# 4 General Equilibrium I Suppose there exist a representative agent . Agent derive utili ty from consumption ( . If agent work for firm , the wage ate…

Suppose there exist a representative agent. Agent derive utility from consumptionC. If agent work for ﬁrm, the wage rate is w; however, working hours L brings disutility. Agent has to pay for consumption and labor income tax τL and consumption tax τC. Agent’s maximization problem can be formalized as follows:

max C,L U(C,L) = logC −Lα whereα > 1 s.t (1 + τc)C = (1−τw)wL + π

• Specify agent’s eﬃciency condition. Explain the intuition behind. A representative ﬁrm sell goods in the competitive market, with technology

Y = AL

All the markets are assumed to be competitive. The goods price P is normalized to be 1. Now we have “government” in the economy. Government need to ﬁnance its ﬁscal policy G (τL, τC are exogenous variables, while G is endogenously determined) through labor income tax τL and consumption tax τC. Speciﬁcally, government’s budget constraint must hold

τLwL + τCC = G

Noted that, after considering government spending. The goods market market clearing conditions becomes

Y = C + G

• Specify ﬁrm’s proﬁt maximization problem.

• Specify ﬁrm’s eﬃciency conditions and the intuition behind.

• Specify market clearing conditions.

• Deﬁne the equilibrium

• Solve the prices {w} and allocations. {L,Y,C}.

• Discuss the eﬀect of each taxes to the equilibrium output and price.

4 General Equilibrium ISuppose there exist a representative agent . Agent derive utility from consumption ( . If agent work for firm , the wageate is in however , working hours I brings disutility . Agent has to pay for consumption and labor income tax In andconsumption tax To . Agent’s maximization problem can be formalized as followsmax U ( C , D )logo Is whened &gt;8 . ( 1 1 TOO( 1 Ton ) LolSpecify agent ‘s efficiency condition . Explain the intuition behindA representative firm sell goods in the competitive market , with technologyYEARAll the markets are assumed to be competitive . The goods price Pis normalized to beNow we have &quot; government &quot; in the economy . Government need to finance its fiscal policy ? ( To To are exogenousariables , while ( is endogenously determined , through labor income tax Ty and consumption tax To . Specifically , govcrument ‘s budget constraint must holdTOOL + TOO = CNoted that , after considering government spending . The goods market markout clearing conditions becomestoSpecify firm’s profit maximization problemSpecify firm’s efficiency conditions and the intuition behindSpecify market clearing conditions .Define the equilibriumSolve the prices (w / and allocations . ( L K , C )Discuss the effect of each taxes to the equilibrium output and price .