Behavioral economics Assignment | Top Essay Writing

(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.

a) [10 points]Find the profit for factory and fishermen under the following scenarios. Fill out the following table. What is the efficient outcome?

	No filter + No treatment	filter + no treatment	No filter + treatment
Factory’s profit
Fishermen’s profit
Total profits

b) [6 points]Suppose there is no well-defined property rights and no cooperation between fishers and factory. What will be the outcome? Is it efficient?

c) [6 points] What is the outcome of bargaining if fishers have right to clean water? Who, factory or fishers, get the benefits?

d) [8 points] Suppose factory have the right to emit effluent. What is the maximum amount fishers are willing to pay for clean water? What is the minimum factory is willing to accept to install filter? Is there any possibility for bargaining? In that case what will be the outcome?

2- [15 points]Two investors have each deposited $10 with a bank. The bank has invested these deposits in a long-term 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 two-stage game: player 1 and player 2.

At the beginning, each player is endowed with $5.
Stage 1: player 1 decides whether to Exit and keep his endowment, which results in ($5, $5) payoffs or to Engage and pass his money to player 2.
Money sent is tripled.
Stage 2: Before making his/her, move player 2 knows the decision of player 1.
If player 1 decided to Exit, player 2 has no decision to make.
If player 1 decided to Engage, player 2 can either Cooperate and reciprocate player 1’s behavior which results in payoffs ($7.5, $12.5) or Defect and keep all the money, which yields payoffs ($0, $20).

a) [6 points]Draw the extensive form of the game.

b) [9 points]draw the matrix of payoff for the normal form of the above game. Find all the Nash equilibria.

c) [5 points]Find the subgame perfect Nash equilibria. Is it efficient?

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.

a) [4 points]If a producer i decides to produce individually, . Why should a producer join the team and don’t produce individually?

b) [8 points]What is the efficient effort level of each team member?

c) [8 points]Suppose that the team members agree the divide the output, q equally, i.e. What will be the Nash equilibrium effort level by each team member?

d) [10 points]Now suppose that every team member agrees to get , where F is a fixed amount. What will be the Nash equilibrium effort level by each team member in this case? Find the value of F.

2- [16 points] Consider a hypothetical economy in which each worker has to decide whether to acquire education and become a high-skilled worker or remain low-skilled. Let and denote the incomes earned by a high- and low-skilled 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 high-skilled 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) = n-36. 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

a) [5 points]Assume Ana and Beatriz are self-interested. Do players have a dominant strategy? What is it? What is the equilibrium outcome? Is it efficient?

b) [10 points] Now supposeAna and Beatriz are altruistic and get utility not only from their own payoff but from the other player’s payoff. Draw the indifference curves for Ana(label the graph properly). What is the possible dominant strategy for Ana & Beatriz in this case? In that case, what will be the equilibrium?

c) [10 points]Now suppose that Ana and Beatriz have utility functions based on self-interest and inequality aversion as follows: where , where stands for payoff andif i stands for Ana, then j refers Beatriz; if i stands for Beatriz, then j refers Ana. For what values of and will both players work?

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.

[5 points]What is the industry supply function?

[5 points]What is the equilibrium market price and quantity?

[5 points]What is the per period profit of each firm?

[6 points]Suppose a N+1 firm can enter this industry but must pay an entry cost of 1. The firm will compare the present discounted value of its profits after entry with the entry cost. It will enter if the present discounted value of the profits exceeds the entry cost and stay out otherwise. If the firm’s discount factor is δ = 0.9 and the firm expects no change in the demand and supply sides of this industry would it want to enter the industry if N=10? How about if N=20?

Assume that the entrant takes into consideration the effect that its entry will have on the market price. Also note:

[4 points]What is the maximum number of the firms that will enter the market?

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.

[6 points]Suppose the entrant stays out of the market. What would be the optimal quantity that the incumbent wants to produce? What would be the profit? Show your work.

[8 points]Suppose the entrant has already entered the market. The incumbent and the entrant now play a Cournot duopoly. How many units would each firm produces? Find the price and each firm’s profit under the equilibrium quantities. Sow your work.

