Part 2: long problems (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 VXY . 1=$20 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. ( 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 MRSyx? Why? (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=$1 per unit and Py=$2 per unit. 1) Write down the equation of the 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 of this budget line? ( 5 marks) 3) What is the optimal bundle that maximizes utility 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