Problem
Consider the one-period following model
Utility function: u(c,m)=ln(c) + 2ln(m) Budget constraint: c + m = y
A. Set up the Lagrangian with a Lagrange multiplier ? .
B. Find the first-order conditions with respect to c and m .
C. Find the expression for money demand. How is money demand affected by changes in consumption?
2) Consider the one-period following model
Utility function: u(c,m) =c^2 +5m^2
Budget constraint: c + m = y
A. Set up the Lagrangian with a Lagrange multiplier ? .
B. Find the first-order conditions with respect to c and m .
C. Find the expression for money demand. How is money demand affected by changes in consumption?
3) Consider the one-period following model
Utility function: 2 1 u(c,m) =ln(c) + 2m^(1/2)
Budget constraint: c + m = y
A. Set up the Lagrangian with a Lagrange multiplier ? .
B. Find the first-order conditions with respect to c and m .
C. Find the expression for money demand. How is money demand affected by changes in consumption?
4) Consider the two-period following model First-period utility function: u(c1,m1)= ln(c1)+2ln(m1)
1 1 1 m1 u c m ? c ?
Second-period utility function: u(c2)=ln(c2)
First-period budget constraint: c1+s1+m1=y1
Second-period budget constraint: c2=y2+m1+(1+r)s1
Discount factor between period 1 and period 2=B. Interest rate= r.
A. Find the lifetime budget constraint.
B. Set up the Lagrangian with a Lagrange multiplier ? .
C. Find the first-order conditions with respect to 1 c , 2 c and m1 .
D. Find the expression for money demand. How is money demand affected by changes in consumption and the interest rate?
E. Find the Euler equation.
F. When will c1=c2 ?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.