m2Q.pdfMidterm2.pdfA.pdfB.pdfC.pdfD.pdfG.pdfGA.pdfEcon 301Intermediate MicroeconomicsProf. Marek WeretkaMidterm 2 (Makeup)You have 70 minutes to complete the exam. The midter m con sists of 5 quest ions (10,30,20,15 and 25points)+Just For Fun quest ion.Problem 1. (10p ) (Uncertainty)Rober t’s Bernoulli utility function is given by u(c) = c2. A lottery ticket pays 12 wit h p robability14and zero otherwise and thus the lottery is C = (12; 0).a) Is Robert is risk averse, risk neutra l or risk loving (choose one).b) Write down Von Neumann -Morgenstern (ex pected ) util ity function over lotteries U (C1; C2) (give aformula ) and …nd utility from lo ttery C.c) Find the certainty equivalent CE of lottery C (one number) and the expected val ue E(C) of thelotter y (one number). Is certainty equivalent bigger or smaller than expected value? Why? (one sentence)Problem 2. (30p ) (Edgeworth box and e quilibrium)Two favorite ice cream ‡avors of Jerry and Ben are Creme Brulee x1and Ban ana Split x2. Jerry isinitially endowed w ith !J= (5; 15) of th e two ‡avors and Ben’s endowment is !B= (15; 5). The utilityfunction of Jerry and Ben is the same and is g iven byU (x1; x2) = 7 ln x1+ 7 ln x2a) Plot a n Edgeworth box and mark the initial en dowments.b) Using the MRS condition verify that the initial endowments are Pareto ine¢ cient (compare twonumber s + graph argument).c) Find competitive equilibrium (give six numbers) and depict the equilibrium i n the Edgeworth box.d) Ve rify that the allocation in the competitive equilibrium is Par eto e¢ cient (co mpare two numb ers).e) Hard: Suppose !J= (20; 0) and !B= (0; 10) and utility functio n UB(x1; x2) = 2x1+ x2for Ben andUB(x1; x2) = x1+ 2x2for Jerry. Depict the contract curve in an Edgeworth Box .Problem 3 (20p). (Short questions)a) Given productio n fu nction y = 2K2L12and short-run level of capitalK = 1 derive labor demand(formula) of a competitive …rm. Find equilibrium real wage rate if labor supply is given by Ls= 4 (onenumber ). Find the unemployment rate if the minimal wage is wmin= 1 (one number +grap h).b) Hard: Consider a standard problem of insurance with two states (‡ood, no ‡ood ) with Bernoulliutility function u (c) = ln c. Demonstrate that if premium is greater than probability of ‡ood, > F.consumer will not purchase full insurance. (Hint: Use "MRS" secret of happiness to show that in opt imumCF< CN F)Problem 4. (15p ) (Producers)A producer has the fo llowing technologyy = K14L14a) What are the returns to scale? (chose: IRS, DRS or CRS)b) Fin d analytically a cost function given wK= wL=12(formula). Plot the cost function in the graph.c) Assumi ng …xed cost F = 1 …nd analytically yM ESand AT CM ES(give two numbers) and plot asupply of the …rm , marking a threshold for non-zero produ ction.1d) D etermine the number of …rms operating in the industry if demand is y (p) = 20 p, …rms arecompetitive and there is free entry. (one number)1If you do not know how to answer b) to get partial credit you can assume c(y) = y21Problem 5. (25p ) (Market Power)Consider a monopoly with total cost T C(y) = 0:5y2facing inverse demand p(y) = 200 y.a) Find the optimal level of producti on and price (two numbers+ graph).b) Find Total Surplus, Cons umer Surplus, Producer Surplus and DW L (four numbe rs +graph) . Isoutcome Pareto e¢ cient? (yes-no answer + one sentence)c) Find the elasticity of t he demand at the optimal point (one number). Is demand elastic at optimum?d) Hard: Prove formally that any monopoly operates on th e elastic part of the demand.2Just For FunProve that in any economy with Cobb-Douglas preferences, in any competitive e quilibrium, the allocationis Pareto e¢ cient (Hint: use "MRS" secrets of happiness)2To get partial credit you can assume that T C(y) = cy where c is a constant.2Econ 301Intermediate MicroeconomicsProf. Marek WeretkaMidterm 2 (Group B)You have 70 minut es to complete the exam. The midterm consists of 5 questions (10,30,20,15 and 25points)+Just For Fun quest ion.Problem 1. (10p ) (Uncertainty)Rober t’s Bernoulli utility function is given by u(c) = c2. A lottery ticket pays 8 with probability14andzero otherwise and thus the lotter y is C = (8; 0).a) Is Robert is risk averse, risk neutra l or risk loving (choose one).b) Write down Von Neumann -Morgenstern (ex pected ) util ity function over lotteries U (C1; C2) (give aformula ) and …nd utility from lo ttery C.c) Find the certainty equivalent CE of lottery C (one number) and the e xpected value E(C) of thelotter y (one number). Is certainty equivalent bigger or smaller than expected value? Why? (one sentence)Problem 2. (30p ) (Edgeworth box and e quilibrium)Two favorite ice cream ‡avors of Jerry and Ben are Creme Brulee x1and Ban ana Split x2. Jerry isinitially endowed with !J= (100; 20) of the two ‡avors and Ben’s endowment is !B= (20; 100). The util ityfunction of Jerry and Ben is the same and is g iven byU (x1; x2) = 2 ln x1+ 2 ln x2a) Plot a n Edgeworth box and mark the initial en dowments.b) Using the MRS condition verify that the initial endowments are Pareto ine¢ cient (compare twonumber s + graph argument).c) Find competitive equilibrium (give six numbers) and depict the equilibrium i n the Edgeworth box.d) Ve rify that the allocation in the competitive equilibrium is Par eto e¢ cient (co mpare two numb ers).e) Hard: Suppose !J= (0; 2) and !B= (4; 0) and utility function U (x1; x2) = min(x1; x2) for Ben andJerry. Depict th e contract curve in an Edgeworth Box .Problem 3 (20p). (Short questions)a) Given prod uction fun ction y =14K2L12and short-run level o f capitalK = 2 de rive labor demand(formula) of a competitive …rm. Find equilibrium real wage rate if labor supply is given by Ls= 9 (onenumber ). Find the unemployment rate if the minimal wage is wmin= 1 (one number +grap h).b) Hard: Consider a standard problem of insurance with two states (‡ood, no ‡ood ) with Bernoulliutility function u (c) = ln c. Demonstrate that if premium is greater than probability of ‡ood, > F.consumer will not purchase full insurance. (Hint: Use "MRS" secret of happiness to show that in opt imumCF< CN F)Problem 4. (15p ) (Producers)A producer has the fo llowing technologyy = 4K14L14a) What are the returns to scale? (chose: IRS, DRS or CRS)b) Find analytically a cost f unction given wK= wL= 8 (formula). Plot the cost function in the graph.c) Assumi ng …xed cost F = 1 …nd analytically yM ESand AT CM
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