Exam 4: Demand

Recall that the Cobb-Douglas Utility function U(X,Y)= X^aY^1-a has the unusual property that the demand for each good depends only on its own price.Therefore,a consumer will always allocate the same proportion of income to each good.Specifically,the demand for X is X* = aI/p_x where I is income and p_x is the price of X. a.What is the price elasticity of demand for X? b.What is the direction of the income effect on X of an increase in p_x?

After Joyce and Larry purchased their first house,they made additional home improvements in response to increases in income.After a while,their income rose so much that they could afford a larger home.Once they realized they would be moving,they reduced the amount of home improvements.Their Engel curve for home improvements on their current home is

Median household income is $50,000 per year.The typical household spends about $125 per year on milk,which has an income elasticity of about 0.07.From this information,we can conclude that

Explain what the slope of the income consumption curve shows about the income elasticity of demand.

Suppose that the interest rate paid to savers increases.As a result,Tom wishes to save more.This suggests that,for Tom,

In the relevant price range a demand curve for a Giffen good would be

An increase in the price of a good causes

Shin likes to spend a (relatively small)portion of his income on vacations to Cabo San Lucas (a popular resort area in Mexico).On these trips,he either stays at a four star resort with panoramic ocean views or a more modest,and slightly deteriorating hotel in the noisy part of town.Understandably,the four star hotel is significantly more expensive.Suppose that the four-star hotel costs $5000/trip while the hotel costs just $500/trip.In recent years,the price of airfare has risen significantly,a change that effects the cost of his trips the same regardless of where he stays.Suppose that airfare has increased from $300/trip to $1000/trip.Why is it that following the higher travels prices,Shin is likely to spend more of his vacations at the four star resort when he travels.(Assume that the hotel rates and Shin's preferences are fixed).

Many elderly people have Social Security payments as their sole source of income.Because of this,there have been attempts to adjust these payments so as to keep up with changing prices.This process is called "indexing";this question will lead you through the process. Suppose that in the year 2000,a typical Social Security recipient consumed only Food and Housing.The price of housing was $15/unit and the price of food was $5/unit.Denote the quantities of food and housing per month by F and H respectively.This consumer received $150/month and consumed five units of housing and 15 units of food. a.Write down the algebraic representation of this consumer's budget constraint. b.Show that the bundle (5,15)is just affordable.Identify another bundle on the budget constraint where both goods are consumed in positive amounts.Suppose that in 2004 the price of food rose to $10/unit and housing rose to $20/unit. c.How much additional income is required such that the original bundle is just affordable at the new prices. d.On the graph with Housing on the horizontal axis and food on the vertical axis,depict the original budget constraint and the new budget constraint after income is compensated according to c.Include the indifference curve going through the point (5,15). f.Is the consumer better,worse,or equally well off in 2004 relative to 2000 following the compensation? Explain.What will happen to the consumer's choice of food and housing consumption? How can you tell? g.The Laspeyres Price Index,as we have been describing above,measures inflation by looking at how the cost of a particular bundle of goods a consumer purchases in a previous year changes.Critics claim that this measure of inflation overstates changes in the cost of living.Do you agree or disagree? Explain.

Show that the following preferences are not consistent for a rational individual. i.An individual when confronted with prices of p₁ = $4 and p₂ = $8 chooses q₁ = 1 and q₂ = 5. ii.The same individual facing prices of p₁ = $6 and p₂ = $9 chooses q₁ = 5 and q₂ = 3.

Suppose that the interest rate paid to savers increases.As a result,Tom wishes to save less.This suggests that,for Tom,

When the price of a good changes,the total effect of the price change on the quantities purchased can be found by comparing the quantities purchased

Louie purchases the same quantity of Bones even after the price of bones rises.Draw Louie's price-consumption curve and demand curve (two separate graphs!)based on this information.Discuss directions and magnitudes of the income and substitution effects (or graph them clearly).Are Bones normal or inferior for Louie? Explain.

-The above figure shows three different Engel curves.Rank them in terms of income elasticity.

A consumer purchases housing (H)and spends the remainder of income on the composite good (C).The government is considering one of two policies.Policy A taxes housing by $50 per unit consumed.With the tax in place,the consumer purchases 100 units of housing.Policy B collects a lump-sum tax of $5,000 from the consumer's income.Compare the effects of the policies on the consumer's utility/well-being and the amount of housing and composite goods purchased.

Draw two graphs,one directly above the other.On the upper graph,label the vertical axis Good X and label the horizontal axis Good Y.On the lower graph,label the vertical axis the Price of good Y and label the horizontal axis Good Y.In the upper graph,show the income and substitution effects of a decrease in the Price of good Y when Y is a Giffen good.Draw the corresponding demand curve for Good Y in the lower graph.

-The above figure shows Larry's indifference map and budget lines for ham and pork.Which of the following statements is TRUE?

Jill consumes nothing but soup and cola.If cola is a luxury good for Jill,then soup must be a necessity.

Suppose you have $400,000 saved up and purchase a medium-sized house for $200,000.Consider the following 2 scenarios: i.The very next day,the prices of all houses,including the one you have just bought,double. ii.The very next day,the prices of all houses,including the one you bought,fall by half. Show that both scenarios increase your utility.

Suppose the only goods you consume are apples and peaches.One day the price of apples goes up and the price of peaches goes down,and you find that you can still just afford to buy the same combination of peaches and apples that you were buying all along.The price changes leave you neither better nor worse off.