Question

2. (A simulated economy) Let Y,-F(K,,Lt)-AK) L. The discrete time version of the capital accumulation equation is given by Lo-1 and labor grows at a rate of n-0.01. A-1, Ko-0.01 and 6-0.07 a) Assume that s-0.2. Find the level of consumption in the economy in periods 1,2,3,4 and 100. b) Repeat the computations in (a) assuing s 03 consumption over time after s increases to s = 0.33 d) Do the sanne as in part (c) but assuming that s increases to s = 0.5.

Answer 1

This is a basic simulation exercise and can easily be solved using Excel

Part a)

Please follow these steps:

Keep column A for time period t

Column B for constant A

Column C for variable K_t

Column C for variable K_t

Column D for variable K_t^1/3

Column E for variable L_t

Column F for variable L_t^2/3

Column G for variable Y_t

Formulae in row 2 are as follows:

A2 = 0

B2 = 1

C2 = K₀ = 0.01

D2 = K₀^1/3 = 0.01^(1/3)

E2 = L₀ = 1

F2 = L₀^2/3= 1^(2/3)

G2 = Y₀ = B2*D2*F2

t	A	K	K^(1/3)	L	L^(2/3)	Y
0	1	0.01	0.215443	1	1	0.215443

Formulae for row 3 are as follows:

Formula in row 2 should be as follows:

A3 = t = 1

B3 = A = 1

C3 = K1 =

=((0.2*G2)+((1-0.07)*C2))

where G2 is Y₀ and C2 is K₀

D3 = K₁^1/3 = C3^(1/3)

E3 = L1 =

=E2*1.01

F3 = L₁^2/3= E3^(2/3)

G3 = Y₁= B3*D3*F3

null

Copy formulae of row 3 till row 102 which is t = 100

Thus, for s=0.2, level of consumption in the economy is as follows:

Y1	0.377
Y2	0.505
Y3	0.612
Y4	0.705
Y100	4.267

b) Repeat the steps with s = 0.3

C3 = K₁ =

=((0.3*G2)+((1-0.07)*C2))

Thus, for s = 0.3, level of consumption in the economy is as follows:

Y1	0.423
Y2	0.588
Y3	0.725
Y4	0.842
Y100	5.226

c) Given that economy is in a steady state and s changes from 0.3 to 0.33, we have to find out what happens to consumption. For this we will do the simulation as conducted in part b for s = 0.33

We see that it reaches steady state at similar time period when s = 0.3 and when s = 0.33 at around t = 36 (% change in consumption becomes 1% Year on year)

	s=0.3	s=0.33
Y1	0.423	0.434
Y2	0.588	0.610
Y3	0.725	0.754
Y4	0.842	0.878
Y100	5.226	5.481

d) When s = 0.5

	s=0.3	s=0.33	s=0.5
Y1	0.423	0.434	0.492
Y2	0.588	0.610	0.718
Y3	0.725	0.754	0.901
Y4	0.842	0.878	1.057
Y100	5.226	5.481	6.746

As, s increases steady state is reached a little later in time. Moreover, the steady state consumption increases with increase in s.

% change in s	s changes from 0.3 to 0.33 = 10%	s changes from 0.33 to 0.5 = 52%
Change in Y1	3%	13%
Change in Y2	4%	18%
Change in Y3	4%	19%
Change in Y4	4%	20%
Change in Y100	5%	23%