Question

This problem adds the government to the Solow model with s, n and δ. Suppose that a government purchases goods in the amount of g per worker every year; with N t workers in year t total government purchases are g ⋅ N t. The government has a balanced budget so that its tax revenue in year t , T t , equals total government purchases. Total national saving, S t , is S = s ( Y t − T t ) where Y t is total output and s is the saving rate.

a) Graphically show the steady state for the initial level of government purchases per worker.

b) Suppose that the government permanently increases its purchases per worker. What are the effects on the steady-state levels of capital per worker, output per worker, and consumption per worker? Does your result imply that the optimal level of government purchases is zero?

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Answer 1

Answer: a) In order to show the steady state for Pnitial level of goverment purchasesper worker grouphically, observe that with budget being balanced, I = g. Neational saving & s= SCY-T) ESN (4-5) ESN (7-9 > set savings equal to investment I = entd) K & substitute y=f(1) SN(4-8)= (htdk s(y-9) = md) R S (f(K)-g) (n+d) k. Following drawn below is the grouph that clearly shows the steady state for initial level of goverment purchases per worked k* = equilibrium point of coupital- a labor ratio. Here +dJk Sf(K). S[F )-9 K*

o suppose of government increases Its purchase per worker, then curve s[fci)-g) will shift downwards. Hence, the coupital laubor ratio is lower in the steady-state edullibslum, Hence does the output per worker, consumption per worked and coupital per worker. The optimal level of the government Purchauses is depends upon the costs and benefits of these purchases and PS not zero necessarfly.