Part 1: multiple choice (30 marks) 5 marks each 1) Which of the following utility functions has a diminishing MRSxy ? a) U = 5X + 7Y b) U = 2X + 4Y2 C) U = XY d) U = X + InY e) U = min{2X, Y} 2) Suppose in a competitive market, the equilibrium price = $ 2.5 and the equilibrium quantity = 2.5 units and the price elasticity of supply EQ.s,p = 0.5 . Based on this information which of the following equations is the supply function? A) Q=P B) Q= 2+2.5P C) Q= -2.5 + 2P D) Q= 1.25 + 0.5P E) None of the above 3) Suppose the utility function is given as U = X + InY . Which of the following statements is correct? A) The more is better assumption is not satisfied for x in this utility function. B) The more is better assumption is satisfied for x in this utility function. C) This shows a positive and increasing marginal utility of x. D) The marginal rate of substitution of X for Y must be diminishing. E) None of the above5] 4) A) B] C] D) E) Consider a perfectly competitive market with market supply Qa = 2 + P and market demand Qd = 3DP. Suppose the government imposes an excise tax of$l per unit on this market. What is total surplus of the society after the government imposes the tax? T2 98 144.5 196.35 182.25 Based on the displayed gure, which of the following equations represents the linear 8. function? H] b] 0] dl 6] Q: 2.21: Q=2P4 Q=12+2P Q=4+4P Q=4+2P 6) Suppose that the government imposes a $9 per unit tax on good X. Suppose also that price elasticity of demand EQ.ap = -0.5 and price elasticity of supply EQs,p = 00 . Based on this information, which of the following statements about the incidence of this per unit tax is correct? A) Tax burden on consumer= $6 , while the tax burden on the producer= $3 B) Tax burden on consumer= $3 , while the tax burden on the producer= $6 C) Tax burden on consumer= $4.5 , while the tax burden on the producer=$4.5 D) Tax burden on consumer= $0 , while the tax burden on the producer= $9 E) Tax burden on consumer= $9 , while the tax burden on the producer= $0 You can draw a Table like this to answer your multiple-choice questions 1 2 3 4 5 6Part 2: longprublems [70 marks] Problem 1 [30 marks} Suppose a consumer buys two goods, good X and a composite good Y. The utility function is given as U(X, Y) = 5 var _ r=szu PX = $2 Where I is income level, PX is the price of good X 1) Find the optimal basket that maximizes utility and calculate its corresponding utility level.(5 marks) 2) Show your answer for Questions {1) on a graph. :1 5 marks) 3) Suppose a $0.5 per unit subsidy is levied on good X whose supply curve is perfectly inelastic. What is the new optimal basket that maximizes utility, and calculate its corresponding utility level_( 5 marks} 4) Does the given utility function have a diminishing MRSW? Why? :1 5 marks) 5) Does the given utility function satisfy the law of diminishing MU? why? ( 5 marks) 6) Does the given utility function satisfy the assumption that more is better? why?(5 marks} Problem 2 {20 marks} The domestic demand for calculators is given by Q = 60 P and the domestic supply is given by Q = 2P _ The world price for a calculator is $10 per unit- 1) Suppose there is a free trade, how many units of calculators will be imported? ( 5 marks) 2) Suppose a tariff of $10 is imposed on each unit of the imported calculators- How many units of calculators will be imported now? { 5 marks) 3) How much revenue does this tariff policy generate for the government? ( 5 marks} 4) Calculate the change in consumer surplus, the change in producer surplus and the deadweight loss resulting from the tariff. { 5 marks) Problem 3 {20 marks! Suppose the utility function over two goods X and Y is given by U(X, Y } = X + 3Y . Suppose the consumer's income is $20 and wants to spend it all on these two goods. Px=$l per unit and Py=$2 per unit. 1) Write down the equation ofthe budget line. Draw it on a graph, labeling the intercepts. Graph consumption of X on the horizontal axis, and consumption of Y on the vertical axis. { 5 marks) 2) What is the slope ofthis budget line? ( 5 marks} 3) What is the optimal bundle that maximizes utilityr and show it on a graph. { 5 marks] 4) At the optimal bundle, compare the marginal rate of substitution to the rate at which the consumer can substitute one good for another along the budget line? {5 marks) 4