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Investment in CE Model

Investment in CE Model. Definitions Profit Maximization Competitive Equilibrium. Investment. Incorporating capital goods & investment into CE model is important for study of (i) Business Cycles: Productivity, monetary & fiscal policy shocks.

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Investment in CE Model

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  1. Investment in CE Model Definitions Profit Maximization Competitive Equilibrium

  2. Investment • Incorporating capital goods & investment into CE model is important for study of (i) Business Cycles: Productivity, monetary & fiscal policy shocks. (ii) Long-Term Economic Growth: saving  capital  future productivity and growth. • Reading: Williamson Ch 9

  3. Definitions • Kt = capital stock (at beginning of time t) • d = capital depreciation rate • Net Investment = (Kt+1 – Kt) • Gross Investment (It) = net investment + depreciation investment = (Kt+1 – Kt) + dKt = Kt+1 – (1 – d)Kt

  4. Figure 4.5Gross and net investment, 1929–2002

  5. Profit Maximization • Production Function: • Timing in each period t for Firms: • Firms begin with capital stock Kt. • Hires labor Nt and produces yt = f(Kt,Nt) (iii) Pays labor costs wtNt and buys capital It. • Ends period with Kt+1.

  6. Capital purchased today is not productive until tomorrow (“time-to-build”) • Two Period Model of Investment: Period 1: Period 2: • Households lifetime BC:

  7. Firm’s goal is to maximize PDV profits paid to shareholders: where K1 is given and K3 = 0. • First Order Conditions N1 and N2: for t = 1,2 K2: “Expected future MPK = user’s cost”

  8. There will be a negative relationship between K2 (I1) and r. • The interest rate is the opportunity cost of investment.

  9. Competitive Equilibrium w/ Investment • Households: Given wt and rt, chooses ct and Nst solving • Firms: Given wt and rt, chooses Kt+1 and Ndt solving

  10. Market-Clearing: Determines wt* and Nt*: Goods: Labor:

  11. Productivity Shocks • Temporary Positive Shock Supply  higher ND and N* shifts Ys right. Decreases r* and shifts NS left  increase in w. Demand  Higher w increases c*  Yd shifts right. No change in future MPK  no (direct) effect on I. Overall  Increase in y* and decrease in r* (C and I increases)

  12. There will be persistence: Higher I today  Higher future output. • Future Positive Shock Supply  Current z unchanged  Ys fixed. Demand  Increases c* (from PIH) and increase in I  Yd shifts right. Overall  Increase in y* and increase in r*

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