This Statement Is False. the Quantity Bought Is Always Equal to the Quantity Sold Even

Economics 331

Fall 2007

EXAM #1

1.State whether the following statement is true or false. Provide a brief explanation as to why the statement is true or false: “When the quantity bought is equal to the quantity sold, the market is at equilibrium.”

THIS STATEMENT IS FALSE. THE QUANTITY BOUGHT IS ALWAYS EQUAL TO THE QUANTITY SOLD EVEN WHEN THE MARKET IS NOT AT EQUILIBRIUM. FOR EXAMPLE, AT A PRICE CEILING THE AMOUNT SOLD IS EQUAL TO THE AMOUNT BOUGHT, BUT SINCE THE QUANTITY DEMANDED IS GREATER THAN THE QUANTITY SUPPLIED, THE MARKET IS NOT AT EQUILIBRIUM.

2.Suppose that anincrease in the price of wine has no effect on the quantity of wine Jamie demands. Predict the effect of an increase in income on her demand for wine. Explain.

SINCE THE INCREASE IN PRICE HAS NO EFFECT ON QUANTITY DEMANDED, THE DEMAND CURVE IS PERFECTLY INELASTIC AND THE SUBSTITUTION EFFECT MUST BE EQUAL TO THE INCOME EFFECT. FOR THE SE, AS P ↑, QD ↓ . SINCE QD DOES NOT CHANGE, FOR THE IE, AS P ↑, QD ↑. THE GOOD MUST BE INFERIOR, SINCE AN ↑ IN PRICEMEANSREALINCOMEFALLS. THEREFORE, AN INCREASE IN INCOME WILL CAUSE DEMAND TO DECREASE.

3.Lee uses his income to buy only two goods, beer and sausage. Lee’s price elasticity of demand for beer is greater than one. Show that sausage must be a COMPLEMENT for beer.

IF THE eBEER > 1, THEN BEER IS ELASTIC. THIS MEANS THAT WHEN PBEER ↓ ANDD QBEER ↑ , TOTAL SPENDING ON BEER ↓. SINCE THERE ARE ONLY TWO GOODS, TOTAL SPENDING ON SAUSAGE MUST ↑ AND MORE SAUSAGE IS BOUGHT (PRICE OF SAUSAGE IS HELD FIXED). THEREFORE, A ↓ IN PBEER LEADS TO A HIGHER DEMAND FOR SAUSAGE, SO THE GOODS ARE COMPLEMENTS.

4.Kristen has just purchased a new Mustang for $20,000. The most she could get for it if she sold it would be $15,000. Now, Kristen learns that BMW is offering its car, which normally sells for $25,000, at a special price of $20,000. If Kristen had known before buying the Mustang that she could buy a BMW at the same price she would have bought the BMW.

True or False: If Kristin is a rational individual, she should definitely not sell the Mustang and buy the BMW. Explain.

WE KNOW THAT BMUST AND BBMW > 20,000. WE ALSO KNOW THAT

BMUST – 20,000 > BBMW – 25,000 → BMUST > BBMW – 5,000. WE KNOW THIS BECAUSE SHE COULD HAVE BOUGHT A BMW AT 25,000 BUT CHOSE TO BUY THE MUSTANG AT 20,000. THEREFORE, THE BBMW ARE > THAN BMUST BY LESS THAN $5,000. THE STATEMENT IS TRUE IF BMUST – 15,000 >

BBMW – 20,000 → BMUST > BBMW – 5,000. THIS IS ALWAYS TRUE GIVEN HER PREFERENCES.

5.Suppose the demand curve for marijuana is linear. A new strand of marijuana is developed, which is identical to the old marijuana except that it is twice as strong – provides twice the high per ounce. How does the new demand curve for marijuana compare with the old one. Illustrate on a diagram and provide a brief explanation.

THE DEMAND CURVE SHOULD PIVOT IN ON THE QUANTITY AXIS AND UP ON THE PRICE AXIS. FOR ANY GIVEN PRICE YOU ARE WILLING TO BUY LESS, AND FOR ANY GIVEN QUANTITY, YOU ARE WILLING TO PAY MORE.

Section II: Calculation Problems (33 points). Answer BOTH questions. Make sure you show all your work when solving these problems.

1(9).Consider the market for oranges. The demand and supply curve for oranges is given by QD = 1,000 – 200P, and QS = 800P. Calculate the equilibrium price, equilibrium quantity and total welfare.

QD= QS→1,000-200P = 800P→1,000 = 1,000P→P* = $1.00

Q*=1,000-200(1) = 800

W = ½ x (5-0) x 800 = $2,000orW = ½ x (5-1) x 800 + ½ x (1-0) x 800 = $2,000

2(24).Harold and Maude consume peanut butter and jelly. The price of peanut butter is $2.00 and the price of jelly is $1.00. Although they each have $200 income, they have different preferences. Maude always likes to eat 2 units of jelly with 1 unit of peanut butter. Harold’s preferences are given by: U(P,J) = P3J2.

a.What is the MRS in terms of the number of units of jelly given up for one unit of peanut butter?

