Intermediate Microeconomics Intertemporal Choice and Uncertainty Tin Cheuk (Tommy) Leung CUHK

Tin Cheuk (Tommy) Leung (CUHK)

Intermediate Microeconomics

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Intertemporal Choice

Divergence in income and consumption inequality in the last 25 years in the US income inequality: ↑ 20% consumption inequality: ↑ 5%

Why consumption smoothing? Important to analyze intertemporal choice of consumption

Tin Cheuk (Tommy) Leung (CUHK)

Intermediate Microeconomics

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From Krueger and Perri (2005)

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Intermediate Microeconomics

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Present Value

If you come up with a great idea–iPhone that can give you net profit of $20 million for the next 10 years, but but you need to pay $180 million R&D expenses to develop it. Interest rate is 5%. Would you develop iPhone?

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Intermediate Microeconomics

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Intertemporal Choice

Two period: t = 1, 2 One good consumed at both period: xt Income in both period: yt Parameter for impatience: β Concave utility: U(x1 , x2 ) = ln(x1 ) + β ln(x2 ) Bond: b Interest rate: r

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Intermediate Microeconomics

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Demand for Goods and Bond

max U(x1 , x2 )

x1 ,x2 ,b

s.t. x1 + b = y1 x2 = (1 + r )b + y2

How do agents choose to consume and save? Would income be more volatile than consumption? Why?

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Intermediate Microeconomics

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Tin Cheuk (Tommy) Leung (CUHK)

Intermediate Microeconomics

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Decision under Uncertainty

Income uncertain over time Consumption smoothing still possible under income uncertainty? Challenge: bring in uncertainty in demand analysis

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Intermediate Microeconomics

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Decision under Uncertainty

Setting the same as before, but β = 1 Income uncertainty at t = 2 two possible events k = 1, 2 with probabilities πk

Expected Utility: U(x1 , x2,k ) = ln(x1 ) + β

P

k

πk ln(x2,k )

still concave independence assumption

State-contingent bond for insurance: bk with price qk Demand for consumption and saving?

Tin Cheuk (Tommy) Leung (CUHK)

Intermediate Microeconomics

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Tin Cheuk (Tommy) Leung (CUHK)

Intermediate Microeconomics

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Equilibrium

Price/interest rate exogenous in previous analysis Equilibrium: find a market clearing price Market clearing: demand = supply

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Intermediate Microeconomics

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Equilibrium without Uncertainty Suppose Two agents: i = 1, 2 P Aggregate income constant over time: Y = i yti , t = 1, 2

Equilibrium: Bond r∗P such that P i∗price ∗ i x (r ) = i yt = Y , t = 1, 2 Pi ti∗ ∗ i b (r ) = 0

What is the equilibrium interest rate? Consumption smoothing under this price? Equilibrium under uncertainty?

Tin Cheuk (Tommy) Leung (CUHK)

Intermediate Microeconomics

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Equilibrium under Uncertainty Bond prices qk∗ : Consumer i solves max U(x1 , x2,k ) x,b

s.t. x1i +

X

qk∗ bki = y1i

k i x2,k

i = y2,k + bki ∀k

Market clears X

x1i∗ =

X i

i

X

y1i∗ = Y

i∗ x2,k =

i

X

i∗ y2,k = Y ∀k

i

X

bki∗ = 0 ∀k

i Tin Cheuk (Tommy) Leung (CUHK)

Intermediate Microeconomics

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