Exam 13: Consumers Surplus-Part A

If Bernice (whose utility function is min{x, y}, where x is her consumption of earrings and y is money left for other stuff)had an income of $12 and was paying a price of $4 for a pair of earrings, then if the price of earrings went up to $6, the equivalent variation of the price change would be

The indirect utility function for a consumer with a utility function U(x₁, x₂)is defined to be a function V(p₁, p₂, m)such that V(p₁, p₂, m)is the maximum of U(x₁, x₂)subject to the constraint that the consumer can afford (x₁, x₂)at the prices (p₁, p₂)with income m. a.Find the indirect utility function for someone with the utility function U(x, y)= 2x + y. b.Find the indirect utility function for someone with the utility function U(x, y)= min{2x, y}.Explain how you got your answers.

Reginald is fond of cigars.His utility function is U(x, c)= x + 10c - .5c², where c is the number of cigars he smokes per week and x is the money that he spends on the consumption of other goods.Reginald has $200 a week to spend.Cigars used to cost him $1 each, but their price went up to $2 each.This price increase was as bad for him as losing income of

Sam has quasilinear preferences and his demand function for x is D(p)= 15 -p/3.The price of x is initially $15 per unit and increases to $24 per unit.Sam's change in consumer's surplus is closest to

Ellsworth's utility function is U(x, y)= min{x, y}.Ellsworth has $150 and the price of x and the price of y are both $1.Ellsworth's boss is thinking of sending him to another town where the price of x is $1 and the price of y is $2.The boss offers no raise in pay.Ellsworth, who understands compensating and equivalent variation perfectly, complains bitterly.He says that although he doesn't mind moving for its own sake and the new town is just as pleasant as the old, having to move is as bad as a cut in pay of $A.He also says he wouldn't mind moving if when he moved he got a raise of $B.What are A and B?

If Bernice (whose utility function is min={x, y}, where x is her consumption of earrings and y is money left for other stuff)had an income of $15 and was paying a price of $8 for a pair of earrings, then if the price of earrings went up to $13, the equivalent variation of the price change would be

Kristina consumes only goods X and Y.Her income is $600 and her utility function is U(x, y)= max{x, y}, where x is the number of units of X she consumes and y is the number of units of Y she consumes.The price of good Y is 1.The price of good X used to be 1/2 but is now 2.The equivalent variation of this price change for Kristina is

Consumer's surplus is another name for excess demand.

If there is Cobb-Douglas utility, compensating and equivalent variation are the same.

Bernice has the utility function u(x, y)= min{x, y}, where x is the number of pairs of earrings she buys per week and y is the number of dollars per week she has left to spend on other things.(We allow the possibility that she buys fractional numbers of pairs of earrings per week.)If she originally had an income of $18 per week and was paying a price of $6 per pair of earrings, then if the price of earrings rose to $10 per pair, the compensating variation of that price change (measured in dollars per week)would be closest to

Lolita, the Holstein cow, has a utility function is U(x, y)= x -x²/2 + y, where x is her consumption of cow feed and y is her consumption of hay.If the price of cow feed is $.10, the price of hay is $1, and her income is $2, and if Lolita chooses the combination of hay and cow feed that she likes best from among those combinations she can afford, her utility will be

Albin has quasilinear preferences and he loves pretzels.His inverse demand function for pretzels is p(x)= 49 - 6x, where x is the number of pretzels that he consumes.He is currently consuming 8 pretzels at a price of $1 per pretzel.If the price of pretzels rises to $7 per pretzel, the change in Albin's consumer surplus is

Pablo's utility function is U(x, y)= x + 10y - y²/2, where x is the number of x's he consumes per week and y is the number of y's he consumes per week.Pablo has $200 a week to spend.The price of x is $1.The price of y is currently $5 per unit.Pablo has received an invitation to join a club devoted to the consumption of y.If he joins the club, Pablo can get a discount on the purchase of y.If he belonged to the club, he could buy y for $1 a unit.How much is the most Pablo would be willing to pay to join this club?

At the initial prices, Teodoro is a net seller of apples and a net buyer of bananas.If the price of apples decreases and the price of bananas does not change,

Ella's utility function is min{5x, y}.If the price of x is $20 and the price of y is $20, how much money would she need to be able to purchase a bundle that she likes as well as the bundle (x, y)= (7, 15)?

Bernice's utility function is U(x, y)= min{x, y}.The price of x used to be 3 but rose to 4.The price of y remained at 1.Her income is 12.She would need an income of $15 to be able to afford a bundle as good as her old one at the new prices.

Minnie gets 4 tapes for her birthday, but they are currently useless to her because she doesn't have a tape recorder and she cannot return them for a refund.Her utility function is U(x, y, z)= x + f(y)z⁵, where z is the number of tapes she has, y is the number of tape recorders she has, and x is the money she has to spend on other stuff.Let f(y)= 0 if y < 1 and f(y)= 7 otherwise.The price of tapes is $7.99.What is her reservation price for a tape recorder?

Sam's utility function is U(x, y)=2x + y, where x is the number of x's he consumes per week and y is the number of y's he consumes per week.Sam has $200 a week to spend.The price of x is $4.Sam currently doesn't consume any y.Sam has received an invitation to join a club devoted to the consumption of y.If he joins the club, Sam can get a discount on the purchase of y.If he belonged to the club, he could buy y for $1 a unit.How much is the most Sam would be willing to pay to join this club?

Producer's surplus at price p is the vertical distance between the supply curve and the demand curve at price p.

Quasimodo from your workbook has the utility function U(x, m)= 100x - x²/2 + m, where x is his consumption of earplugs and m is money left over to spend on other stuff.If he has $10,000 to spend on earplugs and other stuff and if the price of earplugs rises from $50 to $70, then his net consumer's surplus