Question
In: Economics
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
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
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Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + βu(Ct+1) that satisfies...
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βu(Ct+1) that satisfies all the standard assumptions listed in the
book. The period t and t + 1 budget constraints are Ct + St = Yt
Ct+1 + St+1 = Yt+1 + (1 + r)St
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U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5 As a mathematical function, does U have a maximum...
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As a mathematical function, does U have a maximum or minimum
value? What values of Ci correspond to the minimum value of U? What
values of Ci correspond to the maximum value of U? Do these values
of Ci make sense from an economic standpoint?
Now let us connect the idea of economic utility to actual dollar
values. To keep the values more manageable, we will use household
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As a mathematical function, does U have a maximum or minimum
value? What values of Ci correspond to the minimum value of U? What
values of Ci correspond to the maximum value of U? Do these values
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How do I calculate these?
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constraint. 3. Set up the consumer’s optimization problem using the
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