Economics

  Question 1. (25%) Albert and Beth are looking at a new camera at a store that offers a no-questions-asked return policy. They are not sure the new features are worth it. Albert decides to take one home, thinking that he can always return it tomorrow. Beth decides against taking one home, thinking that she can always come back and pick one up tomorrow. They are both loss averse over cameras, with the same value function over cameras: v(x) = x for gains v(x) = 2x for losses They both use their endowments as their reference points. Ignore any transaction costs. 1. After Albert has taken his camera home, he incorporates it into his endowment. How much of a loss in utility would he incur by returning it tomorrow? 2. Beth, who does not take her camera home, does not incorporate it into her endowment. How much of a foregone gain in utility does the camera she does not own represent to her? 3. Who is more likely to end up the owner of the camera, Albert or Beth? 4. Does this help to explain why stores are willing to offer the no-questions-asked return policy despite the potential costs on repackaging and refurbishment? Question 2. (25%) Sam’s preferences over cake, c, and money, m, can be represented by the utility function u (c, m) = c + 4m + µ (c c rc) + 4µ (m m rm) 1 where rc is his cake reference point, rm is his money reference point, and the function µ (·) is defined as µ (z) = z z ≥ 0 . 3z z < 0 1. If his reference point is the status quo (that is, his initial endowment), what is the maximum price Sam would be willing to pay to buy a cake? (Hint: use the indifference condition that Sam’s utility does not change after gaining a cake and losing his willingness-to-pay.) 2. If his reference point is the status quo, what is the minimum price Sam would be willing to accept to sell a cake he already owned? 3. If his reference point is the status quo, what is the minimum amount of money Sam would be willing to accept instead of receiving a cake (that he did not already own)? In other words, if Sam were a “chooser,” how much money would he demand to compensate for not accepting a cake? 4. Use the concepts we discussed in class to explain your answers to Questions 2.1, 2.2, and 2.3. Question 3. (15%) Suppose you are trying to market a smartphone called M, and your main competitor sells a smartphone called N. They differ along two attributes: battery life and processing speed. Comparing to N, your product M has a longer battery life but a slower processing speed. Suppose there is a consumer who currently prefers N to M. You want to manipulate the consumer’s choice by introducing a new product D, which will act as a decoy for M. 1. Draw a graph with battery life on the x-axis and processing speed on the y-axis. 2. Mark the locations of smartphones M and N. 3. Use solid lines to represent the current indifference curves of the consumer before the introduction of a decoy. 4. Use a “D” to mark the area where the decoy should locate. Explain why. 5. Use dashed lines to show what the voter’s indifference curves would look like if the introduction of the decoy had the intended effect. 2 Question 4. (35%) There are three students named Alex, Beth, and Charlie. All three of them are loss averse over money, with the same value function for money: v(x dollars) = √ x x ≥ 0 32√⃐x x < 0 All three of them are also loss averse over Apple watches, with the same value function for Apple watches: v(y Apple watches) =  10y y ≥ 0 20y y < 0 Total utility is the sum of the gain/loss utility for Apple watches and the gain/loss utility for money. The reference point is the status quo, that is, a person’s initial endowment. Alex owns an Apple watch and is willing to sell it for a price of a dollars or more. Beth does not own an Apple watch and is willing to pay up to b dollars for buying it. Charlie does not own an Apple watch, and values it at c dollars (that is, he prefers getting an Apple watch over getting x dollars if x < c, and prefers getting x dollars if x > c). 1. Solve for a, b, and c. 2. Instead, suppose Alex, Beth, and Charlie are only loss averse over Apple watches, but not over money. That is, their value function for money is instead: v(x dollars) = √ x x ≥ 0 √᳐x x < 0 and their value function for Apple watches remains: v(y Apple watches) =  10y y ≥ 0 20y y < 0 Solve for a, b, and c. 3. Instead, suppose Alex, Beth, and Charlie are not loss averse: v(x dollars) = √ x x ≥ 0 √᷐x x < 0 and v(y Apple watches) = 10y 3 Solve for a, b, and c. 4. Suppose Alex, Beth, and Charlie are not loss averse (as in the previous question), but their value for an Apple watch varies with ownership. Specifically, the value of the Apple watch is 10 for someone who does not currently own an Apple watch , and 20 for someone who currently owns an Apple watch . Solve for a,