Exam 4: Demand

Lewis has preferences given by the Cobb-Douglas utility function U(q₁,q₂)= q₁ᵃq₂¹⁻ᵃ,where a > 0.Show that Lewis's total amount spent on each good,does not change with the prices.

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

The substitution effect can be measured holding ________ constant.

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

Draw budget constraints,indifference curves,and the income consumption curve for a good that has an income elasticity that is perfectly inelastic.

-The above figure shows Bobby's indifference map for juice and snacks.Also shown are three budget lines resulting from different prices for snacks.As the price of snacks rises,the price for juice

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

Due to inflation,nominal prices are usually

Jon spends all of his income on energy drinks (E)regardless of the price and his income.Derive Jon's demand equation for energy drinks,E*(p,Y).

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

-When John's income was low,he could not afford to dine out and would respond to a pay raise by purchasing more frozen dinners.Now that his income is high,a pay raise causes him to dine out more often and buy fewer frozen dinners.Which graph in the above figure best represents John's Engel curve for frozen dinners?

-When John's income was low,he could not afford to dine out and would respond to a pay raise by purchasing more frozen dinners.Now that his income is high,a pay raise causes him to dine out more often and buy fewer frozen dinners.Which graph in the above figure best represents John's Engel curve for dining out?

One characteristic of a Giffen good is that it

Suppose the price of X goes up and a consumer goes on consuming the exact same amount of X as before.Then X cannot be an inferior good.

-When John was in college and his income was low,he drank "Red Ribbon" beer.As his income increased,he purchased better-quality beer and less "Red Ribbon." Which graph in the above figure best represents John's Engel curve for "Red Ribbon" beer?

If the income elasticity of hamburgers is -0.8 for John,then his share of income spent on hamburgers will ________ when his income increases.

A consumer has the following utility function for goods X and Y: U(X,Y)= 5XY³ + 10 The consumer faces prices of goods X and Y given by pₓ and pᵧ and has an income given by I. a.Write out the Lagrangian expression for the consumer's utility maximization problem. b.Write out the first order conditions necessary for maximizing utility subject to the budget constraint. c.Show that the first order conditions imply the budget constraint and MRS condition.Provide the economic (i.e.non-mathematical)interpretation of these conditions - specifically,why are they necessary for the consumer to be at the optimal bundle? d.Solve for the Demand Equations,X*(pₓ,pᵧ,I)and Y*(pₓ,pᵧ,I) e.Show that the demand equations are homogeneous of degree zero.That is,show X*(cpₓ,cpᵧ,cI)= X*(pₓ,pᵧ,I) for any positive constant,c.

Suppose the only two goods you consume are wine and roses.On Tuesday,the price of wine goes up and at the same time your income increases by just enough so that you are equally happy as you were on Monday.What happens to the amount of wine you consume? Are you able to afford the same bundle as you did on Monday? Use a graph of budget constraints and indifference curves to illustrate your answer.

Suppose Ian consumes bread and mustard with his income.He views these goods to be Perfect Complements.He currently consumes 15 units of each good each week.Suppose that the price of Mustard increases by $1/unit and bread increases by $2/unit.Ian's union automatically provides him with a CPI adjustment in his income amounting to an increase by $45.Is Ian better off,worse off,the same or is it uncertain as compared to previously? Explain and provide a graph to demonstrate your answer.

A Californian student consumes Internet services (I)and books (B).Her preferences are represented by a Cobb-Douglas utility function: U(I,B)= I¹/⁴ᴮ¹/⁴ The prices of each good is $2 and the student has an income of $200.Over the course of the past year,the price of internet services has risen to $4,but the price of books has remained the same.The government has decided provide this student with additional money to compensate for the higher price of internet services.In order to determine the transfer the government has three consultants who have made the following suggestions: Consultant A: The student's income should be increased by a percentage found using a consumer price index (CPI). Consultant B: The additional income should allow the student to get her initial level of utility. a.Find the consumer's optimal bundle before the increase in price occurs. b.Find the consumer's optimal bundle after the increase in price occurs with income still at $200. c.Find the amount of the transfer implied by consultant A. d.Is the student necessarily better or worse off than before from such a transfer implied by consultant A? Explain why. e.Is the transfer implied by consultant B more or less than the amount implied by A? Explain. What is the precise dollar amount implied by consultant B?