Midterm Review AnswersHomework Assignment 5 Answers 1. Max enjoys windsurfing (W) and snorkeling. He obtains the following total utilityfrom each of these sports:Half-hours(per month) TUWMUWMUW PWMUW PW′ TUSMUSMUS PS1 60 60 6 12 20 20 42 110 50 5 10 38 18 3.63 150 40 4 8 53 15 34 180 30 3 6 64 11 2.25 200 20 2 4 70 6 1.26 206 6 .6 1.2 75 5 17 211 5 .5 2 79 4 .88 215 4 .4 .8 82 3 .69 218 3 .3 .6 84 2 .4 (a) Calculate Max’s marginal utility from windsurfing and from snorkeling. (You mayadd this information to the above table with columns for the MU for windsurfingand the MU for snorkeling.(b) If Max has $35 to spend, and equipment for windsurfing rents for $10 per half-hour,while snorkeling equipment rents for $5 per half-hour, how long will Max choose towindsurf? 3 units or 1 ½ hrs. Snorkeling? 1 unit or ½ hour Why? When all income is spent… (compare columns 4 and 8) MUS = MUW and Total Utility is maximized. TU = 170 utils. PS PW(c) What is Max’s budget constraint? Explain verbally and write the equation for hisbudget constraint below.B = I = PWQW + PSQS $3(5) = $10(3) + $5 (1)(d) Now, suppose Max’s sister gives him $20 to send on his leisure pursuits, so he nowhas $55 to spend. How long will Max windsurf? 4 units or 2 hours Snorkeling? 3 units or 1 ½ hours When all of the income is spent… (compare columns 4 and 8) MUS = MUW and Total Utility is maximized. TU = 233 utils. PS PW(e) If Max has $55 to spend and the rent on windsurfing equipment is cut to $5 per half-hour, how will Max now spend his time windsurfing? 6 units or 3 hours Snorkeling? 5 units or 2 ½ hours. Additional Problem 1 Answers: Utility AnalysisAssume that Maxi Mizer is trying to decide which combination of ice cream cones, Good A, and magazines, Good B, she should purchase with her limited income of $20. Maxi’s preferences for ice cream and magazines, Goods A and B, are given in the table below. Further assume that the prices of ice cream cones and magazines, Goods A and B, are $2 and $4 respectively.Unit ofGoodMarginalUtility of IceCream Cones(Good A)MUAPAPurchase OrderPrice of B=4 B=2MarginalUtility ofMagazines(Good B)MUBPBB=$4 MUB'PB'B=$21 20 10 (2) (6) 48 12 (1) 24 (1)2 16 8 (4) (7) 40 10 (2) 20 (2)3 14 7 (8) 36 9 (3) 18 (3)4 12 6 (9) 32 8 (4) 16 (4)5 10 5 24 6 12 (5)6 8 4 12 3 6 (9)7 6 3 8 2 4a) How many ice cream cones and magazines will Maxi purchase? ___2A, 4B___Why?Maximum Total Utility = 192Total Expenditures = b) Now assume that the price of magazines falls to $2. How many ice cream cones and magazines will Maxi purchase now? __________4A, 6BMaximum Total Utility = 254Total Expenditures = MUAPA= MUBPB2x $2 = $44x $4 = $16$20MUAPA= MUBPB'4x $2 = $86x $2 = $12$20c) On the basis of the information determined so far, determine the demand curve formagazines. Provide a graph of the demand for magazines.PB = $4 QB = 4PB' = $2 QB' = 6Does the demand for magazines follow the “law of demand”? ____Yes___ (Yes;No) Give reasons to explain the “law of demand” and explain them briefly.1) Diminishing Marginal Utility2) Income Effect3) Substitution Effectd) Compute the price elasticity of demand for the price change for magazines indicated in part (b). Interpret this elasticity coefficient and provide the formula for calculations for this price elasticity.P1 = $4 Q1 = 4P2 = $2 Q2 = 6Q2 – Q1Q2 + Q12=6-45= 2-3 = -6 = -3 = -.60P2 – P1-2 5 -2 10 5P2 + P123Demand InelasticA 1%  P  .6%  QD + vice versaDBQBPB0$4$264Additional Problem #3: Consumer and Producer Surplus (Note: This is listed on the course website as part of Homework #3 Answers).Now consider the market for pizza. Suppose that the market demand for pizza is given bythe equation P = 40 – 4QD, and the market supply for pizza is given by the equation P = 10 +2QS, where QD = quantity demanded, QS = quantity supplied, P = price consumers pay (perpizza) and the price producers receive (per pizza).(1) Graph the supply and demand schedules for pizza and indicate the equilibrium priceand quantity. (Your answer must contain your complete algebraic solution).Calculate the consumer surplus and producer surplus and identify these areas in thegraph below.(Be sure to label the axes and functions, and number your intercepts.) P 40 S CS PE = $20 PS 10 D 0 QE = 5 10 QEquilibrium Price: $20 Equilibrium Quantity: 5 (Show your complete algebraic solution for the equilibrium price andquantity in the space below.)In Equilibrium: S = D 40 – 4Q = 10 + 2Q 30 = 6Q 5 = QE PE = 40 – 4 (5) = $20 for demand and PE = 10 + 2 (5) = $20 for supplyConsumer Surplus at Equilibrium: $50 (Show all work.)CS = ½ (20 x 5) = $50Producer Surplus at Equilibrium: $25 (Show all work.)PS = ½ (10 X 5) = $25Handout 2: Market Analysis (Answer Key)The table below gives the individual demands’ of Lisa and Chuck for movies:Quantity of movies demanded / mo.Price / movie Lisa Chuck$7 1 06 2 05 3 04 4 13 5 22 6 3a) Calculate the market demand for movies assuming that only Lisa and Chuck have individual demands for movies. Explain this market demand.Sum of individual demand curves Price / movie Market QD$7 16 25 34 53 72 9b) Graph the market demand for movies found in (a). Does this market demand follow the “law of demand.”? Explain and offer reasons for this law. PYes, it follows “law of demand.” SMInverse relationship between P and Q . 7Reasons for law: 6a) Income effect 5 b) Substitution effect 4 c) Diminishing Marginal Utility 3d) Simple reasoning: 2 DM Buy more at lower prices. 1 0 1 2 3 4 5 6 7 8 9 Q (mov/mo)c) Calculate the price elasticity of demand for movies given your market demand in (a) for each price change. Is demand elastic, unit elastic, inelastic? Explain in detail. (Show all your work and give the complete elasticity formula). %-QD Q2 - Q1 P2 - P1EP = ——— = ————— / ————— %-P Q2 + Q1 P2 + P1 ——— ——— 2 2Price / movie Market QDEP$7 16 2 - 4.335 3 -