n answering the following questions, use the Solow

-

Swan model of a closed

economy without government

,

described below. The economy has clearing factor

markets (prices adjust to ensure that quantities demanded equal quantities supplied)

.

(i)

Express the production function as a relationship between output per worker,

y

,

and capital per worker,

k

, and calculate the saving rate that would make the

initial capital stock

a steady state. Use a diagram to explain your answer.

(3 marks)

(ii)

If the starting saving rate had been 15% (or 0.15), calculate the initial steady

state levels of

,,

KYC

, and

I

. The saving rate now rises to 25% (or 0.25). Write

the equation of motion of capital per worker and use it to calculate the first year

values of

Y

and

K

in the transition to the new steady state.

(3 marks)

(iii)

Explain, using a diagram, th

e nature of the ?

G

olden

R

ule

?

steady state and

calculate the saving rate at which this occurs in the model given above.

(3 marks)

(iv)

Assume that the current saving rate is 25% (or 0.25). The government adopts

policies to alter sav

ing rate to accord with the ?

G

olden

R

ule? level. Calculate

consumption per worker in these two steady states and compare them. Without

calculating the transition, describe and explain the immediate change that takes

place in consumption per worker and the

subsequent changes. Sketch what you

think the path of consumption per worker in the transition to the ?

G

olden

R

ule?

steady state. Comment on any policy dilemma implied

2. answering the following questions, use the Solow-Swan model of a closed economy without government, described below. The economy has clearing factor markets (prices adjust to ensure that quantities demanded equal quantities supplied). Output: Y = K L1 Labour supply: 10 s L = Expenditure on GDP: Y = C + I Consumption: C = (1 s)Y Savings: S = sY = Y C where s is the average saving rate (S Y ) and it is constant Investment: I = S Depreciation: K where the parameter values are: Production function: = 0.5 Initial capital stock: 0 K = 40 Depreciation rate: = 0. (i) Express the production function as a relationship between output per worker, y , and capital per worker, k , and calculate the saving rate that would make the initial capital stock a steady state. Use a diagram to explain your answer. (ii) If the starting saving rate had been 15% (or 0.15), calculate the initial steady state levels of K,Y,C , and I . The saving rate now rises to 25% (or 0.25). Write the equation of motion of capital per worker and use it to calculate the first year values of Y and K in the transition to the new steady state. (iii) Explain, using a diagram, the nature of the 'Golden Rule' steady state and calculate the saving rate at which this occurs in the model given above. (iv) Assume that the current saving rate is 25% (or 0.25). The government adopts policies to alter saving rate to accord with the 'Golden Rule' level. Calculate consumption per worker in these two steady states and compare them. Without calculating the transition, describe and explain the immediate change that takes place in consumption per worker and the subsequent changes. Sketch what you think the path of consumption per worker in the transition to the 'Golden Rule' steady state. Comment on any policy dilemma implied