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Economic Modelling

Economic Modelling. Lecture 5 Optimal Investment (Micro-foundation). Profit Maximisation Problem of Firms Marginal Product of Capital = User Cost of Capital. y=f(k). y. Max. Subject to:. k. Investor Compare user cost of capital with its productivity. MPK=. k*.

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Economic Modelling

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  1. Economic Modelling Lecture 5 Optimal Investment (Micro-foundation)

  2. Profit Maximisation Problem of Firms Marginal Product of Capital = User Cost of Capital y=f(k) y Max Subject to: k Investor Compare user cost of capital with its productivity MPK= k*

  3. Investment Decision Analysis(See Problem 16.3 in Blanchard) Breaks even point: The value of this investment project: Cost of the Project (K): Earning = 18000 100,000

  4. Analysis of Earnings (R) and Cost (C) from an Investment Project K = 100000; d = 0.08; R (Earning) =18000 C =(r+d)*K 23,000 C > R Cost And Earning Break Even 18,000 Earning (R) C < R 13,000 0.1 0.15 r 0.05

  5. Low interest rate induces producers to substitute out labour by capital o Producer’s like to maximise profit given factor prices, r and w. They use more capital relative to labour if wage rate is higher.

  6. Marginal Productivity Theory of Investment -calculations Output depends on capital stock: Capital stock depends on investment: Investment depends on expected profits: Expected profits depends on productivity of capital: Producers invest more until the marginal product of capital equals the user cost of capital:

  7. Derivation of the Marginal Productivity = User Cost of Capital Condition Producer’s Problem: Optimality Condition: Implication: Assumptions:

  8. Role of Investment Tax Credit in Promoting Investment Why Manufacturers Lobby for a Tax Credit? MPK MPK = 0 K1 K2 K

  9. Optimal Capital Stock for the Car Company The user cost of capital : = 6% +3%-3% =6% Let Marginal product of capital: Optimal Investment condition: = 6.25 million

  10. Role of Financial Market in Optimal Saving and Investment Saving r=i- Investment S*, I* 0 Saving and Investment

  11. Elasticity of Substitution is 1 in Cobb-Douglas Function (Factors are paid according to their marginal productivity)  is the elasticity of substitution between capital and labour.

  12. References • Blanchard (4,5,16) • Bank of England (2001) Financial Stability Review, www. Bankofengland.co.uk. • Cass, David, (1965) Optimum Growth in Aggregative Model of Capital Accumulation, Review of Economic Studies, 32:233-240. • Lucas, Robert E. (1993) The Determinants of Direct Foreign Investment, World Development, March 21:3, 391-406. • Modiogliani Franco, and Miller, Merton H. (1958) The Cost of Capital, Corporation Finance and the Theory of Investment, AER, vol. XLVII, June. • Levine, Ross and Sara Zervos (1998) “Stock markets, banks and economic Growth” American Economic Review, 88, 537-58. • Ramsey, F.P. (1928) “A Mathematical Theory of Saving,” Economic Journal 38, 543-559. • Romer, Paul "Capital Accumulation in the Theory of Long Run Growth" in Barro R. J. (1989) ed. Modern Business Cycle Theory, Harvard University Press.

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