course materials

1. Production function – nursing writers
Consider a production functionYt = F(Kt,Lt) = ¯AKαt L1−αt(1)and the resource constraintYt
= Ct + It + Gtand the capital accumulation equationKt+1 = It + (1 − ¯d)KtConsumers consume
a certain fraction of the output so the consumption equation isCt = (1 − ¯s)YtThe
government spending Gt is a fraction of capital stock, so with the higher capital stock,
thereis more government spending.Gt = ¯gKtAssume there is no population growth, so Lt =
Lt+1 = ¯La. Derive a Solow-Growth model and describe the intuition of the equation.b. What
is the key assumption in this modelc. Find the steady state per-worker quantities of capital,
output, and consumptiond. Draw the Solow model (the x-axis is Capital stock, the y-axis is
output)e. Suppose there was a big government spending. Therefore, ¯g increased. What is
the new steady state per-worker quantities of capital, output, and consumption? The post
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