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# 2010_RL3 - EC 210 Revision Lectures Milan Lisicky...

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EC 210 Revision Lectures Milan Lisicky [email protected] May 4, 2010 1/29

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1 Consumption two period model 2 Investment two period model tobin’s q 3 unemployment efficiency wage model search model 4 financial markets: yields 5 diamond-dybvig: TK Maxx example 6 dynamic model 2/29
Two Period Utility Maximization Problem motivation a fundamental feature of the dynamic macro model what are we after: condition that describes optimal behaviour takes the form of MRS C , C 0 solution: slope of IC = slope of BC slope of IC: MRS C , C 0 BC: C + C 0 1+ r = we or C 0 = (1 + r ) we - ( 1 + r ) C optimal [ C , C 0 ]: MRS C , C 0 = 1 + r such that C + C 0 1+ r = we 3/29

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mathematical appendix so far, we’ve defined MRS C , C 0 rather informally: an internal value of C in terms of C 0 a slope of the IC Δ C 0 Δ C so that we stay on the same IC Deriving MRS C 1 , C 2 = u 0 ( C 1 ) β u 0 ( C 2 ) in the 2-period model: max u ( C 1 ) + β u ( C 2 ) s . t . C 1 + C 2 1+ r = we max u ( C 1 ) + β u [(1 + r ) ( we - C 1 )] FOC: u 0 ( C ) + β u 0 ( C 2 )(1 + r )( - 1) = 0 rearrange: u 0 ( C 1 ) = β u 0 ( C 2 )(1 + r ) rearrange: u 0 ( C 1 ) β u 0 ( C 2 ) = MRS C 1 , C 2 = 1 + r 4/29
1 Consumption two period model 2 Investment two period model tobin’s q 3 unemployment efficiency wage model search model 4 financial markets: yields 5 diamond-dybvig: TK Maxx example 6 dynamic model 5/29

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Two-period Maximization Problem of Firms motivation firms choose labour demand and investment to max present discounted value of dividends V = π + π 0 1+ r = Y - wN - I + Y 0 - w 0 N 0 +(1 - d ) K 0 1+ r subject to K 0 = (1 - d ) K + I derivation substitute for investment: max V = Y - wN - [ K 0 - (1 - d ) K ] + Y 0 - w 0 N 0 +(1 - d ) K 0 1+ r FOC [ K 0 ]: - 1 + Y 0 1 ( K 0 , N 0 )+(1 - d ) 1+ r = 0 rearrange: MP 0 K = r + d = user cost of capital 6/29
relationship to stock market: Tobin’s q MP 0 K is hard to measure, can we link it to stock prices? YES investment pays off if the return to it (i.e. whatever owners of capital get) is bigger than what we could get by selling the purchased equipment value of investment: π 0 1+ r = Y 0 - w 0 N 0 +(1 - d ) K 0 1+ r use Y = MP N N + MP K K = w N + MP K K π 0 1+ r = MP 0 K K 0 +(1 - d ) K 0 1+ r selling price of capital including new investment: K 0 define q as the value of firm (installed capital) per unit of capital q = MP 0 K K 0 +(1 - d ) K 0 (1+ r ) K 0 = MP 0 K +1 - d (1+ r ) measure it as the stock market value per unit of capital invest if q > 1, which is equivalent to MP 0 K > r + d 7/29

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1 Consumption two period model 2 Investment two period model tobin’s q 3 unemployment efficiency wage model search model 4 financial markets: yields 5 diamond-dybvig: TK Maxx example 6 dynamic model 8/29
Efficiency Wage Model of Unemployment

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