Question I [30 marks] Consider an economy in which the representative consumer preferences are described byU(C, l) = 2C1/2+ 3l.The total number of hours available to the representative consumer ish=...

Question I [30 marks]

Consider an economy in which the representative consumer preferences are described byU(C, l) = 2C1/2+ 3l.The total number of hours available to the representative consumer ish= 1, and the market real wage isw. The representative firm produces the final consumption good using the technology functionY=N1/2, whereNis the labour. Additionally, assume that there is no government in the economy, that isG= 0.

1. 
   

   Describe the relationship betweenMRSl/C, andMPNat the equilibrium. [05 marks]

   
   


2. 
   

   Solve for the equilibriumN⋆by combining the equilibrium condition stated in Question 1

   
   

   and the income-expenditure identityC+G=Y=N1/2. [15 marks]

   
   

Hint: Use the identityC=N1/2to write bothM RSl/CandM PNas functions

ofNand solve the equation relating both.
3. What are the equilibrium values ofw⋆,Y⋆, andπ⋆. [10 marks]

Question II [35 marks]

Consider an economy in which the representative consumer preferences are described byU(C, l) =1ln(C) +2ln(l).The total number of hours available to the representative consumer ish= 1, and

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the market real wage isw. The representative firm produces the final consumption good using the technology functionY=zNwhereNis the labour, andz= 1. Assume the government sets the level of its spending toG= 0.25 which has to be financed through a proportional taxt.

1. 
   

   Given the linear specification of the production function, what will be the equilibrium wagew⋆. [05 marks]

   
   


2. 
   

   Characterize the competitive equilibrium allocationt⋆,l⋆,N⋆,Y⋆. [10 marks]

   
   


3. 
   

   Characterize the Pareto Optimal Allocation. [10 marks]

   
   


4. 
   

   What can you conclude? [05 marks]

   
   

   1

   
   

Question III [35 marks]

Assume the representative consumer lives in two periods and his preferences can be described byU(c, c′) =√c+β√c′, wherecis the current consumption,c′is next period consumption, andβ= 0.98. Let’s assume that the consumer can borrow or lend at the interest rater= 5%. The consumer receives an incomey= 100 in the current period andy′= 200 in the next period. There is no government in the economy sot=t′= 0.

1. Write down the consumer’s intertemporal budget constraint. [05 marks]
2. Is it optimal for the consumer to consume his full income in the current period? [10 marks] 3. Solve the consumer’s problem by finding the optimal allocationsc⋆andc′⋆. [15 marks]
4. Is the consumer and lender or a borrower? [05 marks]