Econ 301Intermediate MicroeconomicsProf. Marek WeretkaProblem set 4(due Thursday, February 17th, before class)Problem 1As in the previous problem set, Benjamin spends his time either watching movies (x1) (as you know heis taking advantage of ”on demand” option, cable TV) or listening to the songs - MP3 downloaded from theInternet (x2)His preferences areU (x1, x2) = 4 ln x1+ ln x2.His total income is m = 100, the price of MP3 is one dollar (per each song) (p2= 1). Suppose that theprice of a movie drops from p1= 10 to p1= 5.a) By how much the “consumption” of movies changes due to the price drop?b) Are movies ordinary or Giffen goods? Explain why.c) By how much x1changes because movies are cheaper relative to MP3 (find substitution effect)d) How about the effect of increased purchasing power of Benjamin’s income? (find income effect)e) Is the income effect in d) positive or negative? Why? (Hint: is a movie a normal of inferior good?)f) Show the total change, and the substitution and income effects on the graph.Problem 2Consider Trevor from our previous problem set. He begins a day with a strawberry milkshake (milk andstrawberries mixed in proportion 1:5). His income is equal to m = 200 , and one strawberry costs p2= 1 .Suppose the price of milk drops from p1= 15 to p1= 5.a) What is the total change in demand for milk.b) What is a substitution effectc) How about income effectProblem 3Miriam has quasilinear preferences over consumption of coffee (x1) and muffins (x2) given by U (x1, x2) =5 ln x1+ x2. Her income is equal to m = $10, and p2= $1.a) Find MRS as a function of consumptions of two commodities. Write down two secrects of happiness.b) Find optimal consumption of x1and x2for arbitrary value of p1, p2, m using two secrets of happinessfrom a) (assume interior solution)c) Suppose price of coffee drops from p1= $5 to p1= $1. Find substitution effect.d) Find income effectProblem 4Dave is initially endowed with 20 apples and 20 oranges ω = (20, 20)a) Assume p1= p2= 2.Write down Dave’s budget constraint, and plot budget constraint in the graph.Mark all bundles on budget line for which Dave is selling apples and is buying oranges.b) Suppose U(x1, x2) = x1x2. Find indifference curve that passes though endowment point analyticallyand find its slope (MRS) at endowment point. Depict the curve and the slope in the graph.c) Assume p2= 2 and find optimal choices of Dave under three scenarios: p1= 1, p1= 2 and p1= 3.Determine net demands of Dave for apples and oranges.d) Is Dave buying or selling apples on the market under the three scenarios? Explain why he is using suchtrading strategy by comparing MRS at the endowment point with relative price.e) Connect the three optimal bundles to obtain price offer curve and plot it in the graph with indifferencecurve passing though endowment poin. Is your price offer curve located above the indifference curve?1Tuesday, February 21Problem 5Kate is not sure how many hours she should spend at work and we have to help her. Her total availabletime is 24h. She has no other source of income but salary. She is a lawyer, and a current wage rate for lawyers(per hour) is w = $100. She only consumes bananas that cost pc= $5 per pound.a) what is her real wage rate (wage rate in terms of bananas?)b) show her budget set on the graph.Suppose her utility function isU(C, R) = R × Cwhere R is leisure (or relaxation time) and C is consumption of bananas.c) find her optimal time spent at work, the relaxation time and consumption of bananas.d) How your answer in c) would change if her wage rate was w=$200. How would you explain thechange (or possibly no change) in her labor