Download 6 Problems on Intermediate Microeconomic Theory - Final Exam | ECON 301 and more Exams Microeconomics in PDF only on Docsity! Econ 301 Intermediate Microeconomics Prof. Marek Weretka Final (Group B) Problem 1. Monica consumes bananas x1 and kiwis x2: The prices of both goods are p1 = p2 = 1 and Monicas income is m = 100. Her utility function is U (x1; x2)= (x1) 37 (x2) 37 a) Find analytically Monicas MRS as a function of (x1; x2) (give a function) and
nd its value for the consumption bundle (x1; x2)= (80; 20) :Give its economic and geometric interpretation (one sentence and
nd MRS on the graph) b) Give two Monicas secrets of happiness that determine her optimal choice of fruits (give two equation). Explain why violation of any of them implies that the bundle is not optimal (one sentence for each condition). c) Show geometrically the optimum bundle of Monica do not calculate it. Problem 2. Georgina loves two types of owers: Cuban lilies x1and calla lilies x2: Her utility from having a bouquet (x1; x2) is U (x1; x2)= 2x1+2x2 a) Propose a utility function that gives a higher level of utility for any (x1; x2), but represents the same preferences (give utility function). b) Suppose the prices of both types of lilies are p1= 2 and p2= 1 and the Georginas total income m = $10. Plot her budget set. Find the optimal bouquet (x1; x2) and mark it in your graph (give two numbers) c) Are the owers Gi¤en goods (yes or no and one sentence explaining why)? d) Suppose in the ower shop currently there are only six calla lilies x2 in stock (hence x2 6). Plot a budget set with the extra constraint and
nd (geometrically) an optimal level of consumption given the constraint. Problem 3. (Equilibrium) Tomorrow it may rain or shine and the chances are 50% 50%. Today, there are two commodities traded on the market: umbrellas x1 and swimming suits x2. Jeremy has ten umbrellas and no swimming suits (!J= (10; 0) ) :Bill has twenty swimming suits and no umbrellas (!J= (0; 20)). Jeremy and Bill have identical utility functions given by U i (x1; x2)= 1 2 ln (x1)+ 1 2 ln (x2) a) Plot an Edgeworth box and mark the point corresponding to endowments of Jeremy and Bill. b) Show in a graph a set of all Pareto e¢ cient allocations (do not calculate it). c) Find prices and an allocation of umbrellas and swimming suits in a competitive equilibrium and mark it in your graph. d) Is the outcome of market interactions Pareto e¢ cient (yes or no, give an argument involving two numbers)? Problem 4.(Short questions) a) You are going to pay taxes of $300 every year, forever. Find the Present Value of your taxes if the yearly interest rate is r = 1%. b) Consider a lottery that pays 0 with probability 14 and 4 with probability 3 4 and a Bernoulli utility function is u (x) = x2. What is a von Neuman-Morgenstern utility function? Find the certainty equivalent of the lottery. Is it bigger or smaller than the expected value of the lottery? Why? (give a utility function, two numbers and one sentence.) 1
