4 questions microeconomics due in 4 hours

1

MICROECONOMICS Part I. Short: 1. Total (domestic) social surplus (TS) is the sum of consumers surplus (CS), producers

surplus (PS) of domestic firms and government revenue (GR). If we compare between a tariff that restricts imports to a maximum of N units (where N is positive) and an equivalent quota that reduces imports to the same amount of N units, the ________________ will generate higher government revenue (GR) and the ________________ will generate higher total domestic social surplus (TS).

2. A shale-fracking mine produces oil at a marginal cost of 𝑀𝐶 = 10 + 0.90𝑞 where q

is barrels of oil. It supplies competitively at a price of P = $55 per barrel. Each barrel of oil generates groundwater pollution which is estimated to have a marginal external cost (MEC) of 𝑀𝐸𝐶 = 0.60𝑞. Without regulation, it would produce q = _________________ barrels. If environmental regulators were to force the firm to fully recognize the costs of the pollution generated by each barrel produced, this firm would end up producing q = ________________ barrels of oil.

3. Below is a graph of a first-degree perfect price discriminating monopolist’s unit cost and revenue curves (D = demand curve, MR = marginal revenue, MC = marginal cost, ATC = average cost). Units of output are measured on the horizontal axis and the vertical axis measures dollars per unit:

For the perfect price discriminating monopolist, total profits (not producer’s surplus) are $________________ and total consumer surplus is $_______________. If this monopolist could not price-discriminate and had to sell its output at a common single price per unit then its total profits would be $________________ and total consumer surplus would be $________________.

2

Part II. Analysis. Provide appropriate analysis and discussion to the following sets of questions. Provide details of your logic or calculations where requested or where relevant. Carefully label and explain any graphs—by themselves graphs are not self- explanatory! I also appreciate clear writing (and handwriting). Make sure you address all the sub-questions asked. You may use the extra sheet at the end of this exam for calculations or extended answers. 1. Question (1) (10 points) Christiane, a typical SAIS M.A. student, derives satisfaction

from her consumption every semester of two goods: leisure activities (L) and SAIS

courses (C). Suppose that her utility function is given by 𝑈 = 𝐿 3

4 𝐶

1

4 where L and C

are the amounts of the two goods consumed per semester. For your convenience,

the marginal utilities of L and of C are supplied in the table below. Also given below

are the prices per unit of L and of C:

MUL MUC PL (in $) PC (in $)

3

4 (

𝐶

𝐿 )

1 4

1

4 (

𝐿

𝐶 )

3 4

15,000 5,000

(a) (7 points) If Christiane’s budget or available income each semester for these two

goods is I = 60,000, what would be her utility-maximizing combination of L and

C? Provide some details of how you came up with these numbers.

3

(b) (3 points) Does Christiane regard SAIS courses (C) as a normal good or an inferior

good? Double the value of the appropriate variable or element of Christiane’s

budget constraint and show numerically that C is actually a normal good. Show

details of your calculations below:

2. Question (2) (22 points) Economists see security arrangements like the North

Atlantic Treaty Organization (NATO) as means of providing of a public good called

“common security” to its members. Suppose we measure security in terms of

amounts of military force, units of which we represent by the variable G. Units of

this military good must be jointly consumed by three member governments, A, B, C

which have the following respective demand functions for G:

PA = 8 – G

PB = 40 – 2G

PC = 2 – 2G

where G is the amount of (jointly consumed) military force. With the above, among

the three governments, C seems to be the most pacifistic (in the sense that it

exhibits the smallest willingness to pay for military force).

Units of X can be produced at a constant cost of MC = AC = 30.

4

(a) (8 points) Given the above information, derive the demand curve of the group of

three governments for units of G and obtain the (socially) efficient quantity of

military force G to provide. (Show some details of your calculations.)

(b) (6 points) Given the socially efficient amount of G obtained in (a), suppose that

you were to now charge each member government of the group a different price

per unit of G, one based on their respective willingness to pay for G. What

amount you charge government C, and how would you interpret this amount?

