How to Ramsey

Question 1

How to Ramsey Model with phase diagram

Answer 1

1. Find the marginal products of kapital and labour, which maximizes the firms profit.
   - Take FOC wrt. K and L
2. Write the Lagrangian, where you combine the households utilities and budget constraint
   - take the FOC wrt. c_t and a_t+1
   - Combine the FOCs to get the Euler
   - Substitute in the expression of rental rate of capital and wage rate.
   - commentate on the Euler. Optimal consumption path, where the consumption today is equal to discounted consumption tomorrow…
3. Find the c-locus and k-locus under Steady State.
   - c-locus: Insert the marginal product of kapital in the Euler.
   - k-locus: Take the derivative of the Lagrangian wrt. lambda, which is the budget constraint. Insert the the marginal product of kapital and labour, and remember that a is equal to k, because there is no net borrowing in equilibrium, due to the NPGC.
   - Phase diagram the c-locus is the straight line and the k-locus is the curved line.
4. Shocks
   - beta changes, which mean the discount factor changes and then the patience. If the beta falls, patience falls, because future consumption is discounted harder. Only affects the c-locus, not the genereal level in the economy.
   - tax on capital income (dividends). The genereal level of capital will fall, due to the income tax, which means that there will be a lower interest rate of capital, thus the general level of consumption will fall. The entire economy will fall.
5. We assume that the households have CRA utility with the riskaversion theta (or another sign). The consumption on impact depends on the degree of riskaversion given theta.

Question 2

How to Ramsey Model, special case with dividends. What should you remember, when determining the SS share price. How do you find out how it is affected by the marginal cost of labour.

Answer 2

You should read the assignment to see how the dividend is determined, but normally it is equal to the firms profit function.

To find out how dividends is affected by the marginal cost of labour. Take the FOC wrt. w.

Question 3

How to Ramsey Model, special case with population growth.

Answer 3

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