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12127 .I 2* Cl 8 coursehero.com Econ 33 1 0 Dr. Deza Fall 2016 Problem Set #1 QUESTION 1: True/False. Please indicate whether each statement is true or false and justify your answer with a brief explanation or graph if appropriate. a] Assume that orange juice and apple juice are perfect substitutes. An unexpected frost damages the orange crops and raises the prices of orange juice. If this is the case, consumers will demand less apple juice at every price. b) Dan views a cup of coffee and a cup of tea as perfect substitutes. He is always willing to exchange one cup of coffee for one cup of tea. Suppose that he has $10 to allocate towards beverages and the price of coffee is $2 while the price of tea is $1 per cup. He will buy 10 cups oftea. (Explain in terms of Marginal utilities) c] The demand curve for tshim is Q = 1000 101'. The price of these tshirts are $10 per shirt. The manager claims that the demand is elastic at this point and a lower price will increase the total revenue from the sale of these shirts. d] In a very poor and small town, Larry hits the lotto and decides to give every person in the town $1,000. The quantity of spam demanded in the town declines. The local grocery store decides to lower the price of spam to increase the quantity of spam that is being demanded. A lower price of spam will increase the quantity of spam demanded. e] Consider the following. With probability "fa you win $100. With probability 9% you gain nothing. A risk loving person prefers to accept the gamble rather than accepting $50. 0 The demand for SMU football tickets is the following Q=25,000-25P. An economist from SMU claims that the marginal revenue is zero at the point on the demand curve where the price is equal to $500 and the economist claims that the elasticity is 1 at that point (Do the math and compute the elasticity!) g) Beth always buys two scoops of vanilla ice cream with a tablespoon of chocolate syrup. If the price of chocolate syrup goes down then Beth's demand for vanilla ice cream goes down. QUESTION 2: Suppose you have the following utility function U(x, y) = X21!2 and you have $80 to spend between goods X and Y. The prices are the following. P, = 2 and Py = 4 a) Write down the budget constraint b) How many units of Y is the "market" willing to exchange for one additional unit of X? c] What is the marginal utility of X and Y? d) How many units of Y is the "consumer" willing to exchange for one unit of X while holding the utility level constant when Y=4 and X=2? hltps:ffwww.coursehero.comfie/25469343/DezarPS 1733 I nrspringzo I new e] Given the above prices. income and preferences, what is the utility- maximizing level of x? and y? QUESTION 3: Suppose you have the following utility function U(X. Y) = X2 + I'2 Again, let's assume you have $80 to spend, and the prices are PX = 2 and P, = 4 Find the utility maximizing consumption level of X and Y QUESTION 4-: Suppose you have the following utility function U(X,Y)=min{2X,Y} Again, let's assume you have $80 to spend, and the prices are P, = Z and F, = 4 Find the utility maximizing consumption level of X and Y QUESTION 5: Suppose you have the following utility function U[X.Y)=2X+Y I MA- I x u . n n Ln 1 r3 [I]