ECON10004: INTRODUCTORY MICROECONOMICS

ECON10004: INTRODUCTORY MICROECONOMICS

ASSIGNMENT 1: SEMESTER 2, 2024

Due: Wednesday, August 21, 6pm

• Assignments must be submitted via the LMS subject webpage.

• Remember to keep a copy of your assignment.

• This assignment will account for 15% of your final grade.

• Maximum word limit: 1000 words (diagrams and equations do not count toward the word limit.)

• Points are awarded according to the quality of the answers. Most questions can be answered with a supply and demand graph and one to two sentences.

Melbourne Tullamarine Airport is located about 24 kilometers from the CBD and requires passengers arriving at the airport to use a variety of transportation methods to travel to the city or their home. In this problem, we will think about substitution patterns between taxis and Ubers.

Part 1: The Taxi Market

We will consider a simple setting where all passengers wish to go from the airport to the CBD. In this setting, we can think of all trips occurring in the same market and the price paid reflecting the actual amount paid by customers to their transport provider.

Passengers have different opportunity costs代  写ECON10004: INTRODUCTORY MICROECONOMIC  for using alternative transportation methods such as Skybus or Uber. As a result, there is a downward-sloping demand curve in the taxi market that can be represented by the following demand equation:

Taxi cabs who wish to pick up passengers must first queue in a holding area and wait for all the other taxis ahead of them to fill up passengers. When the price of a taxi is P and the wait time in the queue (in hours) is W, the total supply of taxis is given by:

Finally, the taxi industry is regulated so that trips to the CBD are all undertaken at a fixed price of $40. We will assume that the wait time is always below two hours so that the total quantity supplied at the regulated price is always positive.

Question 1.1 (10 points): Draw the supply and demand graph of the taxi market with the quantity on the horizontal axis and the price on the vertical axis when the total wait time is 0 hours. What is the total number of taxis that would be demanded and supplied at this price and wait time?

Question 1.2 (6 points): At the airport, taxis are allocated on a first-come-first-serve basis for picking up passengers and an excess supply of taxis results in additional wait time. Given the fixed price of taxis, what is the amount of time that each taxi ends up waiting in the queue? Based on the information provided in the question, what is the indirect opportunity cost of a taxi driver’s time? (Hint: It is easiest to answer this question if you first create (i) an “inverse” supply equation where P is a function of QS and W and (ii) an inverse demand equation where P is a function of QD .)

Question 1.3 (4 points): What is the elasticity of demand at the market price set by the regulator? Is demand elastic, inelastic, or unit elastic?

Part 2: The Uber Market

We are now going to explore the market for Ubers. We will assume that there is a downward-sloping demand for Ubers given by

Like taxi cabs, we will assume that Ubers also must wait in a queue in order to pick up passengers. We will assume that this queue is separate from the taxi queue and that when the price of an Uber is P and the wait-time is W, the total supply of Ubers is given by:

Finally, we will assume that Uber is a ride-sharing platform, and that the platform. takes 50% of the total amount price paid by each consumer. As such

Finally, we will assume that Uber can control the total number of cars it assigns into the queue at a given time and therefore can directly control wait-time W. It then sets the market price that clears supply and demand given this wait time.

Question 2.1 (8 points): Suppose that Uber chooses a “just-in-time” approach and chooses a wait time of W=0. Draw the supply and demand curves with quantity on the horizontal axis and the prices observed by consumers on the vertical axis. What is the price of an Uber ride for a passenger and how many Uber rides occur?

Question 2.2 (6 points): Based on your graph in question 2.1, shade the producer welfare, the consumer welfare, and the revenue that Uber receives.

Question 2.3 (4 points): What is the elasticity of demand at the competitive equilibrium?  Is demand elastic, inelastic, or unit elastic?

It turns out that Uber drivers at the airport often spend significant time waiting in line despite the technology to control the queue length. One rationale may be that it helps to minimize the wait time of passengers. However, in this part of the problem, we will explore whether Uber also has a profit motive for expanding the queue

Question 2.4 (2 points): Using the supply and demand equations, write down the market price that would be charged in equilibrium to passengers as a function of W.

Question 2.5 (10 points) We will assume that Uber has no fixed costs and that its profits can be calculated as

Where and are the equilibrium price and quantities. Note that you found in Question 2.4. Using this equation, calculate the wait time W that maximizes Ubers profits. Given this wait time, what is the new equilibrium price and quantity of an Uber?

Part 3: Cross-Price Elasticities

In class, we have concentrated on own-price elasticities, which can be thought of as the percent change in own-quantity when there is a percent change in own price. In some markets, it is also possible to talk about cross-price elasticities, which tell us the percent-change in quantity in one market for a percent change in price in another.

Question 3.1 (2 points) Using your results in Question 2.1 and 2.5, calculate the percent change in prices that occur in the Uber market if they were to move from a just-in-time model with 0 wait time to the one that maximizes Uber’s profits.

Question 3.2 (2 points) Suppose that the cross-price elasticity of demand for taxis and Ubers is 1/3 and that the demand equation in Part 1 was estimated under Uber’s just-in-time wait-time policy. Using what you know about elasticities, what would be a good prediction as to the percent change in demand for taxis that occurs when Uber switches to the wait time policy that maximizes its profits?

Question 3.3 (4 points) Draw a supply and demand picture for the taxi market that shows how Uber’s policy change is likely to affect taxi demand. You may assume a linear shift in the affected supply or demand curve. What is the new predicted quantity demanded?

Question 3.4 (2 points) What is the approximate equilibrium wait time for taxi drivers after Uber adopts its new policy?