1. Consumption-Savings. The representative consumer’s utility function is u(c1,c2)=lnc1 + Blnc2 , 0<B<1 in which the...

1. Consumption-Savings. The representative consumer’s utility function is
u(c1,c2)=lnc1 + Blnc2 , 0<B<1
in which the parameter  (the Greek lowercase letter “beta”) is a fixed number between
zero and one.
The consumer begins period 1 with zero net wealth. The period-1 and period-2 budget
constraints, stated in real units, are, respectively, c1+a1=y1 and c2+a2 = y2+(1+r)a1 .
a. Based on the utility function above, construct the sequential Lagrange function.
b. Based on the sequential Lagrange function from part a, obtain the five first-order
conditions.
c. Using the first-order conditions from part b, construct the consumption-savings
optimality condition. Provide algebraic steps as needed for clarity.
d. Based on the consumption-savings optimality condition obtained in part c above,
compute the point elasticity of perod-2 consumption (i.e., of the optimal choice
c2*) with respect to the gross real interest rate (1+r). (Note on terminology: r is
referred to as the net real interest rate, and 1+r is referred to as the gross real interest

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Expert Solution

Rahul Sunny answered 1 year ago

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