How to RBC

Question 1

How to RBC (Ramsey model with technolegy)

Answer 1

1. Find the marginal products of labour and capital. Define the households optimality solution (Lagrangian, FOC wrt. c, h og en til, derive the Euler, comment).
2. Interpretation of an increase in phi on current consumption, when c_t+1 is constant. Phi increases -> 1/c_t increases -> c_t decreases.
   - So if next period consumption is constant, then a tightening of financial constraint (phi increases) will decrease consumption.
3. Characterize the labor demand and supply schedules and derive equilibrium wages and labour hours.

Labour supply schedule:
- Isolate h.
- Insert y=c and y=zh^alpha.

Labor demand schedule:
- which is just the marginal products of labour.

To find equilibrium wages and labour hours
- Combine the two schedules, where you first isolate h, getting the equilibrium labor hours.
- then plug it into the labor demand schedule and isolate for w, getting the equilibrium wages.

4. comment on why labour hours remain constant when sigma = 1.
   - If sigma = 1, then h_t = 0 and w_t = 0, meaning they are constant, because the substitution and income effect cancels each other out.
5. What happens to equilibrium labor hours as v -> infinity. Explain:
   - When v -> infinity equilibrium labor hours goes to infinity, meaning that the households equilibrium quantity is using all of its time on working. Technically because the elasticity of labor supply to the wage rate decreases, thus households allocate inelastically all of their time endowment to working.

Question 2

Important mathematics

Answer 2

Potensregneregler:

X^b/X^a =X^(a−b)

X^a∗X^b=X^(a+b)

Question 3

How to RBC (Ramsey model with technolegy) with equilibrium dividends and assumption of negative dividends.

Answer 3

1. Decide the equilibrium dividends:
   - Substitute the expression of y_t in
   - Insert the equilibrium wages and labor hours.
2. Comment on the assumption that they are negative.
   - Look at the defintion of the values in the assignment, thus it is possible to say that because alpha e[0,1], then the dividends was positive, so the assumption was false.