Question 1 - 100%

1.1 Solve the following integral:                                              (10 points)

.0 10 3 e t dt

1.2  One-good model. Consider the utility function

1 − e-yc  

γ

A consumer solves

max u(c)

c

subject to the constraint

y = cp

Use the following values:

y = 35, 000       γ = 2.7       p = 12

i. As a preliminary step, write down the formula for u\ (c).       (20 points)

ii. Write down the Lagrangian.                                      (20 points)

iii. Solve for optimal consumption c as a function of the Lagrange multiplier. [HINT: Start by writing down the first order condition for c. Then take the logarithm.]                                (25 points)

iv. Solve for the Lagrange multiplier. [HINT: Substitute the answer from the previous question into the budget constraint.] (25 points)

Question 2 - 100%

Deterministic optimal growth model. Let

u(c) =

1 − e-yc

γ

f (k) =

1 − e-ak

α

A representative individual solves

m xc(a) .0 o e-ptu(ct )dt

subject to

k˙t  = f (kt ) − ct           k0  = k*

(a) Write the appropriate Hamiltonian                                   (10 points)

(b) State the solution for consumption as a function of the costate vari-