5

(c) (8 points) Under the pricing scheme in (b), would there be losses generated in

providing this optimal amount of joint military force? Obtain numbers for

revenues and cost of providing this good, and show your results below:

6

3. Question (3) (28 points total) Stark Industries, Inc. a profit-maximizing US firm

specializing in advanced weapons systems owns a patent on the technology of Iron

Man™ armored battle suits (quantities denoted by Q) and is effectively a monopolist

in the armored battle suit industry. It has decided to sell these suits to both Russia

and China. These two countries have respectively the following demand curves:

QR = 300 – 3P

QC = 200 – 2P

where QR and QC are the quantities that Russia and China are willing to pay at

various levels of and price P (in million USD)

Suppose that its marginal cost is MC = 40 per battle suit. Further there are no longer

any fixed costs of production so its average cost AC is 40 as well.

(a) (8 points) Suppose Stark Industries can’t separate the Russian and Chinese

markets and must combine the two demand curves into a single global demand

curve. What is the total quantity Q of battle suits that Stark Industries would

produce if it were an ordinary (single-price) monopolist? Show calculations.

7

(b) (12 points) Suppose that Stark Industries’ initial market success in China attracts

a competitor firm— Mandarin Technologies— which can produce virtually

identical armored battle suits for the Chinese market. The two firms won’t

compete in Russia, but now they share the Chinese (inverse) demand curve:

P = 100 – (1/2)Q

Mandarin Technologies however has a cost advantage as it can produce suits at a

lower marginal cost of MC = 25 per battle suit (this is also its AC). If the two were

to behave as Cournot duopolists, how many battle suits would each firm end up

producing for the Chinese market? Show details of your logic.

8

(c) (8 points) Suppose Stark Industries and Mandarin Technologies enter into a

(collusive) partnership agreement to jointly sell battle suits to the Chinese

market, which as before has (inverse) demand given by

P = 100 – (1/2)Q

Suppose further they agree to use the less costly production methods of

Mandarin Technologies so that for their joint operations, MC = AC = 25. How

many battle suits would the partnership produce for the Chinese market, and

how much total profit would this generate?

9

Extra Sheet for Calculations/Continuation of Answers:

1

MICROECONOMICS Part I. Short: 1. Total (domestic) social surplus (TS) is the sum of consumers surplus (CS), producers

surplus (PS) of domestic firms and government revenue (GR). If we compare between a tariff that restricts imports to a maximum of N units (where N is positive) and an equivalent quota that reduces imports to the same amount of N units, the ________________ will generate higher government revenue (GR) and the ________________ will generate higher total domestic social surplus (TS).

2. A shale-fracking mine produces oil at a marginal cost of 𝑀𝐶 = 10 + 0.90𝑞 where q

is barrels of oil. It supplies competitively at a price of P = $55 per barrel. Each barrel of oil generates groundwater pollution which is estimated to have a marginal external cost (MEC) of 𝑀𝐸𝐶 = 0.60𝑞. Without regulation, it would produce q = _________________ barrels. If environmental regulators were to force the firm to fully recognize the costs of the pollution generated by each barrel produced, this firm would end up producing q = ________________ barrels of oil.

3. Below is a graph of a first-degree perfect price discriminating monopolist’s unit cost and revenue curves (D = demand curve, MR = marginal revenue, MC = marginal cost, ATC = average cost). Units of output are measured on the horizontal axis and the vertical axis measures dollars per unit:

For the perfect price discriminating monopolist, total profits (not producer’s surplus) are $________________ and total consumer surplus is $_______________. If this monopolist could not price-discriminate and had to sell its output at a common single price per unit then its total profits would be $________________ and total consumer surplus would be $________________.

