Section 4: Adding Government and Money

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1 Section 4: Adding and Money Ec 123 April 2009

2 Outline This Section Fiscal Policy Money Next Keynesian Economics Recessions Problem Set 1 due Tuesday in class

3 Fiscal Policy Fiscal Policy is the use of the government s ability to tax and spend in order to influence economic activity. G t is government spending on output. Z t is net tax receipts or Z t = T t Tr t where T t tax receipts and Tr t are transfer payments. When Z t < G t we say the government is running a deficit that must be financed through the accumulation of debt.

4 Fiscal Policy Fiscal Policy is the use of the government s ability to tax and spend in order to influence economic activity. G t is government spending on output. Z t is net tax receipts or Z t = T t Tr t where T t tax receipts and Tr t are transfer payments. When Z t < G t we say the government is running a deficit that must be financed through the accumulation of debt.

5 Fiscal Policy Fiscal Policy is the use of the government s ability to tax and spend in order to influence economic activity. G t is government spending on output. Z t is net tax receipts or Z t = T t Tr t where T t tax receipts and Tr t are transfer payments. When Z t < G t we say the government is running a deficit that must be financed through the accumulation of debt.

6 Fiscal Policy Fiscal Policy is the use of the government s ability to tax and spend in order to influence economic activity. G t is government spending on output. Z t is net tax receipts or Z t = T t Tr t where T t tax receipts and Tr t are transfer payments. When Z t < G t we say the government is running a deficit that must be financed through the accumulation of debt.

7 Debt Let B t be the stock of debt that the government has accumulated up until time t. Then, the stock of debt in the next period is determined by: B t+1 = B t + G t Z t + r t B t where r t B t is the interest payments (service) the government must pay on the stock of outstanding debt. The government must pay the interest rate r t on debt since this debt is a perfect substitute for the decision of the young to save via capital accumulation. Now G t Z t + r t B t is the deficit The debt stock transition equation can be rewritten as B t+1 = (1 + r t )B t + G t Z t.

8 Debt Let B t be the stock of debt that the government has accumulated up until time t. Then, the stock of debt in the next period is determined by: B t+1 = B t + G t Z t + r t B t where r t B t is the interest payments (service) the government must pay on the stock of outstanding debt. The government must pay the interest rate r t on debt since this debt is a perfect substitute for the decision of the young to save via capital accumulation. Now G t Z t + r t B t is the deficit The debt stock transition equation can be rewritten as B t+1 = (1 + r t )B t + G t Z t.

9 Debt Let B t be the stock of debt that the government has accumulated up until time t. Then, the stock of debt in the next period is determined by: B t+1 = B t + G t Z t + r t B t where r t B t is the interest payments (service) the government must pay on the stock of outstanding debt. The government must pay the interest rate r t on debt since this debt is a perfect substitute for the decision of the young to save via capital accumulation. Now G t Z t + r t B t is the deficit The debt stock transition equation can be rewritten as B t+1 = (1 + r t )B t + G t Z t.

10 Debt Let B t be the stock of debt that the government has accumulated up until time t. Then, the stock of debt in the next period is determined by: B t+1 = B t + G t Z t + r t B t where r t B t is the interest payments (service) the government must pay on the stock of outstanding debt. The government must pay the interest rate r t on debt since this debt is a perfect substitute for the decision of the young to save via capital accumulation. Now G t Z t + r t B t is the deficit The debt stock transition equation can be rewritten as B t+1 = (1 + r t )B t + G t Z t.

11 $billions National Debt, Last 100 years fiscal year end

12 120 pct Recent Ratio of National Debt to GDP annual

13 pct Various Govt Expenditures as Percentage of GDP annual Federal Nondefense Defense Federal Total State and Local Total

14 Assumptions of the Model Some assumptions Cobb-Douglas Production of output y(k t ) = Ak β t Profit maximization implies w(k t ) = (1 β)akt β = (1 β)y(k t ) r(k t ) = βakt β 1 = βy(k t) k t No population growth N t = N No technology growth A t = A Allows us to look for a steady-state. Cobb-Douglas Consumer utility u(c y, c o ) = c α y c 1 α o. Oldsters don t work w o = 0. Do not assume α = 0 as in the text.

