Boğaziçi University-Department of Economics

Boğaziçi University-Department of Economics

EC203 Microeconomics I- Levent Yıldıran

PS5

1)  (Chp 12) Under uncertainty you are an expected utility maximizer with U(W)=W. Your wealth, including your computer, is 729. Your computer, which is worth 648, can break down with a probability of 1/9 due to a virus. The insurance company proposes to cover you fully. What is your certainty equivalent, and how much at most would you accept to pay for this insurance?

2)  (Chp 14) Ahmet consumes one good x and y is his income to spend on other goods. His utility function for x and y is given by U(x,y)=100x− x2/2 +y.

a.  What is the inverse demand curve for good x?

b.  Suppose that Ahmet has $4, 000 in total to spend a month. What is his total utility for x and money to spend on other things if the price of x is $50?

c.  What is the change in Ahmet’s utility when the price changes from $50 to $80?

d.  What is the change in (net) consumer’s surplus when the price changes from $50 to $80? Show this on the graph.

3)  (Chp14) Berna’s preferences can be represented by U(x,y) = min{x,y}. X is the pair of earrings and y is dollars to spend on other things. She faces prices (px,py) = (2,1) and her income is 12. Then the price of a pair of earring rises to $3 and Berna’s income stays the same.

a.  What is the maximum amount that Berna would pay to avoid the price increase?

b.  How much should Berna’s income rise in order for her to be as well-off as she was with the original bundle?

4)  (Chp14) Ayşe’s utility function is U (x,y) = max {2x, y}. The price of x is 3 and the price of y is 1 and she has an income of $15. Find the equivalent and the compensating variations and interpret them when the price of x decreases to 1 holding other things (the price of y and the income) constant.

5)  (Chp14) Minnie’s utility function is U(x,y) = 2x+5y. The price of x is $4 and the price of y is $15. Minnie has $150 a week to spend on x and y. Minnie 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 Minnie would be willing to pay to join the club? What is the most that Minnie would be willing to pay to join the club, if he can get y at a price of $7.5?

6)  (Chp15) In Izmit, there are two kinds of consumers, Fiat owners and Toyota owners Every Fiat owner has a demand function for gasoline Df (p) = 20 − 5p for p.≤ 4 and Df (p) = 0 if p > 4. Every Toyota owner has a demand function Dt(p) = 15−3p for p ≤ 5 and Dt(p) = 0 if p > 5.(Quantities are measured in gallons per week and price is measured in dollars.) Suppose that in Izmit there are 150 consumers, 100 Fiat owners, and 50 Toyota owners.

(a) Draw the demand curves representing the total demand by Fiat owners and the demand by Toyota owners separately.

(b) Draw the market demand for the whole city.

7)  (Chp15) The market demand curve for good X in a small community is given by p = 75 – (q/5) where p is the price of X and q is the quantity demanded. If the price is 10 ;

a) What is the price elasticity of demand for X?

b) If the seller (the monopolist here) aims to maximize its revenue, should it raise or lower its price?

c) Show that the seller can only maximize its revenue when the price elasticity of demand for X is equal to -1.

8)  (Chp15) Show that the demand function, Q = aPb, (b Є Q, a Є R)

a) Is a constant elasticity demand curve.

b) The vertical distance between the (inverse) demand and marginal revenue curves is

a constant ratio of the price level for each value of quantity.

9)  (Chp15) Demand function for handmade seats of uncle Ali is D(p)= 400 - p. He has 150 seats in his hand and he will not produce any more.

a) What is the inverse demand function for the seats?

b) Derive the total revenue, marginal revenue and price elasticity of demand functions.

c) What would be the price – quantity bundle that maximizes uncle Ali’s revenue if he

didn`t have a fixed supply? What is the corresponding revenue at this level?

d) Find the quantity of seats sold, total revenue, marginal revenue and price elasticity of

demand at the equilibrium in this market.

10)  (Chp15) Jen, Eric and Kurt are all buyers of chain saws. Jen’s demand function is Qj=520-13P,Eric’s demand function is Qe=40-P, and Kurt’s demand function is Qk=200-5P. Together, these three constitute the entire demand for chainsaws. At what price will the price elasticity of market demand will be –1?

11)  (Chp15) At a large institution of higher learning, the demand for football tickets at each game is 100,000-10,000p. If the capacity of the stadium at that university is 60,000 seats, what is the revenue-maximizing price for this university to charge per ticket? How many tickets can be sold at that price? What is the maximum possible revenue? What price should be charged to sell all seats? What is the revenue in that case?

12)  (Chp 15) TRUE OR FALSE. Explain. In an economy with three goods, there must be at least one a luxury good.

13)  (Chp16) The inverse demand function for nectarines is defined by the equation p=243-10q, where q is the number of units sold. The inverse supply function is defined by p=9+3q. A tax of 26 is imposed on suppliers for each unit of nectarines that they sell. When the tax is imposed, the quantity of nectarines sold falls by how much? What is the deadweight cost of this tax?

14)  (Chp16) In a certain kingdom, demand function for rye bread was q = 435-4p and the supply function was q = 15+8p where p is the price and q is loaves of bread. The king made it illegal to sell rye bread for a price above 21 per loaf. To avoid shortages, he agreed to pay bakers enough of a subsidy for each loaf of bread so as to make supply equal demand. How much would the subsidy per loaf have to be?

15)  (Chp16) The inverse demand function for apples is defined by the equation p = 214 - 5q, where q is the number of units sold. The inverse supply function is defined by p = 7 + 4q. A tax of $36 is imposed on suppliers for each unit of apples that they sell,

a) Find the equilibrium price and quantity before the tax is imposed.

b) Find the equilibrium quantity after the tax is imposed.

c) What part of this tax is paid by suppliers and what part is paid by consumers?

d) Find the deadweight loss due to this tax.