1   The Government and the Macroeconomy

1.1    Government Budget Constraint

• Flow version of the government budget constraint:

Gt + Trt + iBt  = Tt + ∆Bt+1 + ∆Mt+1                                                      (1)

尸        山、        使    尸             山、             使

Uses                                         Sources

– Gt : Government spending on goods and services

– Trt : Transfer payments (unemployment insurance, Social Security, etc.)

– Bt : Stock of government debt

– Tt : Taxes

• With simplifying assumptions Trt  = 0 and ∆Mt+1  = 0, we have

Primary Deficit

使尸       

尸                                                                          使

• Intertemporal budget constraint:

G1 +  + (1 + i)B1  = T1 +

(2)

(3)

Questions

1. Suppose a government has an initial debt of $5 trillion, and the nominal interest is 5%.

(a) If the government keeps its primary budget in balance, what is the growth rate of its

debt?

The government debt evolves according to

Bt+1  = (1 + i)Bt + Gt − Tt .                                          (4)

If the primary budget is in balance, we have Gt  − Tt  = 0.  So the growth rate of the

debt is

Bt+1  − Bt

Bt

which is 5%.

(b) If the government keeps its total budget in balance, what is the growth rate of its debt?

If the total budget is in balance, we have iBt + Gt  − Tt  = 0.  We get Bt+1  = Bt , i.e. the debt is constant and the growth rate is zero.

(c) Suppose the country’s GDP grows at 4% per year.  What happens to the debt-GDP ratio over time in the two cases of parts (a) and (b)?

According to the growth rules, the growth rate of the debt-GDP ratioY(B)t(t)   is gB − gY . We have gY  = 4%. In (a), we have gB  = 5%, so the debt-GDP ratio grows at 5% −4% = 1%. In (b), we have gB  = 0%, so the debt-GDP ratio grows at 0% − 4% = −4%.

2   International Trade

Questions

Suppose that there are only country A and country B in the world.

Assume that workers in each country spend  of their wages on apples and  on computers.

1. Which country has an absolute advantage? Which country has a comparative advan- tage in producing apples?

Country A has an absolute advantage because workers in country A are more pro- ductive in both sectors. Country B has a comparative advantage in producing apples because a worker in country A is 10 times more productive in producing computers while it is just 2 times more productive in producing apples.

2. Suppose that there is no trade between the two countries.

(a) Assume that workers are free to work in either sector.  What are the wages in

each country in terms of apples?

First of all, in each country, the wages must be the same in all sectors (otherwise all workers select the sector providing a higher wage).  The marginal product of labor in the apple sector is 200 (apples) in country A and 100 (apples) in country B. These are the wages in each country.

(b) What are the prices of a computer in each country (in terms of apples)?

A worker in country A can produce either 200 apples or 10 computers. The price of a computer there must be 200 / 10 = 20 (apples).  Why?  If the price of a computer is higher than 20 apples, everyone wants to produce computers while the price of a computer is lower than 20 apples, everyone wants to produce apples.

For the country to produce both goods, the price of a computer must be 20 apples. Likewise, the price of a compute in country B is 100 / 1 = 100 (apples).

Note that the wage is higher and computers are cheaper in country A, which is consistent with the absolute advantage that country A has in producing both goods.

(c) What are the consumption of each good per person in each country?

Country A: Each worker earns 200 (apples).  By assumption, each worker con- sumes 1/4 of his/her wage, so the consumption of apples per person is

 × 200 (apples) = 50 (apples).                                   (6)

The remaining  of wages are spent on computers. The consumption of computers per person is

 × 200 (apples) ×  (computers / apples) = 7.5 (computers)

Country B: Each worker earns 100 (apples).  By assumption, each worker con- sumes 1/4 of his/her wage, so the consumption of apples per person is

 × 100 (apples) = 25 (apples).                                   (7)

The remaining  of wages are spent on computers. The consumption of computers per person is

 × 100 (apples) ×

(computers / apples) = 0.75 (computers)

(d) What are the total production of each good in each country?

Country A: Each person consumes 50 apples and 7.5 computers. Since there are 100 people in country A, the total production of apples is 50 × 100 = 5, 000 while the total production of computers is 7.5 × 100 = 750.

Country B: Each person consumes 25 apples and 0.75 computers. Since there are 200 people in country B, the total production of apples is 25 × 200 = 5, 000 while the total production of computers is 0.75 × 200 = 150.

Summary:                                                                                                

Country A   Country B

Wage (in terms of apples)                              200              100

3. Now suppose that trade is allowed and country A specializes in computers while country B specializes in apples.

(a) What is the total production of apples in the world? What is the total production

of computers in the world? Are they larger or smaller than in the previous case where trade is not allowed?

The total production of apples is

200 (workers) × 100 (apples / worker) = 20, 000 (apples),

which is larger than 10, 000 which is the production of apples when trade is not allowed.

The total production of computers is

100 (workers) × 10 (computers / worker) = 1, 000 (computers),

which is larger than 900 which is the production of computers when trade is not allowed.

(b) What are the wages in each country and the price of a computer in terms of

apples?

We have the two market clearing conditions

population

1                        、使尸山       1

Apple market clearing:  20, 000 =     × wageA  ×    100    +    × wageB  × 200    (8)

尸         使

Demand

Computer market clearing: 1, 000 = [  × wageA  × 100 +  × wageB× 200]/pC     (9)

where pC  is the price of a computer. pC , wageA , and wageB  are all in terms of apples.  There are three unknowns, but we know that the wage in country B is the marginal product of labor, i.e., 100 apples.  Substituting wageB  = 100 into the first equation gives wageA  = 600 (apples). Substituting these into the second equation gives pC  = 60 (apples).

(c) What are the consumption of each good per person in each country?

Country A:

Consumption of apples:  × 600 = 150       Consumption of computers:  × 600 ×  = 7.5

Country B:

(10)

(11)

Consumption of apples:  × 100 = 25           Consumption of computers:  × 100 ×  = 1.25

(12)

(13)