Suppose that we have a Solow model with one twist. The twist is that there is a government. Each period, the government consumes a fraction of output, sG. Hence, the aggregate resource constraint is: Yt = Ct + It + Gt . Where Gt = sGYt . Define private output as Y p t = Yt − Gt . Suppose that investment is a constant fraction, s, of private output (consumption is then 1 − s times private output). Otherwise the model is the same as in the text. 104 (a) Re-derive the central equation of the Solow model under this setup. (b) Suppose that the economy initially sits in a steady state. Suppose that there is an increase in sG that is expected to last forever. Graphically analyze how this will affect the steady state value of the capital stock per worker. Plot out a graph showing how the capital stock per worker will be affected in a dynamic sense
3. Suppose that we have a Solow model with one twist. The twist is that there
is a government. Each period, the government consumes a fraction of output,
sG. Hence, the aggregate resource constraint is:
Yt = Ct + It + Gt
.
Where Gt = sGYt
. Define private output as Y
p
t = Yt − Gt
. Suppose that
investment is a constant fraction, s, of private output (consumption is then
1 − s times private output). Otherwise the model is the same as in the text.
104
(a) Re-derive the central equation of the Solow model under this setup.
(b) Suppose that the economy initially sits in a steady state. Suppose that
there is an increase in sG that is expected to last forever. Graphically
analyze how this will affect the steady state value of the capital stock
per worker. Plot out a graph showing how the capital stock per worker
will be affected in a dynamic sense
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