15 Assumptions of the Model Some assumptions Cobb-Douglas Production of output y(k t ) = Ak β t Profit maximization implies w(k t ) = (1 β)akt β = (1 β)y(k t ) r(k t ) = βakt β 1 = βy(k t) k t No population growth N t = N No technology growth A t = A Allows us to look for a steady-state. Cobb-Douglas Consumer utility u(c y, c o ) = c α y c 1 α o. Oldsters don t work w o = 0. Do not assume α = 0 as in the text.

16 Assumptions of the Model Some assumptions Cobb-Douglas Production of output y(k t ) = Ak β t Profit maximization implies w(k t ) = (1 β)akt β = (1 β)y(k t ) r(k t ) = βakt β 1 = βy(k t) k t No population growth N t = N No technology growth A t = A Allows us to look for a steady-state. Cobb-Douglas Consumer utility u(c y, c o ) = c α y c 1 α o. Oldsters don t work w o = 0. Do not assume α = 0 as in the text.

17 Assumptions of the Model Some assumptions Cobb-Douglas Production of output y(k t ) = Ak β t Profit maximization implies w(k t ) = (1 β)akt β = (1 β)y(k t ) r(k t ) = βakt β 1 = βy(k t) k t No population growth N t = N No technology growth A t = A Allows us to look for a steady-state. Cobb-Douglas Consumer utility u(c y, c o ) = c α y c 1 α o. Oldsters don t work w o = 0. Do not assume α = 0 as in the text.

18 Lump-Sum Taxes The government can finance its spending via Lump-sum taxes, which are just a fixed amount of wages that the consumer cannot affect through their choices. z yt is the net tax payments of a young individual in period t. z ot is the net tax payments of an old individual in period t. Therefore, it must be that Z t = Nz yt + Nz ot

19 Lump-Sum Taxes The government can finance its spending via Lump-sum taxes, which are just a fixed amount of wages that the consumer cannot affect through their choices. z yt is the net tax payments of a young individual in period t. z ot is the net tax payments of an old individual in period t. Therefore, it must be that Z t = Nz yt + Nz ot

20 Effect on Consumers Consumer budget constraints are now given by: c y = w y a z y c o = w o z o + (1 + r)a Eliminating a (savings) we get a lifetime budget constraint: c y + c o 1 + r = (w y z y ) + (w o z o ) 1 + r Clearly, this is the same problem with original wages replaced by wages minus taxes.

21 Effect on Consumers Consumer budget constraints are now given by: c y = w y a z y c o = w o z o + (1 + r)a Eliminating a (savings) we get a lifetime budget constraint: c y + c o 1 + r = (w y z y ) + (w o z o ) 1 + r Clearly, this is the same problem with original wages replaced by wages minus taxes.

22 The utility maximizing savings function is therefore given by: a(r) = (1 α)(w y z y ) α (w o z o ). 1 + r Consumption choices are: ( c y (r) = α (w y z y ) + (w ) o z o ) 1 + r ( c o (r) = (1 + r)(1 α) (w y z y ) + (w ) o z o ) 1 + r

23 The utility maximizing savings function is therefore given by: a(r) = (1 α)(w y z y ) α (w o z o ). 1 + r Consumption choices are: ( c y (r) = α (w y z y ) + (w ) o z o ) 1 + r ( c o (r) = (1 + r)(1 α) (w y z y ) + (w ) o z o ) 1 + r

24 Setting w 0 = 0 and reinserting the appropriate time scripts we obtain: a(r t+1 ) = (1 α)(w t z yt ) + α z ot r t+1 In equilibrium, it must be that k t+1 = a(r t+1 ) (supply = demand), and w t = w(k t ) and r t+1 = r(k t+1 ) (profit maximizing firms). z ot+1 k t+1 = (1 α)(w(k t ) z yt ) + α 1 + r(k t+1 ).

