Exam 14:Consumers Surplus-Part A

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?

Herbie's utility function is U(x,y)= x + 8y -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.Herbie has $200 a week to spend.The price of x is $1.The price of y is currently $4 per unit.Herbie has received an invitation to join a club devoted to the consumption of y.If he joins the club,Herbie 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 Herbie would be willing to pay to join this club?

Holly consumes only goods X and Y.Her income is $500 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 1/3 but is now 2.The equivalent variation of this price change for Holly is

Ellsworth's utility function is U(x,y)F= 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?

The equivalent variation in income from a tax is the amount of extra income that a consumer would need in order to be as well off after the tax is imposed as he was originally.

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 $\lt$ 1 and f(y)=7 otherwise.The price of tapes is $7.99.What is her reservation price for a tape recorder?

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

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

There is a positive consumer's surplus when the total amount the consumer pays for something is less than the amount she would be willing to pay rather than do without it altogether.

Izaak likes to eat pizza and to fish.The more fishing he does the happier he is,up to 8 hours a day.If he fishes longer than 8 hours he gets a sore back and is less happy than if he hadn't fished at all.For y less than or equal to 8,his utility function is U(x,y)= x + 3y,where x is money spent on pizza and y is hours per day spent fishing.His income is $40 a day and he has no expenses other than pizza.The Bureau of Fisheries has just decided to allow people without fishing licenses to fish only 3 hours a day.But if you buy a fishing license,you can fish as many hours as you wish.How much is Izaak willing pay for a license?

Yoram's utility function is U(x,y)= 2x + 5y.The price of x is $4 and the price of y is $15.Yoram has $150 a week to spend on x and y.Yoram is offered a chance to join a club of y consumers.If he joins,he can get y at a price of $10.What is the most that Yoram would be willing to pay to join the club?

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

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

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

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 $75,then his net consumer's surplus

If somebody is buying 10 units of x and the price of x falls by $3,then that person's net consumer's surplus must increase by at least $30.

If Bernice (whose utility function is minF{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

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

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.

With quasilinear preferences,the equivalent variation and the compensating variation in income due to a tax are the same.