微观经济学作业答案1

Managerial Economics

HOMEWORK SET#1

Name:

Class:

Student #:

(Due day: Next class)

Part 1:

1.A perfectly competitive market has:

a)many buyers and sellers.

b)several large buyers.

c) a meeting place for buyers and sellers.

d)a) and b)

e)a) and c)

Choose:a) There must be numerous small buyers and sellers for a market to be perfectly competitive. A meeting place is unnecessary.

2. Boeing Corporation and Airbus Industries are the only two producers of long-range commercial aircraft. This market is not perfectly competitive because:

a) Each company has annual sales over $10 billion.

b)Each company can significantly affect prices.

c) Airbus receives subsidies from the European Union.

d) Airbus cannot sell aircraft to the United States government.

e) All of the above.

Choose:b) The character of monopoly market is each firm can affect prices.

3.If the real price of a college education has risen during a period

of inflation:

a)its nominal price has not changed.

b)its nominal price has risen slower than a general index of prices.

c)its nominal price has risen faster than a general index of prices.

d)its current dollar price has not changed.

e)None of the above is correct.

Choose:c) When the nominal price of a college education rises faster than the rate of inflation, the real price of a college education will rise.

4. The constant dollar price of a good:

a) is the same as its real price.

b) is the same as its nominal price.

c) adjusts for inflation in the overall price level.

d) b) and c)

e) a) and c)

Choose:e) By definition, the constant dollar price is equal to the real price, and both adjust the nominal price for the effects of the inflation.

5. The price of a sandwich was $0.29 in 1970 and $0.99 in 1993. The CPI was 38.8 in 1970 and 144.0 in 1993. The 1993 price of a sandwich in 1970 dollars is:

a) $0.08.

b) $0.27.

c) $0.34.

d) $3.67.

Choose:b) 0.99/x=144/38.8 x=0.27

6. Which of the following would shift the demand curve for new textbooks to the right?

a) A fall in the price of paper used in publishing texts.

b) A fall in the price of equivalent used text books.

c)An increase in the number of students attending college.

d) A fall in the price of new text books.

Choose:c) non-price demand-determining variables

7. Plastic and steel are substitutes in the production of body panels for certain automobiles. If the price of plastic increases, with other things remaining the same, we would expect

a)the price of steel to fall.

b)the demand curve for steel to shift to the right.

c) the demand curve for plastic to shift to the left.

d)nothing to happen to steel because it is only a substitute for plastic.

e)the demand curve for steel to shift to the left.

Choose:b) the definition of substitutes

8. Last month you sold 10,000 stereos nationwide at $400 each. The month before that you sold 9,000 stereos at $410 each. Next month, you are thinking of cutting the price even further to $389.99. Assuming that (i) the market demand for your product is linear, and (ii) all else remains equal, what is your prediction for next month’s sales?

a) 10,100 units.

b) 11,000 units.

c) 11,001 units.

d) 11,051 units.

e) 12,000 units.

Choose: c) Using the two data points, find the slope and intercept of the demand curve: (9,000-10,000)/(410-400)=-100 and 10,000=a-100(400), or a=50,000. Thus, the equation of the line is Q=50,000-100P. When P=$389.99, Q=11,001.

The next 9-11questions refer to the following demand and supply curves: QD = 189 – 2.25P

QS = 124 + 1.5P

Your answers should be correct to two decimal places.

9.The equilibrium price is:

a) $84 b) $82.67 c) $17.33 d) $150 e) None of the above is

correct.

Choose: c) Setting QS =QD, we obtain 124 + 1.5P = 189 – 2.25P. Collecting

terms, 3.75P = 65, or P = $17.33.

10. The equilibrium quantity sold is:

a) 65 b) 150 c) 313 d) 84 e) None of the above is correct Choose: b) Using P =17.33 (from above), QS =124 +1.5(17.33) = 150.

11. At the market equilibrium, the price elasticity of demand equals:

a) -2.25 b) +2.25 c) -0.26 d) -0.17 e) None of the above is correct.

Choose: c) EP = -bP/Q = -2.25(17.33)/150 = -0.26.

12. If the price elasticity of demand for coffee is estimated to be –0.25 in the short of run, which is the most likely value of the long-run elasticity? a) -0.10 b) -0.25 c) -0.40 d) -∞

e) None of the above the elasticity of demand in the long run is always

positive.

