A consumer lives three periods, called the learning period, the working period,

Question

                    A consumer lives three periods, called the learning period, the working period, and the retirement period. Her                     income is 200 during the learning period, 800 during the working period, and 200 again during the retirement period. The consumer's initial assets are 300. The                     real interest rate is zero. The consumer desires perfectly smooth consumption over her lifetime                 

                    
                    a. What are consumption and saving in each period, assuming no borrowing constraints? What happens if the consumer faces a borrowing constraint that prevents                     her from borrowing?
                    b. Assume that the consumer's initial wealth is zero instead of 300. Repeat part (a). Does being borrowing-constrained mean that consumption is lower in all                     three periods of the consumer's life than it would be if no borrowing constraints applied?                 

Explanation / Answer

a) average consumption = ( 300 + 200 + 800 + 200 ) / 3 = 500

so, consumption is 500 in each perio with savings of -300, 300 and -300 during the three phases

if he faces borrowing constraint, he has assets of 300 to support the initial -300 savings, so he anyways does need to borrow and will have the same lifestyle

b)

If the initial wealth is 0 and without borrowing constraints, the average spending is ( 200 + 800 + 200 ) / 3 = 400

Now with borrowing constraint, in the first phase he has to borrow 400 - 200 = 200 which he cant an hence has to stick with an expenditure of just 200 and has to settle with a lower consumption in the first perio   

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