Exam 5: Demand

Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of cheese. If the total cost of x units of cocoa is x², the price of cheese is $8, and Casper's income is $174, how many units of cocoa will he consume?

Between 1990 and 2000, a particular consumer's income increased by 25%, while the price of X and of "all other goods" both increased by 10%. It was observed that the consumer's consumption of X and of all other goods both increased by 15%.

Carlos consumes only two goods, apples and bananas. His utility function is U(a, b) = a³b². Before he trades, his initial endowment is w_a apples and w_b bananas. After he trades to his optimal consumption point at these prices, the relative prices change. Carlos is allowed to make further trades if he wishes.

Prudence was maximizing her utility subject to her budget constraint. Then prices changed. After the price change she was better off. Therefore the new bundle costs more at the old prices than the old bundle did.

Georgina consumes only grapefruits and pineapples. Her utility function is U(x, y) = x²y⁸, where x is the number of grapefruits consumed and y is the number of pineapples consumed. Georgina's income is $105, and the prices of grapefruits and pineapples are $1 and $3, respectively. How many grapefruits will she consume?

Mike consumes two commodities, x and y, and his utility function is min{x + 2y, y + 2x}. He chooses to buy 8 units of good x and 16 units of good y. The price of good y is $.50. What is his income?

An Engel curve is a demand curve with the vertical and horizontal axes reversed.

With some services, a. Write down the budget equation that you would have after you paid the entry fee for each of the two plans. b. If your utility function is xy, how much y would you choose in each case? c. Which plan would you prefer? Explain. e.g., checking accounts, phone service, or pay TV, a consumer is offered a choice of two or more payment plans. One can either pay a high entry fee and get a low price per unit of service or pay a low entry fee and a high price per unit of service. Suppose you have an income of $100. There are two plans. Plan A has an entry fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1 per unit for using the service. Let x be expenditure on other goods and y be consumption of the service.

For m > p₂, the demand functions for goods 1 and 2 are given by the equations, - 1 and , where m is income and p₁ and p₂ are prices. Let the horizontal axis represent the quantity of good 1. Let p₁ = 1 and p₂ = 2. Then for m > 2, the income offer curve is

Ambrose's brother Bartholomew has a utility function , where x₁ is his consumption of nuts and x₂ is his consumption of berries. His income is $115, the price of nuts is $5, and the price of berries is $1. How many units of berries will Bartholomew demand?

Briefly explain in a sentence or two how you could tell a. whether a good is a normal good or an inferior good. b. whether a good is a luxury or a necessity. c. whether two goods are complements or substitutes.

Miss Muffet insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $5 and the price of whey is $3, then if Miss Muffet's income is m, her demand for curds will be

A consumer has the utility function U(x, y) = min{x, 2y}. If the price of good x is zero and the price of good y is p, then the consumer's demand function for good y is .

Ambrose's brother Sebastian has a utility function , where x₁ is his consumption of nuts and x₂ is his consumption of berries. His income is $128, the price of nuts is $2, and the price of berries is $1. How many units of berries will Sebastian demand?

Daisy received a tape recorder as a birthday gift and is not able to return it. Her utility function is U(x, y, z) = x + z f(y), where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend. f(y) = 0 if y < 1 and f(y) = 24 if y is 1 or greater. The price of tapes is $4 and she can easily afford to buy dozens of tapes. How many tapes will she buy?

Wilma Q. has a utility function U(x₁, x₂) = x²₁ + 1.5x₁x₂ + 30x₂. The prices are p₁ = $1 and p₂ = $1. For incomes between $20 and $60, the Engel curve for good 2 is

Martha has the utility function U = min{ 4x, 2y}. Write down her demand function for x as a function of the variables m, p_x, and p_y, where m is income, p_x is the price of x, and p_y is the price of y.

If income is doubled and all prices are doubled, then the demand for luxury goods will more than double.

Miss Muffet insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $3 and the price of whey is $3, then if Miss Muffett's income is m, her demand for curds will be

Madonna buys only two goods. Her utility function is Cobb-Douglas. Her demand functions have which of the following properties?