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Microeconomics Practice Problems

## Hotel Bethlehem pricing scheme and demand curve

1. Hotel Bethlehem implements a block pricing scheme for nights in a hotel room. They face inverse demand

P = 260 − QD

2. The marginal cost of having a guest in a room is \$20.

a. If Hotel Bethlehem can charge two separate prices for two separate blocks of guests,what are the two prices they charge? how many rooms do they fill at each price?

b. If Hotel Bethlehem only charges one price, how many rooms do they fill? What pricedo they charge for those rooms?

c. Compare your answers in part a. and part b. Which is more profitable for Hotel Bethlehem?

2. Suppose Megabus finds a way to determine if a potential rider is a student or not. They use this information to engage in group price discrimination on their New York to Boston line. The demand curve for non-students is

Qn = 10000 − 100Pn

The demand curve for students is
Qs = 9000 − 100Ps

3. The marginal cost of allowing another rider on the bus is \$5. (there are no supply constraints)

a. If Megabus group price discriminates, what is the price they charge students andnon-students for a bus ticket? How many tickets do they sell to each group?

b. What is Megabus’s profit from price discriminating?

c. If Megabus could not price discriminate, they would have to set one price for both students and non-students. What demand curve does Megabus face if they cannot pricediscriminate? What is Megabus’s profit maximizing price and quantity if they cannot price discriminate?

d. What is Megabus’s profit from setting one price for both groups? Does Megabus
prefer to price discriminate or not?

e. Does price discrimination make students better off, worse off, or have no impact onthem? How about non-students?

f. In reality, Megabus occasionally offers a ticket price of \$1. What does this tell youabout Megabus’s actual marginal cost of allowing another bus rider?

3. Suppose that steel producers face the demand curve given by

Q = 75 − .25P

a. where Q is steel output and P is the per unit price. The marginal cost of steel production is:
MC = 20 + 3Q

b. Suppose that steel plants are located near rivers and that a by product of steel production is pollution of the river. Specifically, letffs assume that the marginal damage associated with each unit of steel production is given by:
MD = 3Q.

c. How much steel production will there be in the absence of any government regulation?

d. What is the efficient level of output?

e. How large is the welfare cost associated with the externality?

f. Calculate the fixed per unit Pigouvian tax that could be used to achieve the outcomein part b. Confirm that the Pigouvian tax is equivalent to charging the steel producer the marginal damage associated with each unit of steel produced.

4. Sara and Barry live in the same neighborhood. In the winter, both of them like thestreets in their neighborhood plowed. Barry’s marginal benefit of each plowed street is given by MBB = 40 − Q, and Sara’s marginal benefit of each plowed street is given byMBS = 20 − 0.5Q, where Q is the number of total streets in the neighborhood that are plowed. Suppose that the marginal cost of plowing the snow is constant at \$24.

a. Suppose the town does not plow the roads, and Barry and Sara can plow on their ownat a constant marginal cost of \$24. between the two of them, how many streets are plowed?

b. What is the socially optimal amount of streets that should be plowed?

c. The mayor of the town suggests a \$12 per street tax that each individual would need to pay for a public plowing service (The price each individual is mandated to pay for plowing).How many streets would Barry want to have plowed if he had to pay \$12 per street? How about Sara?

d. Imagine that the mayor could charge individual citizens a specific per street tax based on each citizens preferences for street plowing. What would Barry and Sara’s individual per street tax need to be so that Barry and Sara would agree on the socially optimal number of streets being plowed when faced with their specific price per street PB and PS?