1. (100 points) Consider a utility function given by u(ct)=ln(ct)+ln(.pdf

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1. (100 points) Consider a utility function given by u(ct)=ln(ct)+ln(ct+1) where =1+1 and the constraints are given by tt=ct+styt+1+(1+r)st=ct+1 (a) (10 points) Combine the two constraints by eliminating st. (b) (10 points) Solve the constraint for ct+1 (c) (10 points) Plug the constraint into at+1 in the utility function. (d) (20 points) Differentiate the utility function with respect to c. (e) (20 points) Derive the Euler Equation. (f) (20 points) What is the intuitive interpretation of the Euler Equation? (g) (10 points) Suppose =0.05 and the real interest rate is 3%. Which is larger; ac++1 ? Why?.

1. (100 points) Consider a utility function given by u(ct)=ln(ct)+ln(ct+1) where =1+1 and the
constraints are given by tt=ct+styt+1+(1+r)st=ct+1 (a) (10 points) Combine the two constraints
by eliminating st. (b) (10 points) Solve the constraint for ct+1 (c) (10 points) Plug the constraint
into at+1 in the utility function.
(d) (20 points) Differentiate the utility function with respect to c. (e) (20 points) Derive the Euler
Equation. (f) (20 points) What is the intuitive interpretation of the Euler Equation? (g) (10
points) Suppose =0.05 and the real interest rate is 3%. Which is larger; ac++1 ? Why?

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1. (100 points) Consider a utility function given by u(ct)=ln(ct)+ln(.pdf

1. 1. (100 points) Consider a utility function given by u(ct)=ln(ct)+ln(ct+1) where =1+1 and the constraints are given by tt=ct+styt+1+(1+r)st=ct+1 (a) (10 points) Combine the two constraints by eliminating st. (b) (10 points) Solve the constraint for ct+1 (c) (10 points) Plug the constraint into at+1 in the utility function. (d) (20 points) Differentiate the utility function with respect to c. (e) (20 points) Derive the Euler Equation. (f) (20 points) What is the intuitive interpretation of the Euler Equation? (g) (10 points) Suppose =0.05 and the real interest rate is 3%. Which is larger; ac++1 ? Why?