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Review Session 8 Diamond model

Review Session 8 Diamond model. Catalina Martinez c atalina.martinez@graduateinstitute.ch Office hours: Tuesdays 6-8pm Rigot 27 Economics and Development MDev 2012-2013 THE GRADUATE INSTITUTE | GENEVA. Today’s RS. Diamond model Focus on intuitions Solve Quiz. Motivation.

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Review Session 8 Diamond model

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  1. Review Session 8Diamond model Catalina Martinez catalina.martinez@graduateinstitute.ch Office hours: Tuesdays 6-8pm Rigot 27 Economics and Development MDev 2012-2013 THE GRADUATE INSTITUTE | GENEVA

  2. Today’s RS • Diamond model • Focus on intuitions • Solve Quiz

  3. Motivation • Explain the determinants of the savings rate • Relative importance of the present with respect to the future • Difference between different agents in the economy • Role of the government • It builds a link between the optimizing behavior of consumers (households) and firms in a perfectly competitive market to understand the determinants of the savings rate. • It compares that market solution with respect the social optimum that maximizes social welfare.

  4. Building the model: The consumer • To capture the importance of the future, the Diamond assumes that agents live two periods: • t: when they are young, in which they can work, save and consume • t+1: when they are old, in which they can consume only what they saved

  5. Building the model: The consumer • The consumer determines its optimal savings rate depending on how much he values two goods (as we have always seen): present consumption and future consumption • Discount factor Consumption when old U0 Consumption when young (Today)

  6. Building the model: The firm • The consumers savings are invested as capital • As we had before (Solow): Y=F(K,AL) • K in time t is the result of the savings supplied by the old • L in time t represents the workforce supplied by the young Y/AL=F(K/AL,1) y=f(k) • A grows at exogenous rate g as before (Solow) • L grows at exogenous rate n as before (Solow)

  7. Building the model: The firm s.t Quantity of k A Q=constant Quantity of l

  8. Building the model: The firm • Since the markets are perfect and competitive, each factor (labor and capital) is paid its marginal productivity (wage and interest rate). • The marginal productivity of capital is • The marginal productivity of labor is

  9. Building the model: The firm • Since there exists perfect competition, the firms earn zero profits • The idea is that if a firm is earning profits then another firm will be attracted to enter the market • Since there are no barriers to enter, all these firms will enter • Quantity supplied will increase, prices will diminish and profits will decrease until they become zero • If profits become negative, firms will start to exit the market and the reverse logic will apply Profits=Output-Costs=0 Output=Costs

  10. Building the model: The firm • Therefore, the production of the firm is equal to its costs, and it is distributed between workers and capital according to their marginal productivity Y=rK+wAL Y/L=rK/L+wAL/L y=rk+wA Aw=y-rk=f(k)-f’(k)k

  11. The consumer and the firm • In the first period the young are paid • And their savings (which are invested as capital in the firms) in the second period are • Therefore, how much agents save today depends on the expected return to capital tomorrow:

  12. The consumer and the firm • We assume that there is no depreciation • The young consume and save: ct=(1-st)Awt stAwt= s(rt+1)Awt • The capital level tomorrow is equal to the savings of all individuals in the economy today Kt+1 = Lts(rt+1)Awt

  13. The dynamics of capital

  14. The dynamics of capital

  15. When the production function is defined as a Cobb Douglas, it can be shown that WE WILL NOT SHOW HOW TO DERIVE THIS…..WE WILL FOCUS ON THE INTUITION

  16. THE QUESTION IS IF THIS LEVEL OF CAPITAL IS THE SOCIAL OPTIMUM • Disregarding g • The aggregate resource constraint of the economy is: • Yt+ Kt= Cyoung + Syoung+ Cold • f(Kt,Lt)+ Kt= Kt+1 + C1,tLt + C2,tLt-1 In pc terms • f(kt) + kt= (1+n)kt+1 + c1,t + c2,t/(1+n) • In the SS kt=kt+1=k*, c1,t=c1 and c2,t=c2 • f(k) - nk= c1+ c2/(1+n) • This implies that in the level of capital that maximizes consumption kGR(golden rule): • f’(kGR)=n • Again skip derivation and focus on intuition: The marginal productivity of capital offsets exactly the growth of the population

  17. Intuition • There is nothing that guarantees that k*=kGR • There is no guarantee that the solution of the market is the best solution from a welfare point of view • If individuals want to consume more in old age, the only option for them is to hold capital even if the rate of return is low • This means that even if the productivity of capital is low, the economy will continue accumulating it. • Missing market…there is no other option for the old than to save…inefficient

  18. Intuition • The planner can help to solve this by taking consumption from the young and giving it to the old • Since there are 1+n young people for each old person, taking one unit of consumption from the young increases the consumption of the old by 1+n units • If the social planner continues doing this the young will also benefit when they become old • Pensions…

  19. Intuition • Dynamic inefficiency arises due to the heterogeneity of the agents in the economy • Individuals who live at time t face prices (r, interest rate) determined by the capital stock with which they are working • This capital was accumulated by the previous generation • Since the current old did not have any other source of income than their savings (current capital) they might tend to over save (beyond capital marginal productivity) • This makes the interest rate go further down. • Therefore the current generation needs to save more than optimally for when they become old. • If alternative ways of providing consumption to the old were introduced, the over-accumulation could be ameliorated

  20. Quiz

  21. Question 1 • What is the main difference between the Solow model and the Diamond model? • The Solow model takes the savings rate as exogenous • The Diamond model endogenizes the savings rate by introducing the overlapping generations concept

  22. Question 2 • What are the determinants of the savings rate according to the model? • How the agents value the present with respect to the future • The interest rate, which is the marginal productivity of capital • It will be low if capital is over-accumulated • It will be high if capital is scarce

  23. Question 3 • What is dynamic inefficiency? Why does it take place? • It is the tendency of the economy to over-accumulate capital beyond the socially optimal level • It takes place because the old do not have any market mechanisms to consume rather than what they had saved when they were young. • Therefore they tend to save a lot even if the return to capital is low, and therefore the marginal productivity of the capital that they save is low. This leads to an inefficiency. • The market solution is not optimal because there are missing markets and agents are heterogeneous

  24. Question 4 • What is the role of the government in the Diamond Model? Why is it important? Give some examples of how this model can be applied in the context of developing countries. • Since the market cannot lead to an efficient outcome, the government can intervene and lead to a Pareto improvement • Social Security: pensions.

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