FOR HAROLD / FOR MAUDE
MRS = MUP/MUJ = 3P2J2/2P3J1 = 3J/2P / SINCE THE GOODS ARE PERFECT COMPLEMENTS, THE MRS IS 0

b.At the optimum, what is the relationship between the amount of peanut butter and jelly consumed

FOR HAROLD / FOR MAUDE
AT THE OPTIMUM MRS = PRICE RATIO
3J/2P = 2/1 → 3J = 4P → J = (4/3)P OR P = (3/4)J / SINCE THE GOODS ARE PERFECT COMPLEMENTS, HER OPTIMUM OCCURS WHEN SHE EATS 2 JELLY FOR EACH PB. THEREFORE AT THE OPTIMUM: 1J = 2P

c.How many units of peanut butter and jelly will maximize utility?

FOR HAROLD / FOR MAUDE
PLUGJ = (4/3)P IN THE BUDGET CONSTRAINT:
2P + 1J = 200 → 2 x (3/4) J + 1J = 200
1.5J + 1J = 200 → 2.5J = 200 → J* = 80.
SO P* = (3/4)80 = 60
Note that this is consistent with a CD utility function, where U = P3J2 which is equivalent to = P3/5J2/5. You spend 3/5 of $200 income or $120 on P (60 units x $2) / PLUG 1J = 2P IN THE BUDGET CONSTRAINT:
2P + 1J = 200 → 2P + 2P = 200 → 4P = 200
P* = 50 SO J* = 100

d.Given their optimal consumption of peanut butter and jelly, who is happier, Harold or Maude? Explain.

WHO KNOWS. EVEN THOUGH HAROLD’S UTILITY IS A WHOPPING 1,382,400,000 AND MAUDE’S UTILITY IS A MEASLY 100, INTERPERSONAL UTILITY COMPARISONS ARE NOT POSSIBLE.

Section III: (22 points).Answer TWO of the three questions.

1.Consider a market where the demand and supply curves are given by:

QD = a – bP and QS = c + dP.

Suppose that the government can impose a per unit tax, T, on either consumers or producers. Prove that the incidence of the tax is the same no matter on which group the tax is levied. No diagram is necessary.

i.TAX ON PRODUCERS:

a – bP = c + d(P-T)→a – c + dT = P(b+d)→P* = (a-c+dT)/(b+d). At this price consumers buy Q’. Since firms must give the government T per unit, their net price is P* - T = (a-c-bT)/(b+d).

ii.TAX ON CONSUMERS:

a – b(P+T) = c + dP→a – c - bT = P(b+d)→P = (a-c-bT)/(b+d). This is the net price, so to find the new market price you need to add the tax, so P* = (a-c-bT)/(b+d) + T = (a-c+dT)/(b+d).

Since the new market price and the net price is the same in both cases, the tax incidence must be the same.

2.MELISSA’S INITIAL BUDGET CONSTRAINT AND INDIFFERENCE CURVE ARE SHOW IN BLUE. AS THE PRICE OF BOOKS ↑, HER BUDGET CONSTRAINT PIVOTS TO THE GREEN LINE, BUT SINCE HER MOTHER GIVES HER $90, IT ALSO SHIFTS OUT. HER FINAL BUDGET CONSTRAINT IS THE RED LINE. IT HAS TO INTERSECT AT THE INITIAL BUDGET CONSTRAINT SINCE THE $90 COMPENSATES HER FOR THE EXTRA AMOUNT OF MONEY SHE COULD SPEND ON 15 BOOKS. HOWEVER, GIVEN THE NEW BUDGET CONSTRAINT, HER OLD CONSUMPTION BUNDLE NO LONGER MAXIMIZES HER UTILITY. THEREFORE, SHE WILL BUY LESS BOOKS AND MORE OF THE COMPOSITE GOOD, AND HER UTILITY WILL INCREASE FROM U0 TO U1.

3.THE BLACK LINE IS THE ORIGINAL BUDGET CONSTRAINT. THE BLUE LINE IS THE BUDGET CONSTRAINT WITH THE HOUSING VOUCHER. THE RED LINE IS THE CONSTRAINT WITH THE INCOME TRANSFER.

WHICH PROGRAM IS PREFERRED DEPENDS ON THE PERSON’S PREFERENCES. INDIVIDUALS WITH GREEN INDIFFERENCE CURVES WILL PREFER THE VOUCHER OVER THE INCOME TRANSFER. INDIVIDUALS WITH ORANGE INDIFFERENCE CURVES WILL PREFER THE INCOME TRANSFER OVER THE VOUCHER.

IT’S ALSO POSSIBLE THAT SOMEONE IS INDIFFERENT. THIS WOULD BE TRUE IF THEIR INDIFFERENCE CURVE IS TANGENT TO THE RED BC AT THE TOP AND ALSO JUST TOUCHES THE KINK OF THE BLUE CONSTRAINT (THE BROWN INDIFFERENCE CURVE).