Question 1

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 they both have some of each,then efficiency requires their MRS to be the same --- otherwise they can trade and make each other better off.

Question 2

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

a.The current optimal bundle is A in the graph below.
 b.The price of housing increases while the price of other consumption falls.Thus,the budget becomes steeper,as indicated by the steeper constraint in the graph.The new optimal bundle is B.  c.My new budget constraint passes through A,with a portion above A then lying above my original indifference curve.I will therefore choose some point on that portion of the new budget (like bundle B)--- and this will place me on a higher indifference curve.So I will prefer the proposal over the current tax law.

Question 3

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

First order conditions are necessary and sufficient for an optimum if there are no corner solutions and no multiple "solutions" (where some of them are local minima).Ruling out corners solutions is accomplished by assuming that all goods are essential.Ruling out multiple "solutions" is done by assuming convex tastes.Thus,assuming convex tastes and all goods being essential makes first order conditions necessary and sufficient.

Question 4

You have observed a consumer who purchases only goods $x _ { 1 }$ and $x _ { 2 }$ and have concluded that the consumer's tastes are quasilinear in $x _ { 2 }$ .Whether the consumer purchases more or less of $x _ { 1 }$ when the price of $x _ { 1 }$ falls then depends on the size of the substitution effect.

Accepted Answer

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

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

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

Question 6

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

The answer of Suppose you solve a consumer's constrained 2-good...

Question 7

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 the optimal quantity demanded has changed as a result of the increase in price --- and the optimal quantity demanded results from tastes confronting economic circumstances.The change in the price of peaches is a change in circumstances --- which in turn affects demand,not a change in tastes.

Question 8

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

A corner solution where a consumer does not consume some of one good can arise only if indifference curves cross at least some of the axes --- which implies that at least some goods are not essential.

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 might end up optimizing at a corner solution --- but she might also optimize at an interior solution,as illustrated in this graph. 11ea78ab_dc91_936e_8379_99b27a68c0f0_TB2157_00

Question 10

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 11

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

Multiple solutions can only arise from non-convexities --- and if tastes are convex,it must be that the non-convexity is in the choice set.But not all kinks produce non-convexities -- only inward pointing kinks.

Question 12

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

Accepted Answer

When all goods are essential,no indifference curve crosses any axis --- which means no optimum can ever occur on an axis.

Question 13

Currently.the price of consuming housing $x _ { 1 }$ 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 $\left( p _ { 1 } - s \right)$ to $p _ { 1 }$ .At the same time,the government lowers the tax on other consumption,lowering the price from $\left( p _ { 2 } + t \right)$ to $p _ { 2 }$ . 
a.Write down your original budget constraint assuming the consumer has income I.
b.Suppose the utility function
 $u \left( x _ { 1 } , x _ { 2 } \right) = \frac { 1 } { 3 } \ln x _ { 1 } + \ln x _ { 2 }$ captures your tastes,and suppose
 $I = 10,000$ ,
 $p _ { 1 } = 10$ ,
 $p _ { 2 } = 1$ ,
 $s = 6$ and
 $t = 1$ .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 \(x _...

Question 14

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 15

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

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

Question 16

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

If you get any bananas,we can make both of us better off by taking some of your bananas and giving them to me.

Question 17

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...

Quiz 6: Doing the Best We Can