2

Part II. Analysis. Provide appropriate analysis and discussion to the following sets of questions. Provide details of your logic or calculations where requested or where relevant. Carefully label and explain any graphs—by themselves graphs are not self- explanatory! I also appreciate clear writing (and handwriting). Make sure you address all the sub-questions asked. You may use the extra sheet at the end of this exam for calculations or extended answers. 1. Question (1) (10 points) Christiane, a typical SAIS M.A. student, derives satisfaction

from her consumption every semester of two goods: leisure activities (L) and SAIS

courses (C). Suppose that her utility function is given by 𝑈 = 𝐿 3

4 𝐶

1

4 where L and C

are the amounts of the two goods consumed per semester. For your convenience,

the marginal utilities of L and of C are supplied in the table below. Also given below

are the prices per unit of L and of C:

MUL MUC PL (in $) PC (in $)

3

4 (

𝐶

𝐿 )

1 4

1

4 (

𝐿

𝐶 )

3 4

15,000 5,000

(a) (7 points) If Christiane’s budget or available income each semester for these two

goods is I = 60,000, what would be her utility-maximizing combination of L and

C? Provide some details of how you came up with these numbers.

3

(b) (3 points) Does Christiane regard SAIS courses (C) as a normal good or an inferior

good? Double the value of the appropriate variable or element of Christiane’s

budget constraint and show numerically that C is actually a normal good. Show

details of your calculations below:

2. Question (2) (22 points) Economists see security arrangements like the North

Atlantic Treaty Organization (NATO) as means of providing of a public good called

“common security” to its members. Suppose we measure security in terms of

amounts of military force, units of which we represent by the variable G. Units of

this military good must be jointly consumed by three member governments, A, B, C

which have the following respective demand functions for G:

PA = 8 – G

PB = 40 – 2G

PC = 2 – 2G

where G is the amount of (jointly consumed) military force. With the above, among

the three governments, C seems to be the most pacifistic (in the sense that it

exhibits the smallest willingness to pay for military force).

Units of X can be produced at a constant cost of MC = AC = 30.

4

(a) (8 points) Given the above information, derive the demand curve of the group of

three governments for units of G and obtain the (socially) efficient quantity of

military force G to provide. (Show some details of your calculations.)

(b) (6 points) Given the socially efficient amount of G obtained in (a), suppose that

you were to now charge each member government of the group a different price

per unit of G, one based on their respective willingness to pay for G. What

amount you charge government C, and how would you interpret this amount?

5

(c) (8 points) Under the pricing scheme in (b), would there be losses generated in

providing this optimal amount of joint military force? Obtain numbers for

revenues and cost of providing this good, and show your results below:

6

3. Question (3) (28 points total) Stark Industries, Inc. a profit-maximizing US firm

specializing in advanced weapons systems owns a patent on the technology of Iron

Man™ armored battle suits (quantities denoted by Q) and is effectively a monopolist

in the armored battle suit industry. It has decided to sell these suits to both Russia

and China. These two countries have respectively the following demand curves:

QR = 300 – 3P

QC = 200 – 2P

where QR and QC are the quantities that Russia and China are willing to pay at

various levels of and price P (in million USD)

Suppose that its marginal cost is MC = 40 per battle suit. Further there are no longer

any fixed costs of production so its average cost AC is 40 as well.

(a) (8 points) Suppose Stark Industries can’t separate the Russian and Chinese

markets and must combine the two demand curves into a single global demand

curve. What is the total quantity Q of battle suits that Stark Industries would

produce if it were an ordinary (single-price) monopolist? Show calculations.

7

(b) (12 points) Suppose that Stark Industries’ initial market success in China attracts

a competitor firm— Mandarin Technologies— which can produce virtually

identical armored battle suits for the Chinese market. The two firms won’t

compete in Russia, but now they share the Chinese (inverse) demand curve:

P = 100 – (1/2)Q

Mandarin Technologies however has a cost advantage as it can produce suits at a

lower marginal cost of MC = 25 per battle suit (this is also its AC). If the two were

to behave as Cournot duopolists, how many battle suits would each firm end up

producing for the Chinese market? Show details of your logic.

8

(c) (8 points) Suppose Stark Industries and Mandarin Technologies enter into a

(collusive) partnership agreement to jointly sell battle suits to the Chinese

market, which as before has (inverse) demand given by

P = 100 – (1/2)Q

Suppose further they agree to use the less costly production methods of

Mandarin Technologies so that for their joint operations, MC = AC = 25. How

many battle suits would the partnership produce for the Chinese market, and

how much total profit would this generate?

9

Extra Sheet for Calculations/Continuation of Answers: