Exam 6: Doing the Best We Can

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.

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?

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.

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.

Essential goods give rise to corner solutions.

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.

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?

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.

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

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

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.

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?

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.

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.

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

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:

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

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)

Which of the following is correct about a consumer's optimization problem:

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