Econ 1101 Holmes Fall 2009 Practice Questions about Consumer Theory Solution Instructions This worksheet contains practice questions about Consumer Theory The material was discussed in lectures 18 and 19 Oct 23 and Oct 26 This material will also be covered in the discussion sections this week Question 1 Sam eats only green eggs and ham He has an income of 36 Green eggs have a price of PG 2 and ham has a price of PH 6 Sam s preferences are represented by the utility function Utility 10 QG 40 QH where QG and QH are Sam s consumption of green eggs and ham a On the graph below draw in Sam s budget constraint Put ham on the horizontal axis which is how the graph is labeled Label the budget constraint b Sam has which kind of preferences 1 Green Eggs and Ham are Perfect Substitutes 2 Green Eggs and Ham are consumed in fixed proportions 3 Sam s indifference curves feature diminishing marginal rate of substitution MRS between green eggs and ham 1 G r e e n E g g s 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 1011 12 13 14 Ham 2 c At these prices Utility per dollar spent on green eggs is 5 utils Fill in a whole number Let s use util as the unit 10 utils per unit 2 per unit Thus util per dollar is 10 2 5 utils per dollar 7 Utility per dollar spent on ham is utils 40 utils per unit 6 per unit 40 6 6 66 or 7 in this case d Sam s optimal consumption bundle is 04 6 0 green eggs and Fill in the Blank ham We know consumer consumes all ham no green eggs since ham yields higher utility per dollar e Illustrate the optimal consumption bundle on the graph and draw Sam s indifference curve through this point Label the indifference curve f Sam s marginal rate of substitution the value of one more ham in terms of green eggs is 4 green eggs MRS is absolute value of slope of the IC We can see slope is 24 0 0 6 4 Absolute value is 4 g The absolute value of the slope of the budget constraint the opportunity cost of one more ham in terms of green eggs is 3 green eggs for one more ham Slope of BC is 18 0 0 6 3 Absolute value is 3 3 Question 2 Points 20 Jill loves skiing and wants to go as often as she can afford to For each day she skis she needs to rent skis and buy a lift pass Ski rentals are 10 a day and lift passes are 40 a day She has 200 to spend on skiing this winter a In the graph below draw in Jill s budget constraint for the number of ski rental days and the number of lift pass days One bundle of 1 rental 1 lift costs 50 Consumer can afford 4 such bundles b Jill s optimal OCB is 4 rental 4 lift consumption bundle is 4 ski rentals and 4 lift tickets c Illustrate her optimal consumption bundle and draw Jill s indifference curve through it d Draw her indifference curve through QRental 2 QLift 2 and another one through QRental 6 QLift 6 L12 11 i 10 f 9 t 8 7 T6 i 5 k4 I 3 t 2 s1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Ski Rentals 4 Q3 Points 20 Question 3 Frodo eats lembas bread and wine His indifference curves are illustrated in the next page below Suppose the prices of lembas bread and wine are and PL 5 and PW 10 a Suppose Frodo has an income of 40 Draw in Frodo s budget constraint and label it BC I 40 Put lembas bread on the horizontal axis as illustrated 0 5 wine for one more lembas b The slope in absolute value of the budget constraint is bread Note use a decimal answer For example use 1 or 2 or 5 or 7 etc c At this income Frodo s optimal consumption bundle is 2 4 lembas bread units and wine units d The marginal rate of substitution at the optimal consumption bundle is one more lembas bread Again use decimals e g 1 or 2 or 5 etc 0 5 wine for With this type of IC at the OCB the abs value of slope of the IC MRS is same as abs value slope of BC e Suppose prices remain the same but Frodo s income increases to 60 Illustrate the new budget constraint The new optimal consumption is wine units 5 6 lembas bread units and 3 16 15 14 13 12 11 10 W98 i7 6 n5 e43 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Lembas Bread Q3 F Points 5 f From comparing c and e we can tell that wine is a normal good and lembas bread is an inferior good True or False Circle one As income increases from 40 to 60 consumption of both goods increases Thus both goods are normal Q3 g Bonus Points 2 If there are only two goods that Frodo consumes wine and lembas bread then it is still possible for both goods to be inferior That is it could happen that when Frodo s income doubles he consumes less of both goods True or False Circle one 6
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