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Microeconomics 2

Microeconomics 2. John Hey. Intertemporal Choice. Chapter 20 – the budget constraint, intertemporal preferences in general and choice in general Chapter 21 – intertemporal preferences in particular – the Discounted Utility Model Chapter 22 – intertemporal exchange. A question for you.

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Microeconomics 2

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  1. Microeconomics 2 John Hey

  2. Intertemporal Choice • Chapter 20 – the budget constraint, intertemporal preferences in general and choice in general • Chapter 21 –intertemporal preferences in particular – the Discounted Utility Model • Chapter 22 – intertemporal exchange

  3. A question for you • An observation: to reduce consumption in an economy, the government usually raises the interest rate. Why? • If interest rates rise … • … an individual is better or worse off? • … saves more or less? • … spends more or less? • The correct answers?.... • … it depends…

  4. Framework • Intertemporal choice. • Two periods: 1 and 2. • We consider an individual who receives an income in each of the two periods. • Might be happy to consume his or her income in the period in which it is received ... • ... but might prefer to re-distribute it, by saving or borrowing. • That is what these three chapters of the book are about. • (We have already talked about allocation within a period to specific goods and services. Here we are talking about allocation between periods.) • But first some preliminaries about saving and borrowing, rates of interest and rates of return.

  5. When you borrow

  6. When you borrow

  7. When you borrow

  8. When you borrow

  9. When you borrow

  10. When you borrow

  11. When you save

  12. When you save

  13. When you save

  14. When you save

  15. When you save

  16. When you save

  17. Notation and graphical representation • Intertemporal choice. • Two periods: 1 and 2. • m1 and m2: incomes in the two periods. • c1 and c2: consumption in the two periods. • r: the rate of interest (10%, r = 0.1; 20%, r = 0.2) • The rate of return = (1+r) • We will be drawing graphs with c1 and c2 on the axes, and (m1, m2) as the endowment point. • First the budget constraint then the preferences.

  18. The Budget Line 1. • m1 > c1 savings = m1 - c1 • Becomes (m1 - c1)(1+r) in period 2. • Hence c2 = m2 + (m1 - c1)(1+r). • Or: c1(1+r) +c2 = m2 + m1(1+r). • In the space (c1 ,c2) a line with slope -(1+r).

  19. The Budget Line 2. • m1 < c1 borrowings = c1 - m1 • Have to repay (c1 - m1)(1+r) in period 2. • Hence c2 = m2 - (c1 - m1)(1+r). • Or: c1(1+r) +c2 = m2 + m1(1+r). • In the space (c1 ,c2) a line with slope -(1+r).

  20. The Budget Line 3. • maximum consumption in period 2 = m1(1+r) + m2 • – this is called the future value of the stream of income. • maximum consumption in period 1 = m1 + m2/(1+r) • – this is called the present value of the stream of income. • Note: we say that the market discounts the income in period 2 at the rate r.

  21. The Budget Line 4. • The intercept on the horizontal axis = • m1 + m2/(1+r) – the present value of the stream of income.. • The intercept on the vertical axis = • m1(1+r) + m2 – the future value of the stream of income... • The slope = -(1+r)

  22. Generalisation • If the individual receives a stream of income: • m1, m2, m3 … mT • The present value is • The future value is

  23. An imperfect market (10% and 50%)

  24. Chapter 20 • Let us go briefly to the Maple Chapter 20, but note... • ... most of Chapter 20 uses general preferences. (So do not spend too much time on studying the rest of this Chapter.) • But it shows that saving and borrowing depend upon incomes and rate of interest. • In Chapter 21 we use Discounted Utility Model preferences.

  25. Chapter 20 • Goodbye!

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