Question

d) Make a graph of the curve In(Kt) with time on the x-axis. Carefully show the shape and label the slope of this curve. 2. (A simulated economy) Let Yǐ = F(Kt, Lt) = AK capital accumulation equation is given by The discrete time version of the L,-1 and labor grows at a rate of n-001. A = 1, Ko = 0.01 and 0.07. a) A and 100. ssume that s 0.2. Find the level of consumption in the economy in periods 1,2,3,4 b) Repeat the computations in (a) assuming s 0.3. c) Assume the economy is in a steady state and s consumption over time after s increases to s 0.3. Explain what happens to 0.33. d) Do the same as in part (c) but assuming that s increases to 8-05. 3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function F(K, L)- KOLi-a, economy 2 has a production function G(K, L) aK + (1- a)L. For both economies capital grows

Answer 1

a)

t	kt	yt	ct
0	0.01	0.215443	0.172355
1	0.05187	0.37294	0.298352
2	0.121611	0.49544	0.396352
3	0.210085	0.594473	0.475578
4	0.311162	0.677635	0.542108
100	3.925756	1.577518	1.262015

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b)

t	kt	yt	ct
0	0.01	0.215443	0.172355
1	0.073201	0.418317	0.292822
2	0.191656	0.576555	0.403588
3	0.347729	0.703202	0.492242
4	0.529058	0.808787	0.566151
100	7.211475	1.932004	1.352403

===================================================================================

c)

Table 3

t	kt	yt	ct
0	7.26	1.936328	1.355429
1	7.317612	1.941436	1.300762
2	7.37233	1.946263	1.303996
3	7.424291	1.950825	1.307053
4	7.473626	1.955137	1.309942
100	8.372868	2.030602	1.360503

==============================================================================

d)

t	kt	yt	ct
0	7.26	1.936328	1.355429
1	7.643529	1.969842	0.984921
2	8.01327	2.001105	1.000553
3	8.369201	2.030305	1.015153
4	8.711396	2.057608	1.028804
100	15.58342	2.49778	1.24889

In this case, the consumption decreases first then increases over time, but it took a longer time to reach its steady state which is lower than previous steady state.