4. After the pandemic is over, the loss of government revenue due to the economic lockdown and the cost of the worker compensation scheme, made government debt soar and the treasury asks you for advice on how to reduce government debt. a) Currently, the citizens of Korona pay a flat tax on labour income of 20% and a proposal by the minister is to increase the tax rate to 30% if income exceeds the threshold of $20,000. Give your assessment of the likely effect of the proposal on labour supply, paying particular attention to the underlying forces at work. Briefly comment on how these forces may affect government revenue. [You can include a graph if it helps to illustrate your reasoning; word limit 250 words; 8 marks]. b) An alternative policy proposes to introduce a tax on inheritances to raise the same amount. Assess the effect on welfare of this inheritance tax allowing for different behavioural responses. [word limit 200 words; 6 marks]. c) Contrast the proposals in a) and b) regarding the potential for off-shore tax evasion. [word limit 200 words; 6 marks].2. Currently, Krona has currently no compensation scheme for workers infected with the disease and you are advising the government on the introduction of such a scheme (suppose for this exercise that there are no other unemployment or sick benefits and this would most likely concern any future disease). Model the economy with identical individuals who earn a wage of 500 while working and 0 when sick with the disease. With probability q, the individuals get sick with the disease and cannot work. When sick, individuals would receive a sickness compensation s from the government. To finance the scheme, when working individuals pay lax of (500*t) where t is the tax rate. u(c) = c1/$ denotes the individuals utility from consumption of c in any given state. a) Write down the individual's expected utility as function of s, q and t. [3 marks] b) What is the government's budget constraint for an actuarially fair compensation scheme; write down what is balanced government budget in terms of s, q and t. [2 marks] c) Find the value of compensation s that maximizes individuals expected utility, assuming a balanced budget. [6 marks] d) What is the tax rate t required to finance the compensation maintaining a balanced budget? Discuss very briefly the intuition (2 sentences). [4 marks] e) Discuss briefly the merits of the introduction of such a disease specific compensation scheme, including a brief discussion of moral hazard. [5 marks]Evaluate carefully each of the following statements. Decide if they are True, or False. You must explain clearly the reason(s) why the statement is true or false. You should provide a pre- cise justification, including the transmission mechanisms using words and graphs if needed. Your mark will depend on the quality of your response. 1. While monetary policy can be effective at increasing the level of output beyond its natural level in the short run, it becomes ineffective in doing so in the medium run. (5 points) 2. Consider an open economy with fixed prices. If the government spending and taxes in- crease by the same amount, this will not have any impact on net exports since the interest rate would not change. (5 points) 3. The aggregate supply relation suggests that an increase in output leads to an increase in the price level. (5 points)Part 2: True or false questions with justification (30 points) Evaluate carefully each of the following statements; decide if they are True or False and provide a precise justification for your answer. Your mark will depend on the quality of your response. 1. An increase in the marginal tax rate increases the investment multiplier, while an increase in the marginal propensity to consume lowers it. 2. If consumers become thrifty, in the sense that they reduce their autonomous consumption, for example, this will end up lowering their saving. 3. The IS curve is downward sloping because an increase in taxes lowers the level of output. 4. The demand for money does not depend on the interest rate because only bonds earn interest.7. The short-run effects of a change in the money supply on output is reduced when the IS curve becomes steeper? (5 points) + 8. Bonus question: Consider a closed economy where government spending is endogenous in the sense that government must spend all its tax revenue. The latter is a fixed prop tion t of output: G = tY. An increase in the marginal tax rate, t, will reduce equilibrium.. output. (2 points)(a) Suppose a monopolist sells its product in two different markets separated by some distance. The demand curves in the markets given by q1 = 110 -2p1 and q2 = 35 - pz. Marginal and average costs are constant at Rs. 15. (i) If the monopolist can maintain the separation between the two markets, what are total profits in this situation? (ii) Suppose the firm could adopts a linear two part tariff under which marginal prices must be equal in the two markets but lump-sum entry fee might vary. What pricing policy (third degree price discrimination or linear two part tariff) should the firm follow? b) The payoff matrix of the two rival players is given as; Player 2 L R Player 1 T 4.4 2.6 B 6.2 0.0 (i) Find the pure-strategy Nash equilibrium or equilibria. Compute the mixed-strategy Nash equilibrium. As part of your answer, draw the best- response function diagram for the mixed strategies. (iii) Suppose the game is played sequentially, with player 1 moving first. Write down the normal and extensive forms for the sequential version of the game. (iv) Using the normal form for the sequential version of the game, solve for the Nash equilibria. (v) Identify the proper sub-games in the extensive form got the sequential version of the game. Use backward induction to solve for the subgame-perfect equilibrium. Explain why the other Nash equilibria of the sequential game are "unreasonable'. (c) Explain marginal cost pricing dilemma that arises under natural monopoly. (a) There is a 50 KM long beach which has two ice cream stands, A and B, located at 20 KM and 35 km respectively, from the starting point. They sell identical ice cream cones, which for simplicity are assumed to be costless to produce. The buyers of ice cream cones are located uniformly along the beach, one at each unit of length. Each buyer consumes one cone daily. Carrying ice cream a distance 'd' back to one's beach umbrella costs 0.05d', where d is the distance (in km) of the buyer from the ice cream stand. In the context of Hotelling's Beach location model; (i) Find the location of the buyer who is indifferent between buying ice cream from A and B. (ii) Find the total sales of ice cream one ice cream cone. (iii)Find the equilibrium prices cha1. (60 points) Suppose an industry with inverse market demand P = 300-2Q is comprised of three firms which compete in quantities. Firm 1 is a Stackelberg leader and therefore acts first. Firms 2 and 3 observe Firm l's decision, then act simultaneously. Firms produce output with constant marginal cost c = 60. (a) (10) Write the profit functions for the three firms as a function of choice variables (quantities for each firm) only. (b) (15) For any value of 91, find the best response functions for firms 2 and 3. (c) (10) Use your answers to part (b) to express q2 and qa as functions of q only (i.e. not as functions of each other). (d) (10) Find the subgame perfect Nash equilibrium of this game (i.e. the optimal choices which characterize what all firms are doing in equilibrium), equilibrium profits, and market clearing price. (e) (15) Suppose that firms 1 and 2 act simultaneously in the first period, then Firm 3 observes their choices before making its decision. Does social welfare increase or decrease relative to the previous model? (Hint: which is closer to how a perfectly competitive market would behave?) 2. (40 points) Consider a Hotelling model of the type discussed in class: there is a beach that is one mile long, with customers evenly distributed along the beach. Two dif- ferent ice cream shops are located at the endpoints of this beach (at points 0 and 1). Consumers dislike walking down the beach and pay transportation costs t = 2 per mile walked. All consumers have a value of V = 10 for an ice cream. Ice cream shops have constant marginal cost c = 2. (a) (5 points) Consider a consumer who is at the midpoint of the beach, r = }. Write down their total cost (including transportation costs) of buying from each firm, assuming firm 1 (located at 0) sets price Pi and firm 2 (located at 1) sets price (b) (10 points) A consumer is indifferent between the two shops if the total cost they face at both shops is the same. Call this indifferent consumer's location rm. Find I'm for any pair of prices Pi and P2. (c) (15 points) All customers to the right of i'm buy from firm 2, and all customers to the left of I'm buy from firm 1. Write down each firm's profits as a function of Pi and Pr. (d) (10 points) Find the Bertrand equilibrium prices of this market