25 Setting w 0 = 0 and reinserting the appropriate time scripts we obtain: a(r t+1 ) = (1 α)(w t z yt ) + α z ot r t+1 In equilibrium, it must be that k t+1 = a(r t+1 ) (supply = demand), and w t = w(k t ) and r t+1 = r(k t+1 ) (profit maximizing firms). z ot+1 k t+1 = (1 α)(w(k t ) z yt ) + α 1 + r(k t+1 ).

26 Setting w 0 = 0 and reinserting the appropriate time scripts we obtain: a(r t+1 ) = (1 α)(w t z yt ) + α z ot r t+1 In equilibrium, it must be that k t+1 = a(r t+1 ) (supply = demand), and w t = w(k t ) and r t+1 = r(k t+1 ) (profit maximizing firms). z ot+1 k t+1 = (1 α)(w(k t ) z yt ) + α 1 + r(k t+1 ).

27 Balanced Budget Assume Taxes are time independent: z yt = z y and z ot = z o. The government runs a balanced budget: z y + z o = g where g = G N. Then a steady-state will solve: z o k = (1 α)(w(k) z y ) + α 1 + r(k).

28 Balanced Budget Assume Taxes are time independent: z yt = z y and z ot = z o. The government runs a balanced budget: z y + z o = g where g = G N. Then a steady-state will solve: z o k = (1 α)(w(k) z y ) + α 1 + r(k).

29 Role of What good does the government provide? Intergeneration transfers to affect capital accumulation/output. Provides public goods Examples: National Defense, environmental policy, etc. Would need to add a public good good that only the government can create in utility functions. Provide capital goods Examples: Roads, R & D consumption is turned into savings for the next generation. Smooth short-run fluctuations in output. Next Section!

30 Role of What good does the government provide? Intergeneration transfers to affect capital accumulation/output. Provides public goods Examples: National Defense, environmental policy, etc. Would need to add a public good good that only the government can create in utility functions. Provide capital goods Examples: Roads, R & D consumption is turned into savings for the next generation. Smooth short-run fluctuations in output. Next Section!

31 Role of What good does the government provide? Intergeneration transfers to affect capital accumulation/output. Provides public goods Examples: National Defense, environmental policy, etc. Would need to add a public good good that only the government can create in utility functions. Provide capital goods Examples: Roads, R & D consumption is turned into savings for the next generation. Smooth short-run fluctuations in output. Next Section!

32 Role of What good does the government provide? Intergeneration transfers to affect capital accumulation/output. Provides public goods Examples: National Defense, environmental policy, etc. Would need to add a public good good that only the government can create in utility functions. Provide capital goods Examples: Roads, R & D consumption is turned into savings for the next generation. Smooth short-run fluctuations in output. Next Section!

33 Role of What good does the government provide? Intergeneration transfers to affect capital accumulation/output. Provides public goods Examples: National Defense, environmental policy, etc. Would need to add a public good good that only the government can create in utility functions. Provide capital goods Examples: Roads, R & D consumption is turned into savings for the next generation. Smooth short-run fluctuations in output. Next Section!

34 Money Two types of money: 1 Commodity Money Money that is made of a commodity (such as gold or silver) that has other uses and whose supply is limited by the supply of the commodity. U.S. stopped using gold coins in Fiat Money Money that is created by issuers (usually the government) and is essentially worthless except by virtue of being declared to be money. This is what we focus on here.

35 Money Two types of money: 1 Commodity Money Money that is made of a commodity (such as gold or silver) that has other uses and whose supply is limited by the supply of the commodity. U.S. stopped using gold coins in Fiat Money Money that is created by issuers (usually the government) and is essentially worthless except by virtue of being declared to be money. This is what we focus on here.

36 Money Two types of money: 1 Commodity Money Money that is made of a commodity (such as gold or silver) that has other uses and whose supply is limited by the supply of the commodity. U.S. stopped using gold coins in Fiat Money Money that is created by issuers (usually the government) and is essentially worthless except by virtue of being declared to be money. This is what we focus on here.

