Question 1 Tax revue in the country is recorded at 40 Euros, net savings are

equal to 40 Euros. The investments are a third of the size of government spending, there is a budget deficit of 20 and the current account has a surplus with a value equal to 10% of GDP. What is the consumption in this state?

We know Y = C + T + S and Y = C + G + I + X-Z

C = Y - T - S or C= Y- G - I - X + Z

We know: T = 40 S-I = 40 I = 1/3*G T-G = -20 CA =X-Z = 0,1*Y

G: 40-G = -20 G = 60

I : I = 1/3*G = 1/3*60 I = 20

S: S – I = S – 20 = 40 S = 60

(S-I) + (T-G) = (X-Z) 40 – 20 = 20

Y = CA*10 200

Y = C + T + S 200 = C + 40 + 60 C = 100

Question 2 – Solow model

Consider an economy which has a production function where capital K(t) and labor L(t) are combined in order to produce the final output Y(t). Take the population growth rate to be equal to zero, n=0, technological change is absent and assume also that the savings rate is equal to s=20%. Now consider that households savings behavior changes and the savings rate increases to s=25%.

1. Describe (in words with the help of some maths) what happens in the short run and in the long run to output, investment and capital stock in this economy after the increase of the savings rate.

2. Show this effect graphically.

Question 2 – Solow model

Investment

Households have income Y and split this between C and S

Savings rate s refers to the fraction of total income saved by the housholds: sY = total saving

Express everything in per capita variables: y = c + s

Savings = gross investment = sy

If s ↑ sy ↑ Gross investment increases (in the short and long run)

Question 2 – Solow model Capital stock (K/L) and output (Y/L)

L = constant only change in K here

Net investment = gross investment minus depreciation

Δk = sy – δk . In the steady state, Δk = 0.

Here: in the short run: Δk >0 because sy increases and therefore sy > δk

The economy is not in its steady state.

accumulation of capital stock as long as sy > δk. Until we arrive in the new steady state, where Δk = sy – δk =0.

accumulation slows down when coming closer to the new steady state

K/L will be higher with s2 than with s1

Output: with higher K/L also higher output (Y/L)

Increase in the saving rate

0

=s f kold saving ( )

= kdepreciation

y=Y/L

=s f knew saving ( )

k=K/L

y=f kProduction function

( )

A

B

Increase in the saving rate Increase of s: Higher k, higher y, higher investment

0

=s f kold saving ( )

= kdepreciation

y=Y/L

=s f knew saving ( )

k=K/L

y=f kProduction function

( )

s2y

s1y

y1

y2

Question 2 – Solow model

Considering the increase in the savings rate described in the previous question, is this a clear improvement for the people in this economy in terms of current and future consumption? Explain your argument considering the Golden Rule for optimal consumption of the Solow model.

Golden rule saving rate

To ensure maximal consumption, the saving rate has to cross the depreciation line where the distance between δk and f(k) is maximal.

( )s f k

0

= kdepreciation

y=Y/L ( )y = f k

y

k k=K/L

A

}

}investm ent

consum ption

The Golden Rule

In steady state consumption c is given by

What is the level of k that maximizes consumption in steady state?

Marginal productivity of capital = depreciation rate

Golden Rule: the steady state value of the capital-labor ratio k* maximizes consumption when the marginal product of capital equals the depreciation rate

)(' kf

kkfc )(

Increase of s Here we don’t know anything about f(k) or δk no clear

conclusion possible for the long run. In the short run: decrease of c

If k1 < k* in case that sold < snew future steady state consumption (A’B’) increases + current consumption (AB) decreases compared to initial steady state c (AC)

0

y=Y/L

k=K/L

snew

sold

y=f(k)

k

δk

k

B

C

A’

B’

Increase of s

If k1 > k* in case that sold < snew current (AB) consumption and future steady state consumption (A’B’) decreases compared to the initial steady state consumption (AC)

0

y=Y/L

k=K/L

snew

sold

y=f(k)

k

δk

k

B

C

B’

Question 3

Explain Conditional Convergence

Solow model and the Convergence Hypothesis

Solow model: A country’s output per capita in the steady state is affected by

Saving rate, s

Population Growth, n

Level of technology, A Note: a and δ are considered to be equal across countries

Implications

If s, n and A are similar across countries convergence to the same steady state should occur same Y/L

In the steady state in all countries Y/L grows at a

If a country has a capital stock below the steady state level grows faster until it reaches the steady state catch up

Conditional convergence

Convergence hypothesis:

Basic idea: If a country starts out with a low level of k (below the steady state) capital accumulation should occur faster than in advanced economies (closer or at the steady state) K has higher marginal productivity when low K stock Y grows faster

Conditional convergence:

Basic idea: countries with different production functions, s or n will converge to different steady states, characterized by different levels of capital and output per (effective) labor.

Also, when other factors determining Y like human capital or public infrastructure differ, economies will have different steady states