[5 points]Assuming the entrant is in the market, the incumbent wants to fight. Specifically, the incumbent wants to produce qI = 20. Given this, find the entrant’s optimal quantity to produce. Find the price and each firm’s profit under the quantities. Show your work.

[6 points]Relying on the above results, draw the game tree and the payoffs of the following game. The entrant first decides whether to enter or not. If the entrant enters, the incumbent decides whether to compete as in (ii) and or producing qI = 20. If the entrant does not enter, the incumbent maximizes a monopoly profit.

[5 points]Find the subgame perfect equilibrium of the above game. Show your work.

[3 points] Going back to the beginning of the question, suppose the entrant did not yet enter. The incumbent already produced qI= 20. Assuming the entrant does not enter; find the price and incumbent firm’s profit. Show your work.

[7 points]Given the above results, draw the game tree and the payoffs of the following game. The incumbent chooses first. She may not fix the quantity. The other choice is to produce qI= 20. In any case, the entrant decides whether to enter or not. If the incumbent chose not to fix the quantity, the incumbent maximizes a monopoly profit or plays a Cournot duopoly depending on the entrant’s decision. If the incumbent chose to produce qI= 20, the incumbent cannot change the quantity regardless of the entrant’s choice.

[5 points]Find the equilibrium of the above game.

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

[6 points]Calculate profits in each case. Should Telemetafores choose to upgrade?

Another company, StoTsaka, is considering of entering the Telasia market for transporters by building a state-of-the-art 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

[8 points]What are the profits of Telemetafores and StoTsaka as a function of whether Telemetafores invests or does not invest in the upgrade of its plant, assuming that StoTsaka decides to enterthe market? [

[4 points]Use the information in parts (a) and (b) above to fil out the matrix of payoff for the normal form of the game between Telemetafores and StoTsaka, assuming that the two firms make their respective decisions (the former whether to upgrade the plant or not to upgrade, the latter whether to enter the market or not to enter) simultaneously. Use the fact that if StoTsaka does not enter the market, its profit is zero.

Telemetafores	StoTsaka
		Enter	Not enter
	Upgrade
	Not upgrade

[6 points]How low does E have to be for “Not Enter” to be a dominated strategy for StoTsaka? That is, for what values of E is the strategy “Not Enter” dominated by the strategy “Enter”?

[6 points]If the entry cost E is equal to 300, fill out the matrix of payoffs again. What is the Nash Equilibrium of the game?

Telemetafores	StoTsaka
		Enter	Not enter
	Upgrade
	Not upgrade

Econ 480, Spring 2020

Bonus Quiz: total points 80

1-[14 points] Consider a three-firm 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
Firm A	OLD	50, 100	100, 50

[4 points]Find the Nash equilibrium(s) of the simultaneous game if they exist?

[4 points]Draw the tree of a two-stage extensive-form game in which firm A chooses its technology in stage I, and firm B choses its technology in stage II (after observing the choice made by firm A). Make sure you indicate firm’s profits at the termination points on the tree.

[8 points]Write down the normal form of the above sequential game and find the Nash Equilibrium(s), if they exist? [

[4 points]Solve for the subgame perfect equilibrium of the sequential game? Provide an explanation justifying our answer.

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 points] Derive the utility of consumer located at point 0 <x < 1 if she buys from firm 0. Derive the utility if she buys from firm 1.

[6 points]Suppose there are 100 consumers who are uniformly located on the line. Derive the demand for store 0, which is the number of people who want to buy at store 0. Derive the demand for store 1 as well. Show your work:

[6 points] Assume no production cost. Suppose the firms compete over prices. Solve for the Nash-Bertrand equilibrium price and quantity for each firm.

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 per-unit 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.

[10 points]What is the price that you will charge to hospitals (H)? To drug stores (D)?

[10 points]If you were to charge a uniform price to all the buyers, what would it be? [10 points]

[10 points]If the Antitrust Division cares about the sum of your company’s profits plus the total consumer surplus of all the buyers, do you think it should ban price discrimination? (Computation required for full credit. Hint: compute the consumer surplus separately for drug stores and hospitals, even if they buy at the same price, and then add them up.)