# @K.R.Bhattarai, Business School, University of Hull, UK 1 Economic Modelling Lecture 5 Optimal Investment (Micro-foundation)

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@K.R.Bhattarai, Business School, University of Hull, UK 1 Economic Modelling Lecture 5 Optimal Investment (Micro-foundation)

@K.R.Bhattarai, Business School, University of Hull, UK 2 k y y=f(k) k* MPK= Profit Maximisation Problem of Firms Marginal Product of Capital = User Cost of Capital Max Subject to: Investor Compare user cost of capital with its productivity

@K.R.Bhattarai, Business School, University of Hull, UK 3 Investment Decision Analysis (See Problem 16.3 in Blanchard) Breaks even point: The value of this investment project: Cost of the Project (K): 100,000 Capital100000 r0.050.10.15 d0.08 C=(r+d)*K130001800023000 R (Earnings)18000 PV138461.510000078260.87 Earning = 18000

@K.R.Bhattarai, Business School, University of Hull, UK 4 C =(r+d)*K 0.05 0.10.15r Earning (R)18,000 13,000 23,000 Break Even Analysis of Earnings (R) and Cost (C) from an Investment Project Cost And Earning C < R C > R K = 100000; d = 0.08; R (Earning) =18000

@K.R.Bhattarai, Business School, University of Hull, UK 5 Low interest rate induces producers to substitute out labour by capital o Producers like to maximise profit given factor prices, r and w. They use more capital relative to labour if wage rate is higher.

@K.R.Bhattarai, Business School, University of Hull, UK 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:

@K.R.Bhattarai, Business School, University of Hull, UK 7 Derivation of the Marginal Productivity = User Cost of Capital Condition Producers Problem: Optimality Condition: Implication: Assumptions:

@K.R.Bhattarai, Business School, University of Hull, UK 8 Role of Investment Tax Credit in Promoting Investment Why Manufacturers Lobby for a Tax Credit? MPK = K1K2 0 K MPK

@K.R.Bhattarai, Business School, University of Hull, UK 9 Optimal Capital Stock for the Car Company = 6% +3%-3% =6% The user cost of capital : Let Marginal product of capital: Optimal Investment condition: = 6.25 million

@K.R.Bhattarai, Business School, University of Hull, UK 10 Saving Investment Saving and Investment r=i- S*, I* 0 Role of Financial Market in Optimal Saving and Investment

@K.R.Bhattarai, Business School, University of Hull, UK 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.

@K.R.Bhattarai, Business School, University of Hull, UK 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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