Consider a two-period model, inhabited by two individuals, Anna and Bob (or as they like to...

Consider a two-period model, inhabited by two individuals, Anna and Bob (or as they like to be called, A, and B). A has the following preferences

uA(c0,A cA1 ) = ln(cA0 ) + 0.9 ln(cA1 ), while B has the following preferences

u B ( c 0 , B c B1 ) = l n ( c B0 ) + 0 . 8 l n ( c B1 ) .

Consumer A receives an income Y0A = 100 in period 0 and Y1A = 150 in period 1. On the other side, Consumer B receives an income Y0B = 125 in period 0 and Y1B = 100 in period 1. Assume the interest rate is r. The government wants to spend G0 = 50 in period 0 and G1 = 75 in period 1. These spendings are financed through lump-sum taxes. It is assumed that the government collects the necessary tax to finance its spending in each period and the tax burden is equally supported by the consumers in each period.

1. Compute the optimal consumption (c0, c1) for each individual as a function of the interest rate r.

2. Find the equilibrium interest rate that clears the credit market.

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Rahul Sunny answered 1 week ago

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