1. Conceptual Question Personnel Economics. Explain the difference between moral hazard and adverse selection. Discuss three examples of features of the labor market that can be explained as features that ameliorate moral hazard in the employer employee relationship. Some Perfect Competition and Monopoly Problems 2. Suppose you are working for a firm producing a new, innovative product. You are the only producer of this good. The cost function is given by (g) = 500 + % g2, and you have paid a market research firm to assess the demand for your good. They estimate that the market demand curveis Q = 1,000 2P. a) Isthis the short run or long run? b) If the firm is currently charging a price of $325, are they making a profit? c) Should the firm change the price they are charging? What price should they charge? Show your work! d) Given your recommendation to (b) and (c) above, by how much would the firm's profits increase? Suppose the market demand for your good is given by P=120-(1/5)Q. The cost function for each firm is identical, and is given by c(g)=10+(1/10)g?. a) If all firms in this market have the same technology and are price-takers, how many units should each firm produce if the market price for the firm's product is $20? b) If thereis only one firm in the market (i.e. it is a monopoly), what price should it charge and how many units should it sell to maximize profits? Consider a perfectly firm who has a cost function of c(Q) = 3 + 4Q + 6Q2. a) Solve for the firm's supply function. b) If Price is $60, what are the firm's profits? Do they want to produce in the short run? c) If priceis $10, what are the firm''s profits? Do they want to produce in the short run? 5. Duopoly Problem. Consider 2 firms selling fertilizer and competing as Cournot duopolists. The inverse demand function facing the fertilizer market is P = 1 - Q, where Q = qA + qB. Assume that the cost function for firm A is given by c(qA ) = =qA, whereas the cost function for firm B is given by 1 2 c(qA) = 8 qB a) Find the Cournot Nash equilibrium if the BR functions are: BRA (qB ) = qA = = 2 9B and BRB(qA) = 9B = 4 qA b) Find the Stackelberg equilibrium where firm A moves first. c) Compare profits from part (a) and part (b). Would firm A benefit from moving first? Does firm B benefit from moving last?6. Game Theory Problem. Answer the following questions regarding the matrix below, which represents the strategic interaction between Jackson and Dakota this past Sunday, where the two are trying to decide which games they want to play - if they both choose the same game then they get to play together! Dakota Risk Minecraft Barbies Risk 6,3 0, 2 1, 1 Jackson Minecraft 2,0 5,5 2,0 Barbies 1, 1 0, 2 3, 6 a) Suppose Jackson and Dakota make their decisions simultaneously. Are there pure strategy Nash equilibria? If so, what are they? Show your work. b) Suppose they move sequentially, and that Jackson moves first. First set up the game tree. What will be the equilibrium path of the subgame perfect Nash equilibrium outcome? Would Dakota want this to happen? Explain intuitively why or why not.Model of Supply and Demand Problem. Using the model of supply and demand, consider the global market for wheat. lllustrate the impacts on the global market for wheat if (i) war in Ukraine (an important source of wheat) means that half of all farmers there do not plant wheat fields this year while (ii) economic growth picks up, increasing wages for households throughout the economy. Explain the changes to the global wheat market, illustrate those changes graphically, and make conclusions about expected changes to the market price and quantity for wheat. Decision-Making Under Uncertainty. Calculate the profit-maximizing level of output for a perfectly competitive firm in each of the following circumstances: a) Thefirm's cost function is given by c(Q) = i (2, and the price = $50 with probability 1/3, and equals $90 otherwise. b) The firm's cost function is given by c(Q) = % (2, and the price equals $6, $9, or $15, each with equal probability. 9. Choosing Between Innovation Projects. Consider the following three innovation projects: Project 1: invest $100 now in R&D and get back S60 in one year, 575 in two years, and 590 in three Project 2: invest S50 now in R&D and get back 530 in each of the next three years Project 3: invest 525 now in R&D and get back 510 in one year, 25 in two years, and S50 in three (a) if the annual interest rate is 10%, which of the three projects looks like a profitable line of research and development? (b) Which of the three projects should you prioritize? In other words, rank them according to their priority and explain your ranking. 10. Sustainability Conceptual Problem. Explain three ways how engaging in voluntary sustainability initiatives may lead to increased profits for a firm