(economics of coordination)
Quiz Bonus: 65 points
1 [30 points] ASteel factory dumps effluent in the river. Without cleaning water, the factory profit is $500 and the fisherman’s profit is $100. If the water is clean, the fishermen’s profit increases by $400 to $500. There are two ways to clean water: factory can install a filter system at the cost of $200 or fishers can install a treatment plant at the cost of $300.
No filter + No treatment  filter + no treatment  No filter + treatment  
Factory’s profit  
Fishermen’s profit  
Total profits 
2 [15 points]Two investors have each deposited $10 with a bank. The bank has invested these deposits in a longterm project. If the bank is forced to liquidate its investment before the project matures, a total of $16 can be recovered. If the bank allows the investment to reach maturity, however, the project will payout a total of $30. In each case, the return is equally divided among investors. There are two dates at which the investors can make withdrawals from the bank: date 1 is before the bank’s investment matures; date 2 is after. For simplicity assume there is no discounting. If both investors make withdrawals at date 1 then each receives $8 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives $10, the other receives $6, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawal at date 2 then each receives $15 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives $20, the other receives $10., and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns $15 to each investor and the game ends. The following matrices of payoffs illustrate the game described above.
Date 1  
Investor 1  Investor 2  
Withdraw  Don’t  
Withdraw  8, 8  10, 6  
Don’t  6, 10  Next stage 
Date 2  
Investor 1  Investor 2  
Withdraw  Don’t  
Withdraw  15, 15  20, 10  
Don’t  10, 20  15, 15 
Use backward induction to find the two Subgame perfect equilibria of the game.
3 [20 points] Trust game: There are 2 players participating in the twostage game: player 1 and player 2.
Econ 490 (economics of coordination), spring 2020
Quiz 7: 85 points
1 [30 points] There are 10 producers, who work in a team to produce a product. Assume that the production function is , where q is the output, is the effort level and 4 is the fixed cost of production which is independent of the number of team members. The net payoff of each team member is, where is the member i’s income. The sum of is equal to q, i.e.
2 [16 points] Consider a hypothetical economy in which each worker has to decide whether to acquire education and become a highskilled worker or remain lowskilled. Let and denote the incomes earned by a high and lowskilled worker respectively. These incomes are defined as and as , where H and L are constants (H>L) and is the fraction of the population that decides to become high skilled. The gain from education and acquiring skill is thus . However, education and acquiring skill carries a positive cost of C (a constant). Assume that all individuals simultaneously choose whether to become skilled or not.
a)[4 points]Does there exist any complementarity in acquiring skill? Describe it.
b)[12 points]Suppose that H − L < C < 2(H − L). Draw on the same graph the gain from acquiring skill versus f and cost of acquiring skill versus f. Is the situation in which only a fraction of the population becomes highskilled equilibrium? Give an algebraic expression for this fraction. In case it is an equilibrium, is it stable or unstable?Find the other equilibrium values of f and determine which one is stable.
3 [14 points]Consider a group of farmers who want to build an irrigation project. N: The number of farmers; n = The number that participate in the project. The payoff to each farmer depends on how many others participate in the project. If a farmer participates in the project, her payoff is equal to B(n) – C(n)& if the farmer shirks her payoff is B(n), where B(n) = 5n and C(n) = n36. Show that if n < 40 then each farmer will participate. Draw the graph and determine the equilibria of this game in the graph. Determine whether the equilibria are stable or not. Is this game a Prisoner’s dilemma, assurance or chicken game? Why?
4 [25 points] Think about the following social dilemma: there are two classmates, Ana and Beatriz, who have to work on a joint assignment for their biology class. Each has to decide independently whether to spend the afternoon on the project or shirk. The table below shows the payoffs in each case.
Beatriz  
Ana  Work  Shirk  
Work  4,4  1,5  
Shirk  5,1  2,2 
Econ 480, Spring 2020
Quiz 7: total points 100
1[25 points] An perfectly competitive industry consists of N firms, each one of which has a cost function given by: , where qi is the output of firm i in any given period. The per period market demand for this industry is given by P = 20 – 4Q.
Assume that the entrant takes into consideration the effect that its entry will have on the market price. Also note:
2 [45 points] Suppose there is a market which the incumbent firm is already in. The market demand is given by P = 32 – Q. The incumbent (I) firm’s cost function is given by CI (qI) = 8qI. There is a potential entrant (E).The entrant has a cost function is CE (qE) = 8qE + 16.
3 [30 points] The only manufacturer of transporters in the planet of Telasia is Telemetafores, which is using an outdated plant with a production cost of 10 per transporter. Telemetafores can upgrade the plant at a cost of 100. The upgrade will result in a production cost of 7 per transporter. The optimal price and corresponding sales are given by the table below:
Unit Cost  Optimal Price  Quantity Sold  
Upgrade  7  14  120 
Not Upgrade  10  18  100 
Another company, StoTsaka, is considering of entering the Telasia market for transporters by building a stateoftheart plant at a cost of E. This plant produces transporters at a cost of 7 per transporter. The cost of Telemetafores are given above (and depend on whether Telemetafores upgrades the plant or not). The optimal price and corresponding sales for the two firms if StoTsaka enters the market are given below as a function of whether Telemetafores does or does not invest in the upgrade of its plant.
Optimal price  Optimal Quantity  
Telemetafores  StoTsaka  Telemetafores  StoTsaka  
Upgrade  12  12  80  80 
Not Upgrade  15  13  50  90 
Telemetafores  StoTsaka  
Enter  Not enter  
Upgrade


Not upgrade

Telemetafores  StoTsaka  
Enter  Not enter  
Upgrade


Not upgrade

Econ 480, Spring 2020
Bonus Quiz: total points 80
1[14 points] Consider a threefirm oligopoly in which the market demand for the homogeneous good is given by q = 24 – p, and costs are zero. Suppose firm 1 and 2 simultaneously pick their output, and then firm 3, observing these choices, picks its output (i.e. two “leaders”, one “follower”). Find the subgame perfect equilibrium quantities produced by these forms.
2 [20 points] Firms A and B can choose to adopt a new technology (N) or to adhere to their old technology (O). The table below exhibits the profit made by each firm under different technology choices.
Firm B  
NEW  OLD  
Firm A  NEW  200, 0  0, 200 
OLD  50, 100  100, 50 
3 [16 points] consider the following variant to the Hotelling’s model. Two stores are located at points zero (store 0) and one (store 1) along a linear street of length one. Due to heavy winds, it costs more to travel towards store 1. Suppose the marginal travelling cost is 1 towards store 0, but is 3 towards store 1 per unit of distance.Let the consumer’s valuation of the commodity be 10. Each consumer buys only 1 unit. LetP0 and P1 be the prices of the commodity at store 0 and store 1, respectively.
4 [30 points] Suppose that you are the managing director of a pharmaceutical company that sells a unique patented drug to hospitals and drug stores. You are free to charge different perunit prices at these two markets. Let p be the price per unit of drug and q be the quantity demanded. The hospitals demand curve is described by p = 12 – q and the drug stores demand curve is given by p = 8− q. The marginal cost of producing the drug is constant and equal to c = 2 per unit.