Question

Consider the Solow model economic production function,

Y = A * K^a * L^(1-a)

Assume the following initial conditions:

A = 1.2

a = 0.27

K = 16

L = 112

Additionally, you know that depreciation rate is 11 % and the savings rate is 12 %. Assuming no changes in any of the parameters, besides the change in K over time,

what is the long-run equilibrium level of output?

Answer 1

Y=A*K^a *L^(1-a)

A =

1.2

Divinding by L

a =

0.27

Y/L--->

q

K/L--->

k

K =

16

q=

A(K/L)^a

L =

112

q=

Ak^a

S=

0.12q

(Given savings is 12% of the total output)

the equilibrium condition . We shall find that if capital accumulation is the only source of growth, the economy will approach an equilibrium or steady state .

It will reach the steady state when savings is just sufficient to replace the depreciated capital stock. If we assume that in each time period capital depreciates totally, the equilibrium condition is simply

s = depreciation *k

Depreciation =11%

hence,

For long range equilibrium level of output

s=0.11K

s=0.11K

or,

s=

1.76

or, 0.12 *Y/L=1.76

or,Y=1.76*L/0.12

Y=

1,643