Probability and Economics Worksheet
You’re a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $1 million to $3 million. If they are wrong, their prize is decreased to $750,000. You believe you have a 25% chance of answering the question correctly.
Ignoring your current winnings, your expected payoff from playing the final round of the game show is $ . Given that this is
The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is
2 . Individual Problems 17-3
The residential division of Prism’s high-speed Internet service uses one advertising agency, while its commercial division uses another. Two analysts, Andy and Brad, are asked to test the effectiveness of the two agencies. Andy proposes an A/B test that compares the click-through rates per ad of the two agencies. Brad proposes a difference-in-difference test in which the budgets for both agencies are increased by 50%, and the percentage changes in the click-through rates are compared.
True or False: Both Andy’s estimator and Brad’s estimator are unbiased.True
3 . Individual Problems 17-4
Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for a possible future product and estimates that the reservation value is $350,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $400,000, there is a 0.5 chance you will be able to sell the machine. If you commit to a price of $450,000, there is a 0.2 chance you will be able to sell the machine. If you commit to a price of $500,000, there is a 0.15 chance you will be able to sell the machine. These probabilities are summarized in the following table.
For each posted price, enter the expected value of attempting to sell the machine at that price. (Hint: Be sure to take into account the value of the machine to your company in the event that you are not be able to sell the machine.)Posted PriceProbability of SaleExpected Value($)($)$500,0000.15
Assume you must commit to one posted price.
In order to maximize the expected profit of the potential sale, which posted price would you commit to in order to maximize the expected value of the potential sale of the machine?$400,000
5 . Individual Problems 19-1
In the late 1990s, car leasing was very popular in the United States. A customer would lease a car from the manufacturer for a set term, usually two years, and then have the option of keeping the car. If the customer decided to keep the car, the customer would pay a price to the manufacturer, the “residual value,” computed as 60% of the new car price. The manufacturer would then sell the returned cars at auction. In 1999, manufacturers lost an average of $480 on each returned car (the auction price was, on average, $480 less than the residual value).
Suppose two customers have leased cars from a manufacturer. Their lease agreements are up, and they are considering whether to keep (and purchase at 60% of the new car price) their cars or return their cars. Two years ago, Paolo leased a car valued new at $18,000. If he returns the car, the manufacturer could likely get $12,600 at auction for the car. Shen also leased a car, valued new at $12,000, two years ago. If he returns the car, the manufacturer could likely get $6,120 at auction for the car.
Use the following table to indicate whether each buyer is more likely to purchase or return the car.
Keep and Purchase Car
The manufacturer will lose money (at auction, relative to the residual value of the car) if
True or False: Setting a more accurate residual price of each car would help attenuate the problems of adverse selection.True
6 . Individual Problems 19-5
Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 40% chance of actually realizing that cost reduction and a 60% chance of realizing no cost reduction.
Assume the customer has an initial total cost of $700.
According to the customer’s beliefs, the expected value of the accounting system, or the expected reduction in cost, is.
Suppose the sales representative initially offers the accounting system to the customer for a price of $49.00.
The information asymmetry stems from the fact that the
Instead of naming a price, suppose the sales representative offers to give the customer the product in exchange for 50% of the cost savings. If there is no reduction in cost for the customer, then the customer does not have to pay.
True or False: This pricing scheme worsens the problem of information asymmetry in this scenario.True