Review Problems for Test #1 These types of problems demonstrate the formats that will be used on the test. You can bring a calculator (real or virtual) to the test and you can also bring in a two-sided sheet with formulas and drawings on it. A. Answer True, False, or Uncertain, and explain your answer: (1) Inferior goods have negative price elasticity. (2) A change in consumer surplus is an approximate measure of a consumer's change in wellbeing except when the utility function is CobbDouglas in form. (3) The consumer is better off in period bthan in period fit the Paasche price index, .4- .4- th+th p_# P t 2 _ , is greater than 1. p lC'l ND'NI x: + P X (4) The utility function U: 10? , where Y: income, exhibits diminishing marginal utility. (5) If I am a borrower and the interest rate fails, I am worse off. B. Short answers: (1) What is the demand function for Xif U: 4X3Y3 ? (2) Given the utility function in (2), if income M rises from 20 to 30, price PX rises from 2 to 3, and price Py rises from 3 to 6, is the person better off, the same, or worse off? (3) Given a demand curve 00 = 300 - 6P, when the price changes from 5 to 6, what is the associated change in consumer surplus? (4) A person has the utility function U: X+ 2'/. What is the marginal rate of substitution? (5) Given the utility function in (4), if the prices are Px= 3 and Pyz 4, what is the budget share of X? For the following problems, please show the calculations used to arrive at your answers. Draw graphs neatly and label axes and points clearly. Round answers to the first decimal place if necessary. C. A riskloving person with utility function U = Y2, where Y: income, is offered the choice of receiving their income of $50 or participating in a gamble that pays $100 with a probability of 25% and $20 with a probability of 75%. Which will the person choose? D. A person has the utility function U : #10 + 2MB, where C = dollar units of consumption and F? = weekly hours of leisure. (1) What is the marginal rate of substitution between Cand R? (2) Given a wage rate W: $1 Dlhr and nonlabor income M : $240, graph the budget constraint. (3) What is the demand function for leisure? (4) How much leisure is taken? (5) The firm where this person works is trying to discourage people from working overtime. The hourly wage Wis changed so that: W: $1 thr for hours worked 5 40 W: $8fhr for any hours worked in excess of 40 per week Graph the new budget constraint. (6) Would this person increase, not change, or decrease hours worked