Part 2: long problems 170 marks! Problem 1 130 marks! Suppose a consumer buys two goods, good X and a composite good Y. The utility function is given as U[X,Y)=5'JXY. I=Slll Px=$2 Where I is income level, PX is the price ofgood 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 MRSFK? Why?[ 5 marks) 5) Does the given utility function satisfy the law ofdiminishing MU? why? [ 5 marks) 6) Does the given utility function satisfy the assumption that more is better? why?[5 marks) Problem 2 [2|] 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) 2) 3) 4) Suppose there is a free trade, how many units ofcalculatom will be imported? [ 5 marks) Suppose a tariff of$10 is imposed on each unit ofthe imported calculators. How many units of calculators will be imported now? ( 5 marks) How much revenue does this tariff policy generate for the government? [ 5 marks) Calculate the change in consumer surplus, the change in producer surplus and the deadweight loss resulting from the tariff. [ 5 marks) Problem 3 [2|] 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) 2) 3) 4) 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) What is the slope ofthis budget line? [ 5 marks) What is the optimal bundle that maximizes utility and show it on a graph. [ 5 marks) 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