Exam 4: Choice

Joseph's utility function is given by U_J = x_A + 2x_B, where x_A denotes his consumption of apples and x_B his consumption of bananas. Clara's utility function is given by U_C = 3x_A + 2x_B. Joseph and Clara shop at the same grocery store.

Paul's utility function is min{x + 3y, 3x + y}. Simon's utility function is min{ 3x + 9y, 9x + 3y}. Paul and Simon have the same income and face the same prices.

If a consumer does not have convex preferences, then a point of tangency between her indifference curve and her budget line must be an optimal consumption point.

Howard has the utility function . His income is $30.

If his wage rate increases, then a utility maximizing consumer will necessarily

George has $49 which he decides to spend on x and y. Commodity x costs $5 per unit and commodity y costs $11 per unit. He has the utility function U(x, y) = 3x² + 6y² and he can purchase fractional units of x and y. George will choose

Lorenzo lives on x and y alone. His utility function is U(x, y) = min{ 3x + 4y, 7y}. The prices of both goods are positive. He will

Mary Granola consumes tomatoes and nectarines. Mary's indifference curves are kinky. When she is consuming more tomatoes than nectarines, she is just willing to trade 3 tomatoes for 1 nectarine. When she is consuming more nectarines than tomatoes, she is just willing to trade 4 nectarines for 1 tomato. Let P₁ be the price of nectarines, and P₂ the price of tomatoes. Mary maximizes her utility subject to her budget constraint. (Hint: Sketch one of her indifference curves.)

Clara's utility function is U(x, Y) = (x + 2)(Y + 1). If her marginal rate of substitution is -3 and she is consuming 12 units of good x, how many units of good Y must she be consuming?

Linus has utility function U(x, y) = x + 2y. If the price of x is $1 and the price of y is .50 cents then Linus must consume equal amounts of both goods in order to maximize his utility.

Isobel consumes positive quantities of both jam and juice. The price of jam is 5 cents per unit and the price of juice is 10 cents per unit. Her marginal utility of jam is 10 and her marginal utility of juice is 5.

Our old friend, Edmund Stench, of Chapter 2 loves punk rock video tapes. He has no income and therefore has to accept garbage in his backyard in return for money. Each video tape cost $2 and each sack of garbage that he accepts brings him $1. His utility function is given by U(c, g) = min{ 2c, 20 - g}, where c is the number of video tapes and g is the number of sacks of garbage that he gets per month. Each month he will choose to accept

Ed and Al both consume only bread and cheese. Both of them always choose to have some bread and some cheese, and both have strictly convex preferences. However, Ed likes to have a great deal of bread with a little cheese, and Al likes lots of cheese with a little bread. Both face the same prices for both goods and have chosen bundles to maximize their utilities subject to their budgets.

Ollie has a utility function U(x, y) = (x + 2)(y + 3). The price of x is $1 and the price of y is $1. When he maximizes his utility subject to his budget constraint, he consumes positive amounts of both goods. Ollie consumes

Martha's utility function is U(x, y) = min{x + 2y, 2x + y}. George's utility function is U(x, y) = min{ 2x + 4y, 4x + 2y}. If George and Martha have the same income and face the same prices for the goods x and y,

Wanda Littlemore's utility function is U(x, y) = x + 46y - 2y². Her income is $135. If the price of x is $1 and the price of y is $18, how many units of good x will Wanda demand?

As you may know, Mungoites each have two left feet and one right foot. Their preferences for left and right shoes display perfect complementarity. Mungoites find shoes useful only in trios of two lefts and a right. The price of each type of shoe is $10 a shoe, and Mungoites consume nothing other than shoes. A Mungoite's Engel curve for right shoes has the equation

Badger Madison consumes only beer and sausages. His income is $100. Beer costs him $.50 per can and sausages cost $1 each. Where x is the number of cans of beer and y the number of sausages he consumes per week, Badger's utility function is U(x, y) = -[(x - 50)² + (y - 40)²].

Charlie's utility function is U(x, y) = xy². His marginal rate of substitution between x and y does not change if the amount of both goods doubles.

Sharon spends all of her income on peaches and strawberries. Peaches are a normal good for her. Her income increased by 20 percent and prices did not change. Her consumption of strawberries could not have increased by more than 20 percent.