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1、Chapter 5A Closed-Economy One-Period Macro ModelThe ModelThe economy that we consider is a closed economy,i.e.one that does not trade with other economies.Besides representative consumer and representative firm,there is an additional agent:the government.GovernmentThe only action of the government i
2、s to implement fiscal policy.Fiscal policy refers to the governments choices over its expenditures,taxes,transfers and borrowing.The GovernmentSuppose the government wishes to purchase a given quantity of consumption good,G.Since there is only one period,the government cannot borrow to finance G.Thu
3、s G is paid by taxing the representative consumer.The government must observe the balanced budget constraint,G=T.Competitive EquilibriumCompetitive refers to the fact that all consumers and firms are price-takers.Equilibrium refers to the state when the actions of all consumers and firms are consist
4、ent.Formal Definition:A competitive equilibrium is a set of endogenous quantities C,Ns,Nd,T and Y,and an endogenous real wage w,such that,given the exogenous variables G,z,and K,the following are satisfied:1)C and Ns solves the consumers problem,max U(C,h-Ns)C,Ns subject to C=wNs+-T and C 0,Ns 0.In
5、other words,C and Ns must satisfy the FOC,U2(C,h-Ns)-wU1(C,h-Ns)=0.2)Nd solves the firms problem given z,K and w.Thus the FOC is satisfied.3)Market-clearing conditions:Labor market clearing Ns=Nd=N4)Balanced Budget constraint:G=T.We have:Goods market clearing Y=C+GCombining the two FOCs,we have U2(C
6、,l)-zF2(K,h-l)U1(C,l )=0.Since =zF(K,h-l)-w Nd and G=T,from the budget constraintC=zF(K,h-l)-G.From these,we can solve for the equilibrium C and l.Graphical IllustrationsStep 1:Derive the production possibilities frontier(PPF),which describes the technological possibilities for the entire economy,in
7、 terms of the production of C and l.Step 2:Put the PPF together with the consumers indifference curves,so that we can analyze a competitive equilibrium in a single diagram.Production Possibilities FrontierIn equilibrium,we have Nd=Ns=N=h-l.Output is given by Y=zF(K,h-l).which is a relationship betwe
8、en output and leisure.Y*is the level when l=0.Production Possibilities FrontierIn equilibrium,C=Y-G=zF(K,h-l)-G a relationship between C and l,given the exogenous variables z,K and G.This is the PPF which captures the trade-off between leisure and consumption given the production technology.Only the
9、 points on DB are available(where C 0).Production Possibilities FrontierNegative of the slope of the PPF is called the marginal rate of transformation,MRT l,C which is the rate at which one good can be converted into another.MRT l,C =MPN =-(Slope of PPF)In equilibrium,MPN =w.Thus,we must have MRT l,
10、C =w.This helps us determine the equilibrium values C*and l*.Competitive EquilibriumIn equilibrium,C*and l*are chosen by the representative consumer.Note that ADB is the budget constraint.By the FOC of the consumers problemMRS l,C=w.Hence,in equilibriumMRT l,C =MRS l,C=w.OptimalityQuestions:Is the c
11、ompetitive equilibrium efficient?Are there any other ways to obtain a better outcome?A competitive equilibrium is Pareto optimal if there is no way to rearrange production or to reallocate goods so that someone is made better off and no one is made worse off.Since there is only one consumer,we can i
12、gnore how consumption goods are allocated among consumers.Rather,we focus on how production is arranged.Social Planners ProblemConsider a social planner who runs the representative firm and chooses the quantities C and l so as to maximize consumers utility.Graphically,the social planner chooses a co
13、nsumption bundle that is on the PPF and is on the highest possible indifference curve for the consumer.Social Planners ProblemComparison:Representative consumer faces a linear or kinked budget constraint.Social planner faces a concave PPF.The Pareto optimum is at B where the equality holdsMRT l,C =M
14、RS l,C=MPN.Social Planners ProblemThe social planner solves the following constrained maximization problem:Max U(C,l)C,l subject to C=zF(K,h-l)-GLagrangian L=U(C,l)+zF(K,h-l)-G-C.First-order(Necessary)conditions:Combining the first two conditions,which states that the Pareto optimum is the point whe
15、re the indifference curve is tangent to the PPF.Note that we have also derived the same condition for a competitive equilibrium.Two Welfare TheoremsThe first fundamental theorem of welfare economicsUnder certain conditions,a competitive equilibrium is Pareto optimal.“Indivisible hand”:an unrestricte
16、d,free market economy can produce socially optimal outcome.The second fundamental theorem of welfare economicsUnder certain conditions,a Pareto optimum is a competitive equilibrium.Remark:Pareto optimality ignores the distribution issue among individuals and is thus a narrow concept of social optima
17、lity.Sources of Social Inefficiencies A competitive equilibrium may not be Pareto optimal due to:ExternalitiesAn externality is any activity for which an individual firm or consumer does not take account of all associated costs and benefits.Externalities can be negative(e.g.pollution)or positive(e.g
18、.knowledge spillover).The root cause of an externality is that it is too costly,if not impossible,to set up a market to trade for the benefits and costs associated with the externalities(market failure).Distorting TaxesSuppose G is financed by a proportional wage income tax at rate t,rather than by
19、a lump-sum tax T.The wage income is now w(1-t)(h-l).So the effective wage is w(1-t).The consumer optimizes by setting MRS l,C=w(1-t),while the firm still sets MPN =w.Thus,in equilibrium,MRS l,C 0.AEffects of a Change in GUsing Cramers rule,we getConsumption and leisure are normal goods U22-zF2U12 0
20、and-U12+zF2U11 0.Also,F22 0.Thus,Since w=zF2(K,h-l),we haveSince Y=C+G,we have Conclusion:G C,l,w ,and Y.Business cycle facts(Ch3):employment procyclical,consumption&real wage contercyclical.Thus,government spending is not the primary cause of business cycles.Effects of a Change in TFPz production f
21、unction shifts up.Not only more Y can be produced given N,but the MPN,i.e.the slope of the production function also increases for each N.In the second figure,we see that the new PPF is AD which is steeper than the original one(AB).The new Pareto optimum is at H where C and Y.Graphical IllustrationsP
22、PF1 corresponds to z1,while PPF2 corresponds to z2.Construct a PPF3 so that it is just tangent to the initial indifference curve I1.Substitution effect:movement from A to D(C and l ).Income effect:movement from D to B,a parallel shift in PPF(C and l ).Graphical IllustrationsNote:real wage must incre
23、ase even though the effect on labor supply is unknown.Reasons:From A to D,MRS l,C (since moving up an indifference curve).From D to B,l N w Finally,the consumer is better off as z,since a higher indifference curve is reached.Effects of a Change in TFP:The Math.Using Cramers rule,Consumption is norma
24、l good U22-zF2U12 0.Also,F22 0,and U1 0.Thus dC/dz 0.However,we cannot the effect of z on leisure is ambiguous due to the presence of opposing income and substitution effects.Model predicts:technological advances leads to increased output,increased consumption,a higher wage rate,and ambiguous effect
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