Principles of Finance Lecture 2 PDF

Introduction Consumption and Investment Decisions Principles of Finance Lecture 2: Capital markets, Consumption, and Investment (CWS ch. 1) Rikke Sejer Nielsen...

Introduction Consumption and Investment Decisions Principles of Finance Lecture 2: Capital markets, Consumption, and Investment (CWS ch. 1) Rikke Sejer Nielsen 1 / 25  Introduction Consumption and Investment Decisions Consumption/Investment choice Consumption brings individuals satisfaction/utility Investments (foregone current consumption) used to increase future consumption possibilities by increasing wealth. ⇒ Consumption/Investment Decision: Consume now or invest to consume in the future An individual’s life-time expected utility is gained from expected life-time consumption. ⇒ Optimal consumption/investment decision maximizes expected utility of consumption over a life time. All economic decisions relates to consumption 3 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Consumption and Investment without Capital Markets Simple economy One period model, today (t=0) and future (t=1) One good No uncertainty No transaction costs or taxes Income at time t, yt Consumption at time t, Ct Productive investment opportunities exists ▶ Investing one unit increases to more than one unit of future consumption ▶ Investments are independent of each other and perfectly divisible ▶ Income from production investments at time t, Pt 6 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Consumption choice Note, we assume: U ′ (C) > 0 U ′′ (C) < 0 7 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Consumption choice ⇒ Dashed lines are the indifference curves. 8 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Indifference curves ⇒ Indifference curves are preference functions illustrating how individuals will choose among consumption bundles over time. 9 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Indifference curves Marginal rate of substitution (MRS) ∂C1 MRS = = −(1 + ri ), ∂C0 U=constant where ri is the individual’s subjective rate of time preference. 10 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Productive opportunities ⇒ Diminishing marginal returns to investment ⇒ Individual invest in productive opportunities with rates of return ≥ ri ⇒ Marginal rate of return on the last investment = ri 11 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Productive opportunities The schedule of productive investment opportunities in consumption argument plane (On the board) The marginal rate of transformation (MRT) ⇒ The rate at which a dollar of consumption foregone today is transformed by productive investment into a dollar of future consumption at t = 1. 12 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Optimal consumption/investment choice with productive opp. ⇒ Optimal consumption/investment choice for utility-maximizing individual: Point B, where MRS = MRT 13 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Exercise - Optimal consumption/investment choice across individuals All individuals have the same endowment (y0 , y1 ) and the same investment opportunity set. Will all individuals make the same consumption/investment choice in this simple market i.e. without existence of capital markets? 14 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Capital Markets Introduce a capital markets Borrow or lend unlimited amounts at a positive market-determined rate of interest, r > 0 Transfer of funds between lenders and borrowers facilitated by financial markets. ⇒ allow individuals to exchange consumption bundles over time. Capital market is assumed to be perfect and complete. 16 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Capital Markets Borrowing and lending, X X1 = (1 + r )X0 Wealth, W W0 = y0 + (1 + r )−1 y1 W1 = y0 (1 + r ) + y1 = W0 (1 + r ) → W1 = W0 (1 + r ) referred to as Capital Market Line. 17 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Consumption choice with capital markets and without productive opp. ⇒ Optimal consumption choice for utility-maximizing individual: Point B, where MRS = −(1 + r ) 18 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Consumption/Investment choice with capital markets and productive opp. ⇒ Optimal consumption/investment choice for utility-maximizing individual: Point C, where MRS = −(1 + r ) = MRT 19 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Consumption/Investment choice with capital markets and productive opp. The decision process for optimal consumption/investment choice: 1 choose optimal production decision (Invest until the marginal rate of return on investment equals the objective market rate), 2 choose the optimal consumption pattern (borrow or lend until your subjective time preference equals the market rate of return). Known as the Fisher separation theorem: 20 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Consumption/Investment choice with capital markets and productive opp. Fisher separation theorem: Given perfect and complete capital markets, the production decision is governed solely by an objective market criterion (represented by maximizing attained wealth) without regard to individuals’ subjective preferences that enter into their consumption decisions. 21 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Exercise - Optimal consumption/investment choice across individuals The capital markets are perfect and complete. All individuals have the same endowment (y0 , y1 ) and the same investment opportunity set. However, they all have different time-preferences for consumption (different indifference curves). Will two individuals make (a) the same production decision, and (b) the same consumption decision? 22 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Importance of capital markets Capital markets efficiently transfer funds between individuals ▶ Individuals lend out funds if few productive opportunities and great wealth. ▶ Individuals borrow funds if many productive opportunities and insufficient wealth. Both lenders and borrowers are better off ▶ Higher utility (fig 7) ▶ Higher wealth (fig 8) if productive opportunities exist too 23 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets Transaction costs In case of transaction costs (capital market imperfection) ⇒ borrowing rate > lending rate. ⇒ Fisher separation theorem does not hold! 24 / 25  Introduction Consumption and Investment Decisions without Capital Markets with Capital Markets References CWS, ch. 1 25 / 25