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Microeconomics Corso E John Hey

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Part 3 - Applications Chapter 19 – variations. Chapters 20, 21 and 22 – intertemporal choice. Chapters 23, 24 and 25 – choice under risk. Chapter 26 – the labour market.

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Intertemporal Choice Chapter 20 – the budget constraint. Chapter 21 – intertemporal preferences – the Discounted Utility Model. Chapter 22 – intertemporal exchange.

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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…

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When you borrow Rate of interest What you borrow in period 1 You must repay in period 2 10% (r=0.1) 100

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When you borrow Rate of interest What you borrow in period 1 You must repay in period 2 10% (r=0.1) % (r=0.2) 100

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When you borrow Rate of interest What you borrow in period 1 You must repay in period 2 10% (r=0.1) % (r=0.2) r100

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When you borrow Rate of interest What you borrow in period 1 You must repay in period 2 10% (r=0.1) % (r=0.2) r100100(1+r) rm1m1

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When you borrow Rate of interest What you borrow in period 1 You must repay in period 2 10% (r=0.1) % (r=0.2) r100100(1+r) rm1m1 m 1 (1+r) rm2m2

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When you borrow Rate of interest What you borrow in period 1 You must repay in period 2 10% (r=0.1) % (r=0.2) r100100(1+r) rm1m1 m 1 (1+r) rm 2 /(1+r)m2m2

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When you save Rate of interest Saving in period 1 What you get back in period 2 10% (r=0.1) 100

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When you save Rate of interest Saving in period 1 What you get back in period 2 10% (r=0.1) % (r=0.2) 100

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When you save Rate of interest Saving in period 1 What you get back in period 2 10% (r=0.1) % (r=0.2) r100

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When you save Rate of interest Saving in period 1 What you get back in period 2 10% (r=0.1) % (r=0.2) r100100(1+r) rm1m1

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When you save Rate of interest Saving in period 1 What you get back in period 2 10% (r=0.1) % (r=0.2) r100100(1+r) rm1m1 m 1 (1+r) rm2m2

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When you save Rate of interest Saving in period 1 What you get back in period 2 10% (r=0.1) % (r=0.2) r100100(1+r) rm1m1 m 1 (1+r) rm 2 /(1+r)m2m2

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Chapter 20 Intertemporal choice. Two periods: 1 and 2. Notation: m 1 and m 2 : incomes in the two periods. c 1 and c 2 : consumption in the two periods. r: the rate of interest. 10% r = 0.1, 20% r = 0.2. Hence the rate of return = (1+r)

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The Budget Line 1. m 1 > c 1 savings = m 1 - c 1 Becomes (m 1 - c 1 )(1+r) in period 2. Hence c 2 = m 2 + (m 1 - c 1 )(1+r). Or: c 1 (1+r) + c 2 = m 2 + m 1 (1+r). In the space (c 1,c 2 ) a line with slope - (1+r).

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The Budget Line 2. m 1 < c 1 borrowings = c 1 - m 1 Have to repay (c 1 - m 1 )(1+r) in period 2. Hence c 2 = m 2 - (c 1 - m 1 )(1+r). Or: c 1 (1+r) + c 2 = m 2 + m 1 (1+r). In the space (c 1,c 2 ) a line with slope - (1+r).

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The Budget Line 3. maximum consumption in period 2 = m 1 (1+r) + m 2 - this is called the future value of the stream of income. maximum consumption in period 1 = m 1 + m 2 /(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.

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The Budget Line 4. The intercept on the horizontal axis = m 1 + m 2 /(1+r) – the present value of the stream of income.. The intercept on the vertical axis = m 1 (1+r) + m 2 – the future value of the stream of income... The slope = -(1+r)

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Generalisation If the individual receives a stream of income: m 1, m 2, m 3 … m T The present value is The future value is

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An imperfect market (10% and 51%)

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Chapter 20 The rest of Chapter 20 uses general preferences. (So you do not need to study the rest of this Chapter.) In Chapter 21 we use Discounted Utility Model preferences.

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