Question

Economic Analysis (The Roberta Wagner Tire Problem)

When Roberta Wagner first launched e-tire, she thought that she had a home run on her hands. It had always been hard to buy bicycle tires online: e-tire would be a onestop marketplace for bicycle tires, matching bicycle tire producers with customers. But Wagner wasn’t clear on one important detail: how to set the prices at which the producers would sell to consumers. So Wagner did some market research. She surveyed tire producers and came up with a model for supply. Given a price for bicycle tires, p, suppliers would be willing to sell 650 + 5 × p tires. Meanwhile, Wagner’s market research led to a simple equation for consumers’ demand for tires. Given a price, p, consumers would want 1,000 − 2 × p bicycle tires.

At the price of $30 per tire, how many tires are demanded and supplied?

Wagner could tell that the website was not working as well as she had planned. She took a deep breath and then decided to structure e-tire entirely differently. She eliminated the requirement for a fixed price, and instead allowed sellers and buyers to negotiate a price via public text message on the site. Suppose that the sellers decided to follow a simple rule: so long as there were unsold tires, they would cancel all transactions and try a new price, 10 dollars lower than the previous price. Conversely, as long as there were buyers without tires, they would cancel all transactions and try a new price, 10 dollars higher than the previous price. So they next try a price of 60 dollars.

What is the final price at which buyers and sellers will trade tires?

During the Summer and Fall of 2020, the COVID-19 crisis led to an enormous change in the demand for bicycles. Consumers were afraid to take public transportation and so instead purchased bicycles. Describe what this would do to the prevailing price on e-tire, using both a graph and a brief paragraph.

A ride-sharing app company that matches customers who want a ride somewhere with nearby drivers who will drive them. How does Wagner’s e-tire dilemma in Parts 1 and 2 relate to a ridesharing app, which has to set prices for those rides?

Many people, sadly, require a kidney transplant from a living donor. There are typically many more people who need a kidney than there are people donating kidneys. Use any country’s rules for organ donation as an example. Explain what this problem has to do with the shortage or surplus of kidneys facing patients with kidney disease. How would your team recommend solving the kidney shortage or surplus problem? What tradeoffs did you discuss in coming up with your solution?

Answer 1