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

Expert Solution


Related Solutions

please show how to solve Harvey Habit has a utility function U(c1, c2) = min{c1, c2},...
please show how to solve Harvey Habit has a utility function U(c1, c2) = min{c1, c2}, where c1 and c2 are his consumption in periods 1 and 2 respectively. Harvey earns $189 in period 1 and he will earn $63 in period 2. Harvey can borrow or lend at an interest rate of 10%. There is no inflation. a. Harvey will save $60. b. Harvey will borrow $60. c. Harvey will neither borrow nor lend. d. Harvey will save $124....
A person's utility function is U = C1/2 . C is the amount of consumption they...
A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. What is their expected utility? b. Calculate the actuarially fair insurance premium. c. What would their expected utility be if they purchased the actuarially fair insurance premium?
8. Kenny’s intertemporal utility function is U(c1, c2) = 10c1 + 8c1, with time periods 1...
8. Kenny’s intertemporal utility function is U(c1, c2) = 10c1 + 8c1, with time periods 1 and 2 representing consumption today and one year from today, respectively. He earns $100 today and $122 one year from today, and his annual rate of interest for saving and borrowing is 22%. There is no inflation. What values of consumption in each time period are optimal?
The consumer’s utility function is U(a,b) = ab2, where a denotes the quantity of good A...
The consumer’s utility function is U(a,b) = ab2, where a denotes the quantity of good A that the consumer consumes and b denotes the quantity of good B that the consumer consumes. The price per unit of good A is 4 Euros and the price per unit of good B is 8 Euros. Consumer’s income is 120 Euros. a) Find the marginal utility of good A and the marginal utility of good B b) Find the optimal quantity of good...
Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + βu(Ct+1) that satisfies...
Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + 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. Now suppose Ctis taxed at rate τ so consumers pay 1 + τ for one unit of period t consumption. (a) What is the optimal value of St+1? Impose this optimal value...
Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + βu(Ct+1) that satisfies...
Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + 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 (a) What is the optimal value of St+1? Impose this optimal value and derive the lifetime budget constraint. (b) Derive the Euler equation. Explain the economic intuition of the equation
U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5 As a mathematical function, does U have a maximum...
U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5 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 income rather than the entire...
U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5 As a mathematical function, does U have a maximum...
U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5 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 income rather than the entire...
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40...
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? b) What is the marginal utility of good Y (MUy) for the consumer? How do I calculate these?
: Suppose that the representative consumer’s preferences over current consumption (C) and future consumption (C 0...
: Suppose that the representative consumer’s preferences over current consumption (C) and future consumption (C 0 ) are given by the following utility function U(C, C0 ) = CC0β The market real interest rate is denoted by r and β > 0. 1. Write down the consumers’ budget constraint for the current and future period. 2. Using the equations in part (1), obtain the inter-temporal budget constraint. 3. Set up the consumer’s optimization problem using the Lagrangian approach. Next, derive...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT