#### 1 True/false + explanations

Please answer whether a statement is true or false and give a 1-2 sentence explanation of why this is the case. NO PARTIAL CREDIT WILL BE GIVEN IF YOU WRITE “TRUE” OR “FALSE” BUT DO NOT PROVIDE AN EXPLANATION.

1.1 Deadweight loss is always zero under perfect competition.

1.2 A market’s equilibrium price and equilibrium quantity are determined by the intersection of the market supply curve and the market demand curve.

1.3 In a two-player static game, if one player has a dominated strategy, that player’s other strategie(s) must be dominant.

2.1 What is a potential problem that could arise when a government wants to regulate a monopsony with a minimum wage?

2.2 What is the shutdown condition and why is it important to check it?

2.3 Is price discrimination always bad for all consumers?

#### 3 Multi-part problems

Please answer all parts of the question. ALL QUESTIONS WILL BE WORTH THE SAME PERCENTAGE OF THE EXAM REGARDLESS OF THE NUMBER OF SUB-PARTS.

3.1 Perfect competition question

Imagine many small firms selling usb charging cables on a large online marketplace, in a setting of perfect competition. Each individual firm faces costs C(q) = 2q2 + 10q. A. Derive a firm’s supply curve.

Now assume there are 200 firms selling usb cables on the same large online marketplace. B. Derive the market supply curve.

Suppose the market demand curve is QD(p) = 2500 − 50p.

• What are equilibrium price and equilibrium quantity?
• Graph the inverse demand and inverse supply curves for the market andindicate the equilibrium price and quantity.
• What are consumer and producer surplus?

3.2 Price cap monopoly question

Imagine a university called Bavis that is the monopoly in the market for economics degrees, with cost-function C(Q) = 25Q2 + 450. Imagine the inverse demand function for economics degrees is p(Q) = 300 − 25Q. The government has decided it would ensure that there is no deadweight loss in this market for economics degrees by setting a price cap on Bavis.

1. What would be the equilibrium price and equilibrium quantity if the govern-ment did not impose a price cap and Bavis was able to operate as an un-regulated monopoly?
2. At what optimal price should the government cap economics degree sales?
3. What are the new post-price cap equilibrium price and equilibrium quantity?
4. What is Bavis’s new profit at the equilibrium?
5. Prove that this new profit level is a global maximum.
6. Show the new equilibrium price and equilibrium quantity graphically. Includethe original and regulated inverse demand curves, firm’s marginal revenue curve, and firm’s marginal cost curve.
7. What are consumer surplus, producer surplus, and deadweight loss at theequilibrium? How do they compare to the case of the un-regulated monopoly?

3.3 Price discrimination question

Imagine Bavis continues to be the monopoly in the market for economics degrees, though now with cost-function C(Q) = 30Q2. And now the inverse demand function for economics degrees is p(Q) = 4000 − 20Q. The government no longer imposes a price cap on Bavis. A. What are equilibrium price and equilibrium quantity?

• Show the equilibrium price and equilibrium quantity graphically. Include theinverse demand curve, firm’s marginal revenue curve, and firm’s marginal cost curve.

Now assume that Bavis is able to perfectly price discriminate in the market for economics degrees.

• What three conditions must be true for this perfect price discrimination tobe possible?
• What are the equilibrium prices and equilibrium quantity with perfect price discrimination?
• What are consumer surplus, producer surplus, and deadweight loss at theperfect price discrimination equilibrium?

3.4 Static game question

Imagine an airline traveler and TSA are playing a simultaneous static game. The airline traveler has to decide first whether to bring small liquids in their carry-on or not. If the traveler brings small liquids, they then have to decide whether to take their small liquids out of their bag at the security checkpoint. TSA also has three options. TSA can conduct a light search for small liquids, a thorough search for small liquids, or not search at all.

If the traveler does not bring any small liquids, they always make their flight and will get a utility of 8. TSA will get a utility of 8 if they conduct a light search verifying the lack of liquids without much effort, TSA will get a utility of 6 if they conduct no search at all since it’s less work but also they feel less secure, and TSA will get a utility of 5 if they conduct a thorough search since they worked hard and found nothing.

If the traveler brings their liquids and takes the liquids out of their bag, regardless of what TSA does, the traveler will make their flight with their liquids on-hand and will get utility of 9. In this case, TSA will get 9 utility if they conduct a light search verifying the liquids without much effort. TSA will get a utility of 6 if they conduct no search at all since it’s less work but also they feel less secure, and TSA will get a utility of 5 if they conduct a thorough search since they worked hard and found nothing.

If the traveler brings their liquids and does not take their liquids out of their bag, and TSA conducts any type of search (light or thorough), TSA will find the liquids, the traveler will need to stay for extra scanning, and they will miss their flight. They will then get a utility of 5. If the traveler brings their liquids and does not take their liquids out of their bag, and TSA does not search their bag, they will make their flight with their liquids and the least amount of effort and will get a utility of 10. In these cases, TSA will get a utility of 9 if they conduct no search at all since it’s less work and they still find the liquids, they will get a utility of 8 if they conduct a light search since they will feel good about finding the traveler’s liquid with minimal effort, and they will get a utility of 5 if they conduct a thorough search since they will find the liquid but they will have to do the greatest amount of work.

1. Draw the payoff matrix for this game.
2. Does the traveler have any dominated strategies? If yes, what is it/what arethey? If no, why not?
3. Does the TSA have any dominated strategies? If yes, what is it/what arethey? If no, why not?
4. What is/are the Nash equilibrium(s) of this game? If there are more thanone Nash equilibriums, how do we know which one will occur? E. Is this a prisoners’ dilemma?

3.5 Sequential game question

Imagine two roommates that live together in a small apartment—Alex and Chris. Chris likes to bake and made two dozen snickerdoodle cookies. Alex came home late, was hungry, and ate all of the cookies while Chris was sleeping. The next morning, Chris asked what happened.

Alex has three options. Alex can tell the truth, tell a small lie, or tell a big lie. If Alex tell’s the truth, that will be that. Both roommates will get payouts of 5 utils.

If Alex tells a small lie (I thought the cookies were for me!), Chris can then believe this and that will be that. In this case Alex will get 20 utils (that was easy!) and Chris will get 5. Or Chris can choose to ask a follow-up question (what made you think that?). Then Alex has two choices: double-down on the small lie or tell the truth. If Alex doubles down, Chris will stop asking and believe a bit more. This will lead to 15 utils for Alex and 10 for Chris. If Alex tells the truth now, Alex will only get 10 utils while angry Chris will get 5.

If Alex tells a big lie (someone broke in!), Chris can then believe this and that will be that. In this case Alex will get 15 utils (that was easy but now I wonder about Chris) and Chris will get 5. Or Chris can choose to ask a follow-up question (how did they break in and when?). Then Alex has two choices: double-down on the big lie or tell the truth. If Alex doubles down, Chris will stop asking and believe a bit more. This will lead to 10 utils for Alex (I still wonder about Chris) and 10 for Chris. If Alex tells the truth now, Alex will get zero utils (come on!) while very angry Chris will get 0. A. Please draw the game tree for this game.

• How many subgames does this game have?
• What is the subgame perfect Nash Equilibrium for this game?
• What is the minimum we would need to change Alex’s payoff to for telling thetruth at the beginning of the game for the subgame perfect Nash Equilibrium to involve Alex telling the truth then?

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