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Exam 4: Demand

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Question 31

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Jose gets utility from the goods he consumes and also the income he earns.His utility function is given by U(q₁,q₂)= q₁q₂Y Derive Jose's demand equations.Does the fact that he derives utility directly from income affect his consumption in this case?

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The demand equations are
q_i = Y...

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Question 32

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One characteristic of a Giffen good is that it

A) is a luxury good.
B) is an inferior good.
C) has an upward-sloping Engel curve.
D) All of the above.

E) A) and D)
F) A) and B)

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Question 33

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A consumer's utility function is given by: U(x,y)= 10xy Currently,the prices of goods x and y are $3 and $5,respectively,and the consumer's income is $150. a.Find the MRS for this consumer for any given bundle (x,y). b.Find the optimal consumption bundle for this consumer. c.Suppose the price of good x doubles.How much income is required so that the consumer is able to purchase the original consumption bundle (if you were unable to solve d. ,then take a guess at what the optimal bundle is before solving this) d.Now that the price of good x has doubled,how much income is needed for the consumer to reach the original level of utility? Is this more or less that what you found in e.?

A good may be inferior at some income levels and normal at others.

A true cost-of-living adjustment in response to a change in prices would compensate consumers so that they would be able to

A Californian student consumes Internet services (I)and books (B).Her preferences are represented by a Cobb-Douglas utility function of the type: U(I,B)= I^.5B^.5.Initially Y = 100, P_I = P_B = 1.Lately,however,because of the electricity shortage,the price of the Internet services has increased to 2.The government has decided to give a transfer to the student so that she can recover her initial welfare.In order to determine the transfer the government has hired three consultants who have made the following suggestions: Consultant A: The transfer should allow the student to buy her initial bundle. Consultant B: The transfer should allow the student to get her initial level of utility. Consultant C: The government should give her a transfer of 20. a.Using the expenditure function,find the amount of the transfer implied by consultant A. b.Find the amount of the transfer implied by consultant B. c.Determine whether the consumer is better or worse off from Consultant C's suggestion than before the price increases.

-The above figure shows Bobby's indifference map for soda and juice.B1 indicates his original budget line.B2 indicates his budget line resulting from an increase in the price of soda.From the graph,one can conclude that

-The above figure shows Bobby's indifference map for juice and snacks.Also shown are three budget lines resulting from different prices for snacks assuming he has $20 to spend on these goods.Which of the following points are on Bobby's price-consumption curve?

When the price of a good changes,the income effect can be found by comparing the equilibrium quantities purchased

Suppose the typical consumer only purchases food and clothing,and her utility can be expressed as U = F ∗ C.Currently,food costs $5 per unit and clothing costs $2 per unit.Her income is $70.If the price of food increases to $6,compare the resulting Laspeyres price index with a true cost of living index.

An increase in income (all else equal)will ALWAYS lead to a parallel shift of the budget line.

Sam has preferences for weekly Video Games (V)and Sodas (S)described by the utility function U(V,S)= V²S².Suppose the prices are denoted by p_V and p_S and Sam has income given by I.Assume that in Sam's optimal bundle,he consumes strictly positive quantities of both goods. a.Write out Sam's optimization problem and the associated Lagrangian expression. b.Compute the three critical value (first-order)conditions from the Lagrangian. c.Using your answer to b,find the expression for the optimal bundles as functions of the prices and income.

When the price of a good changes,the substitution effect can be found by comparing the equilibrium quantities purchased

Consider a consumer that only purchases two goods,X and Y.The government wishes to collect revenue from taxing this consumer and is considering two policies.The first policy is to only tax good X.The second policy will tax both goods by the same percentage.Assume that the tax rates in each policy are selected such that they collect the same amount of revenue.Which policy will have a smaller reduction in the consumer's well-being? (Use a graph of indifference curves and budget constraints to illustrate your answer)

-The above figure shows Bobby's indifference map for soda and juice.B1 indicates his original budget line.B2 indicates his budget line resulting from a decrease in the price of soda.What change in quantity best represents his substitution effect?

-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?

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 p_x and p_y 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^*(p_x,p_y,I)and Y^*(p_x,p_y,I) e.Show that the demand equations are homogeneous of degree zero.That is,show X^*(cp_x,cp_y,cI)= X^*(p_x,p_y,I) for any positive constant,c.

Consider a consumer with the Cobb-Douglas utility function U(q₁,q₂)= ,where q₁ and q₂ are the quantities of goods 1 and 2 consumed,respectively.This consumer has an income denoted by Y which is devoted to goods 1 and 2.The prices of goods 1 and 2 are denoted p₁ and p₂. a.What is this consumer's MRS as functions of q₁ and q₂? b.Write out the Lagrangian for the consumer's utility maximization problem. c.Using the Lagrangian method,derive the consumer's demand equations for both goods as functions of the variables p₁,p₂,and Y.

If consumer income and prices increase by the same percentage,

Even though Mary's income is very low,she makes sure that she purchases enough milk for her family to drink.As her income rises,she does buy more milk.Which graph in the above figure best represents Mary's Engel curve for milk?