goods are essential, a consumer can still choose to consume a mix of those goods and optimize their utility without ending up at a corner solution. They may allocate some of their budget to non-essential goods while still choosing to consume some essential goods.

Question 10

Ellie and Jenny both brought grapes and crackers in their school lunches.If they have different marginal rates of substitution of grapes for crackers, their parents have not allocated lunch resources efficiently.

Accepted Answer

If Ellie and Jenny have different marginal rates of substitution, it indicates that they value grapes and crackers differently. Efficient allocation would require equalizing their marginal rates of substitution, allowing them to trade until they reach a point where both are maximizing their utility given their preferences.

Question 11

If we were the only two people in the world and I like bananas while you hate them, efficiency demands that I get all bananas.

Accepted Answer

Efficiency demands that resources are allocated in the most productive manner. In this scenario, since I like bananas and you do not, it is more efficient for me to get all the bananas so that no bananas go to waste.

Question 12

The only way a consumer can optimize at a corner of her budget is if at least one of the goods is not essential.

Accepted Answer

If all goods in the budget are essential, the consumer cannot optimize only at a corner of the budget constraint. This is because she needs to allocate some amount of her budget to purchase every essential good. However, if at least one good is not essential, the consumer can choose to allocate zero budget to that good and optimize at the corner of her budget constraint where only the essential goods are being consumed.

Question 13

In the movie "Baby Boom", Dianne Keaton finds out that a relative tragically died in an accident and bequeathed her an infant.The movie then explores how Dianne Keaton makes fundamentally different choices as a result of this unexpected change in her life.It makes the point that new parents often emphasize -- our "tastes change" when children enter the household.
a.Consider Dianne Keaton's budget constraint over leisure (on the horizontal axis) and consumption (on the vertical).What is the slope of the budget constraint? Indicate her optimal choice A prior to finding out she suddenly has an infant child.
b.Suppose that the child came with a trust fund that permits Dianne Keaton to charge any child-related expenses to that fund.Thus, the child does not come with any additional expenses - and the budget constraint you derived in part (a) does not change.Still, we observe that Dianne Keaton now chooses more leisure and less consumption.What must have happened to the marginal rate of substitution at the bundle A in order for us to make sense of Dianne Keaton's change in behavior?
c.Draw the indifference curve through A before and after Dianne Keaton finds out she suddenly has a child.If you ordinarily saw two such indifference curves (outside the context of this example), could you think that these could emerge from the same map of indifference curves or would you think they represent indifference curves from two different people whose tastes differ? Explain.
d.Economists tend to resist the temptation of explaining changes in behavior as resulting from changes in tastes.Rather, we tend to think of changes in behavior as arising from changes in circumstances.Suppose that Dianne Keaton's tastes are actually over three "goods" - consumption of goods and leisure -- and "consumption" of children.Dianne Keaton's true indifference curves would thus be three dimensional - with your graphs so far representing two dimensional "slices".When viewed in this light, could the 2-dimensional indifference curves you graphed in (c) arise from a single set of 3-dimensional indifference surfaces? Explain (without attempting to graph anything in 3 dimensions).
e.Suppose that it had always been an option for Dianne Keaton to adopt a child, and suppose that the cost of doing so is negligible.If Dianne Keaton reports being happier after she inherits her relative's child, was she fully optimizing before (assuming that she attaches no particular value to the fact that the child she inherited was her relative's)?
f.In principle, could Dianne Keaton's tastes be such that she works more when she gets the child and is still happier than before? Under the usual assumption about tastes - and treating children the way we treat goods - could Dianne Keaton be less happy as a result of getting the child?

Accepted Answer

The answer of In the movie "Baby Boom", Dianne Keaton...

Question 14

Which of the following statements is correct and which is not? Explain why.
a.When we all face the same prices, our tastes become the same.
b.When we all face the same prices, our tastes become the same at the margin.

Accepted Answer

The answer of Which of the following statements is correct...

Question 15

Suppose tastes satisfy our usual assumptions.Kinks in budget constraints do not give rise to the possibility of multiple solutions unless the kinds produce a non-convexity in the choice set.

Accepted Answer

The statement correctly states that kinks in budget constraints may give rise to non-convexity in the choice set, which could potentially result in multiple solutions. Therefore, the statement is true.

Question 16

Suppose that choice sets are convex but we tastes may or may not be convex.(Assume all our other usual assumptions about tastes hold.) The first order conditions of the constrained utility maximization problem are then
A)necessary conditions for a true optimum.
B)sufficient conditions for a true optimum.
C)necessary and sufficient conditions for a true optimum.
D)none of the above.

Accepted Answer

The answer of Suppose that choice sets are convex but...

Question 17

Essential goods give rise to corner solutions.

Accepted Answer

Essential goods typically do not give rise to corner solutions because consumers usually allocate some portion of their budget to these goods rather than consuming them in extreme quantities (all or nothing). Corner solutions occur when a consumer allocates all of their budget to one good and none to others, which is less common for essential goods that are necessary for basic living.

Question 18

Currently.the price of consuming housing  is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from  to  .At the same time, the government lowers the tax on other consumption, lowering the price from  to  . 
a.Write down your original budget constraint assuming the consumer has income I.
b.Suppose the utility function  captures your tastes, and suppose  ,  ,  ,  and  .Write out the utility maximization problem for this consumer prior to any policy change. 
c.How much housing and other goods will this consumer consume prior to any policy change?
d.When the policy change goes into effect, will this consumer still be able to afford the bundle you derived in (c)?
e.When the policy change goes into effect, what bundle will the consumer consume?

Accepted Answer

The answer of Currently.the price of consuming housing  is...

Question 19

Currently, the price of consuming housing is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption and at the same time lowers taxes on all other goods.
a.With housing consumption on the horizontal axis and all other consumption on the vertical, illustrate you current optimal consumption bundle.
b.After looking over the government's proposal, you decide that you don't care one way or another whether the government implements this proposal.On your graph, indicate your new budget constraint and new optimal bundle under the proposal.
c.I also look over the proposal and find that my current consumption bundle also lies on the budget constraint I would face under the proposal.Am I also indifferent between the two proposals?

Accepted Answer

The answer of Currently, the price of consuming housing is...

Question 20

You have observed a consumer who purchases only goods  and  and have concluded that the consumer's tastes are quasilinear in  .Whether the consumer purchases more or less of  when the price of  falls then depends on the size of the substitution effect.

Accepted Answer

The answer of You have observed a consumer who purchases...

Quiz 6: Doing the Best We Can