Homework No. 5 (Due in Respective Labs on Oct. 13 and Oct. 15, 2008)

Economics 101 L Homework No. 5 (due in respective labs on Oct. 13 and Oct. 15, 2008)

WORTH 100 POINTS TOTAL

1. A consumer’s budget can be written as: Y = Pf F + Px X WORTH 40 POINTS where Y is income, Pf is the price of food, Px is the price of all other goods besides food, F is the quantity of food consumed, and X is the quantity of all other goods consumed besides food.

a. Suppose a consumer's income is $3,600 per month, Px is equal to $4/unit, and Pf is $3/unit. Using Excel, draw the consumer's budget constraint in a graph with food on the horizontal axis and other goods on the vertical axis, and call it Figure A. 5 POINTS

Figure A

Original Budget New Budget

1000 900 800 700 s d

o 600 o G

500 r e

h 400 t

O 300 200 100 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 Food

b. Suppose the price of food falls from $3/unit to $1.50/unit. 3 POINTS EACH 1. Draw the new budget constraint in Figure A. 2. Draw a hypothetical indifference curve tangent to the original budget constraint at a consumption level of 800 units of food. What is the consumption level of other goods at this point? ~300 units 3. Draw a second indifference curve tangent to the new budget constraint at a consumption level of 1200 units of food. What is the consumption level of other goods at this point? ~450 units 4. Has the demand for food increased or decreased? By how much? Increased by 400 units 5. Draw a line parallel to the new budget constraint tangent to the original budget constraint. (This can be done by tracing a new line over the new budget constraint and dragging it to where it is tangent on the original budget constraint.) See above graph. 6. Are there substitution effects? If yes, by approximately how much did food consumption increase (or decrease) due to the substitution effect? Yes, sub. effects increased food consumption by about 150 units. 7. Are there income effects? If yes, by approximately how much did food consumption increase (or decrease) due to the income effect? Yes, income effects increased food consumption by about 250 units. c. Redraw the original budget constraint from (a) in a new figure, and call it Figure B. In this figure, draw also another budget constraint assuming the original prices (i.e., Px = $4/unit and Pf = $3/unit), but a monthly income of $2,400. 2 POINTS

Figure A

1000 900 800 700 s d

o 600 o G

500 r e

h 400 t O 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 Food

1-4 WORTH 3 POINTS EACH 1. Again, draw a hypothetical indifference curve tangent to the original budget constraint at a consumption level of 800 units of food. See graph 2. Has the demand for food increased or decreased? By how much? Decreased by 200 units. 3. Are there substitution effects on the quantity food consumed? If yes, how much did food consumption increase (or decrease) due to the substitution effect? No sub. effects. 4. Are there income effects? If yes, by approximately how much did food consumption increase (or decrease) due to the income effect? Yes, decreased food consumption by 200 units. 2. Lisa’s total utility from Movies is given in the table WORTH 20 POINTS

Quantity per Total utility Marginal month Utility 0 0 1 50 50 2 88 38 3 121 33 4 150 29 5 175 25 6 196 21 7 214 18 8 229 15 9 241 12 10 250 9 11 256 6 12 259 3 13 261 2 14 262 1

a. Draw a computer-generated graph illustrating Lisa’s total utility from Movies with quantity on the horizontal axis. 5 POINTS

Total utility

300

250

200 y t i l

i 150 t U 100

0 0 5 10 15 Quantity

b. Describe in simple words what is meant by “marginal utility”. 5 POINTS Marginal utility is the change in total utility an individual obtains from consuming an additional unit of a good or service.

c. Calculate Lisa’s marginal utility and draw a new computer-generated graph illustrating this marginal utility. 5 POINTS. See table above and graph below. Marginal Utility

40 y t i l i t U

a 30 n i g r a

M 20

0 0 2 4 6 8 10 12 14 16 Quantity d. Explain, in one or two sentences, the principle of diminishing marginal utility. 5 POINTS Diminishing marginal utility refers to the notion that marginal utility continually decreases as more and more of a particular good is consumed. 3. You have a fixed budget of $30 per month to spend on two types of candy bars: chocks and minties. Your marginal utility (MU) schedules for the two are shown below. WORTH 40 POINTS – 5 POINTS EACH

Chocks MU of Chocks Minties MU of Minties 1 20 1 40 2 18 2 36 3 16 3 32 4 14 4 28 5 12 5 24 6 10 6 20 7 8 7 19 8 6 8 18 9 4 9 17 10 2 10 16

a. Suppose the price of chocks (Pch) and price of minties (Pmi) are equal at $3 per bar. You are consuming two chocks and eight minties per month. What is your utility from the second chock? From eighth minty? 18 from second chock. 18 from eighth minty. b. If you transfer $3 of spending from minties to chocks, what is your reduction in utility from losing the eighth minty? What is your increase in utility from gaining the third chock? Will you make this transfer? Why/why not? Loss of 18 from eighth minty. Gain of 16 from 3rd chock. You would not make this transfer because you are decreasing your overall utility level. c. If you transfer $3 of spending from chocks to minties, what is your reduction in utility from losing the second chock? What is your increase in utility from gaining the ninth minty? Will you make this transfer? Why/why not? Loss of 18 from 2nd chock. Gain of 17 from 9th minty. No you would not make this transfer because your overall utility level would decrease. d. Given your answers to a, b, and c, which combinations of chocks and minties will you choose?

For that option, how does the ratio of marginal utilities MUch /MUmi for the last chock and the last minty compare with the ratio of their prices, Pch / Pmi 2 chocks and 8 minties. MUc/MUm = 1/1 = $3/$3…. Ratio of marginal utilities equals price ratio. e. Now the price of chocks falls to $2 and the price of minties rises to $4. What has happened to the opportunity cost of the chock bar? Suppose you now buy three chocks and six minties. What is your utility from the 3rd chock? From the sixth minty?The opportunity cost of the chock bar has decreased from 1 to 0.5. Utility from the 3rd chock is 16. Utility from the 6th minty is 20. f. If you now transfer $4 of spending from minties to chocks, how much utility do you lose from minties? How much utility do you gain from chocks? What happened to your total utility compared to (e)? will you make this transfer? Why? Loss of 20 from minties. Gain of 26 from chocks. Utility increased by 6. Yes you would make this transfer because your overall utility level has increased. g. If you transfer another $4 from minties to chocks, what happens to your total utility from minties and chocks combined? Will you make this transfer? Why? There is a reduction in overall utility by 6. You would not make this transfer because your overall utility level decreases. h. Given your answers to e, f, and g which combinations of chocks and minties will you choose? For

that option, how does the ratios of marginal utilities MUch /MUmi for the last chock and the last minty compare to the ratio of their prices, Pch / Pmi ? Do you see any similarity between this comparison and the comparison you found in (d)? What do you conclude in the conditions for utility maximization? You would choose 5 chocks and 6 minties. Pc/Pm = 0.5 = MUc/MUm = 12/24. Yes there is a connection. Consumption takes place at a level where the ratio of prices is equal to the ratio of marginal utilities.