Choose: c) For most goods (except those that are durable), the long-run

elasticity is greater in absolute value than the short-run elasticity.

Part 2:

Suppose the table below lists the price and consumption levels of food and clothing during 1990 and 2000. Calculate a Laspeyres and Paasche index

Solution:

The Laspeyres Index is calculated as follows:

()()()20001990200019901990199019901990

6.25100(3.35)75876.25 1.209.5100375725++====++F C F C

P F P C LI P F P C

The Paasche Index is calculated as follows:

()()()20002000200020001990200019902000

6.25110(3.35)87978.95 1.20

7.5110387811++====++F C

F C

P F P C PI P F P C

Part 3:

This exercise uses the market data given in Table 1.1

a) Plot the supply and demand curve with quantity on the

horizontal axis and price on the vertical axis.

b) Derive the intercepts and slops for the demand curve QD = a –

bP and the supply curve QS = c + dP.

c) Make sure that the equations you found are correct by plugging

in P = $10 and P = $ 40 and verifying the quantities with Table 1.1.

d) Find the equilibrium price and quantity.

Answer:

a)

b) First, consider the supply curve. From point (Q1, P1) and (Q2, P2), we

can der ive the slope: d = ΔQS/ΔP =(Q2 – Q1)/(P2 – P1) = (1,300 –900)/(40

–30) = 400/10 =40. The intercept c equals QS –dP =1,300 – 40(40) = -300.

So, the supply curve is QS =-300 + 40P.

The slope of the demand curve is

b = ΔQD/ΔP = (Q5 –Q6)/(P5 – P6) =(800 –1,000)/(20 –10) = -200/10

=-20, so b =20. The intercept is a =QD +bP = 800 +20(20) =1,200. So, the

demand curve is QD = 1,200 – 20P.

a)For supply, at P =10,Q S = -300 + 40(10) = -300 + 400 = 100.

At P = 40, Q S = -300 + 40(40) = 1,300.

For demand, at P = 10, Q S = 1,200 – 20(10) =1,000.

At P =40, Q D = 1,200 – 20(40) = 400.

d) Set Q S= Q D or –300 +40P =1200 –20P. Combining terms we get, 60P

=1,500, or P =25. Substituting back into the supply curve, we obtain Q S = -300 + 40(25) =700. As a check, substitute back into the demand curve to get Q S= 1,200 –20(25) =700. We have verified that P = 25 is the equilibrium price, since Q S =Q D =700 at that price.

Part 4:

The wheat market is perfectly competitive, and the market supply and demand curves are given by the following equations:

QD = 20,000,000 - 4,000,000P

QS = 7,000,000 + 2,500,000P,

where QD and QS are quantity demanded and quantity supplied measured in bushels, and P = price per bushel.

a) Determine consumer surplus at the equilibrium price and quantity.

b) Assume that the government has imposed a price floor at $2.25 per bushel and agrees to buy any resulting excess supply. How many bushels of wheat will the government be forced to buy? Determine consumer surplus with the price floor.

Solution: a.

The first step is to determine the equilibrium price ()e P and quantity ()e Q by equating QD and QS.

20,000,0004,000,0007,000,0002,500,000-=+e e P P 13,000,0006,500,000=e P $2.00.=e P

Substitute into QD or QS

()20,000,0004,000,0002=-e Q

12,000,000.=e Q

To find consumer surplus, we must also determine the choke price (C P ). That is, the price at which quantity demanded is zero. solve for P in terms of QD and QS.

020,000,0004,000,000=-C P 4,000,00020,000,000=C P

5.=C P

()()1

0.55212,000,00018,000,000.2

=

-=-=C e e CS P P Q

b.

At price of 2.25

QD = 20,000,000 - 4,000,000(2.25)

QD = 11,000,000

QS = 7,000,000 + 2,500,000(2.25)

QS = 12,625,000

Excess supply is QS - QD.

12,625,000 - 11,000,000 = 1,625,000

Government should expect to buy 1,625,000 bushels.

Cs = (0.5)(Pc-$2.25)QD = (0.5)(5-2.25)(11,000,000)=15,125,000.

C.S. fell from 18,000,000 to 15,125,000

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