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. 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 ?