37 Notation M t is the stock (supply) of (fiat) money in period t. m t = Mt N t is the stock (supply) of money per young worker in period t. is the price level in period t m t is each young worker s real balance of money in period t. π t+1 is the rate of inflation in period t + 1. The percentage change in prices between period t and t + 1. π t+1 = +1 = +1 1

38 Notation M t is the stock (supply) of (fiat) money in period t. m t = Mt N t is the stock (supply) of money per young worker in period t. is the price level in period t m t is each young worker s real balance of money in period t. π t+1 is the rate of inflation in period t + 1. The percentage change in prices between period t and t + 1. π t+1 = +1 = +1 1

39 Notation M t is the stock (supply) of (fiat) money in period t. m t = Mt N t is the stock (supply) of money per young worker in period t. is the price level in period t m t is each young worker s real balance of money in period t. π t+1 is the rate of inflation in period t + 1. The percentage change in prices between period t and t + 1. π t+1 = +1 = +1 1

40 Notation M t is the stock (supply) of (fiat) money in period t. m t = Mt N t is the stock (supply) of money per young worker in period t. is the price level in period t m t is each young worker s real balance of money in period t. π t+1 is the rate of inflation in period t + 1. The percentage change in prices between period t and t + 1. π t+1 = +1 = +1 1

41 Notation M t is the stock (supply) of (fiat) money in period t. m t = Mt N t is the stock (supply) of money per young worker in period t. is the price level in period t m t is each young worker s real balance of money in period t. π t+1 is the rate of inflation in period t + 1. The percentage change in prices between period t and t + 1. π t+1 = +1 = +1 1

42 The Demand for Money Balances Let m d t+1 be demand for money and m d t+1 is the demand for real balances in period t. Consumers budget constraints are then given by: c yt + a t+1 + md t+1 = w ot c ot+1 = (1 + r t+1 )a t+1 + md t+1 +1 m d t+1

43 The Demand for Money Balances Eliminating a t+1 to obtain a lifetime budget constraint: c yt + c ( ) ot+1 rt+1 m d + t r t r t+1 +1 = w ot or c yt + c ( ) ot+1 1 m d = w ot 1 t r t r t+1 +1

44 The Demand for Money Balances Eliminating a t+1 to obtain a lifetime budget constraint: c yt + c ( ) ot+1 rt+1 m d + t r t r t+1 +1 = w ot or c yt + c ( ) ot+1 1 m d = w ot 1 t r t r t+1 +1

45 Since c yt and c ot+1 are the only two variables in order for m d t+1 0, it must be that ( r t+1 +1 ) < r t+1 +1 > > r t+1

46 The return on money holdings is given by: (m d t+1 /+1) (m d t+1 /) (m d t+1 /) = (md t+1 /+1) (m d t+1 /) 1 = +1 1 > r t+1

47 A necessary condition for money demand to be positive is then: or people expect deflation! +1 1 > 0 +1 > 1 +1 < < 0 π t+1 < 0

48 A necessary condition for money demand to be positive is then: or people expect deflation! +1 1 > 0 +1 > 1 +1 < < 0 π t+1 < 0

49 A necessary condition for money demand to be positive is then: or people expect deflation! +1 1 > 0 +1 > 1 +1 < < 0 π t+1 < 0

50 A necessary condition for money demand to be positive is then: or people expect deflation! +1 1 > 0 +1 > 1 +1 < < 0 π t+1 < 0

51 A necessary condition for money demand to be positive is then: or people expect deflation! +1 1 > 0 +1 > 1 +1 < < 0 π t+1 < 0

52 Deflation? Inflation change in annual avg index pct CPI GDP Price Index

53 Why do people hold real money balances? Some Models: Cash-in-advance constraints (Clower constraints) Cash is a necessary intermediate good for the purchase of consumption. Money in the utility function Auerbach and Kotlikoff (Chp. 7) Consumption Loans (Samuelson 1958) Money is the only durable asset. Money in the production function Transaction models Money makes transaction costs lower.

54 Why do people hold real money balances? Some Models: Cash-in-advance constraints (Clower constraints) Cash is a necessary intermediate good for the purchase of consumption. Money in the utility function Auerbach and Kotlikoff (Chp. 7) Consumption Loans (Samuelson 1958) Money is the only durable asset. Money in the production function Transaction models Money makes transaction costs lower.

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