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# 8b - Government in the Two Period Model We will now place a...

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Government in the Two Period Model. We will now place a government in our model. There are a few preliminary points that we need to make. 1) All government decisions to use some of the production of our real economy (Y) can be thought of as government expenditure (G). 2) This decision is made exogenously –therefore G is an exogenous variable. 3) The “spending” decision can be financed by: a) lump-sum taxes (T) or b) Using the credit market and selling bonds. The interest rate that the government pays is the real interest rate (r). Given these three conditions we can proceed. The government’s CURRENT period budget constraint is: G = T + B Æ this is just a restatement of condition (3). The government’s FUTURE period budget constraint will include future spending, future taxes and repayment with interest of the output (in the form of consumption goods) that was borrowed in the previous period. G ƍ + (1 +r)B = T ƍ Aside- this is still a TWO period economy so anything borrowed in the first period must be paid back with interest in the second period- there can not be any second period borrowing since there is no third period in which to repay. Rearrange this equation Æ B = T ƍ - G ƍ 1+ r Substitute this equation into the current period constraint and rearrange. G + G ƍ = T + T ƍ 1+r 1+r

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Notice that the future variables, G ƍ and T ƍ are discounted down to the present value so we can everything into one equation. This is done by dividing by 1/(1+r). The left hand side of the equation demotes the present values of government purchases and the right hand side is the present value of taxes. COMPETIVE EQUILIBRIUM Now that the government is in the model the equilibrium will entail: 1) Consumer choices c, c ƍ and s 2) The government choice of G ,G ƍ . T and T ƍ .
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