Question One a)What happens to the budget line if the price of good 2 increases, butthe price of good 1 and income remain constant? b)If the price of good 1 doubleand the price of good 2 triples, does thebudget line become flatter or steeper? c)What is the definition of a numeraire good? d)Suppose that the government puts a tax of 15 cents a gallon on gasolineand then later decides to put a subsidy on gasoline at a rate of 7 cents agallon. What net tax is this combination equivalent to? e)Suppose that a budget equation is given by 11+22=. Thegovernment decides to impose a lumpsum tax of u, a quantity tax ongood 1 of , and a quantity subsidy on good 2 of . What is the formulafor the new budget line. f)A college football coach says that given any two linemen A and B, healways prefers the one who is bigger and faster. Is this preference relationtransitive? Is it complete? Question Two a)Consider the utility function (1,2)=12.What kind of preferences does it represent? Is the function (1,2)=1 22a monotonictransformation of (1,2)? Is the function (1,2)=1 22 2 a monotonictransformation of (1,2)? b)Can you explain why taking a monotonic transformation of a utilityfunction doesn't change the marginal rate of substitution? c)Suppose that a consumer always consumes 2 spoons of sugar with eachcup of coffee. If the price of sugar is p1 per spoonful and the price of coffeeis p2 per cup and the consumer has m dollars to spend on coffee and sugar,how much will he or she want to purchase? d)Suppose that you have highly nonconvex preferences for ice cream andolives, like those given in the text, and that you face prices 1,2and havedollars to spend. List the choices for the optimal consumption bundles.e)If a consumer has a utility function (1,2)=12 , what fraction ofher income will she spend on good 2? Question Three a)When prices are (1,2)=(2,1)a consumer demands (1,2)=(1,2),and when prices are (1,2)=(1,2)the consumer demands (1,2)=(2,1).Is this behavior consistent with the model of maximizing behavior? b)Suppose a consumer has preferences between two goods that are perfectsubstitutes. Can you change prices in such a way that the entire demandresponse is due to the income effect? c)Suppose that preferences are concave. Is it still the case that the substitution effect is negative? d)Suppose that the consumer has a demand function for milk of the form 1=50+ 501 Originally his income is 600 per week and the price of milk is 15per quart.Now suppose that the price of milk falls to 10per quart. Calculate (i)Substitution effect (ii)Income effect (iii)Total change Question Four a)How much is 1 million to be delivered 20 years in the future worthtoday if the interest rate is 20 percent? b)As the interest rate rises, does the intertemporal budget constraint become steeper or flatter? c)Would the assumption that goods are perfect substitutes be valid in astudy of intertemporal food purchases? d)A consumer, who is initially a lender, remains a lender even after adecline in interest rates. Is this consumer better off or worse off after thechange in interest rates? If the consumer becomes a borrower after thechange,is he better off or worse off? e)What is the present value of 100 one year from now if the interest rateis 10%? What is the present value if the interest rate is 5%? f)Show using botha diagram and algebraically under the theory of intertemporal choice that if a person is a lender and the interest rate rises, he or she will remain a lender.