Econ117_Top-1 - Ec 117 GROWTH THEORY Foster UCSD LECTURE...

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Ec 117 – GROWTH THEORY LECTURE NOTES Foster, UCSD 1-Jul-09 TOPIC 1 – MATHEMATICS OF GROWTH THEORY A. Elements of Growth Models 1. Focus: a) Growth theory uses results from both microeconomics and macroeconomics to explore the causes and patterns of growth in economies. b) For example, what rate of investment (capital formation) will allow an economy to achieve a steady, adequate and sustainable level of per capita GDP (Q/N) if the population is growing at 2% per year? And what rate of current consumption is achievable if current saving must rise in order to increase the rate of investment to a higher desired level? 2. Growth and Change over Time: a) Discrete growth. 1) Discrete time-dependent variables can only be observed at the beginning or end of discrete time intervals. For example, quarterly GDP is not even determined until the end of the quarter. 2) Let X t = value of variable X at the end of time period t , for t = 1,2,… X t-1 = value at beginning of period t (end of previous period) X 0 = starting value (at beginning of period 1) 3) Rate of change (absolute change during period t): 1 - - = t t t X X X 4) Proportional and percent rates of growth. Proportional change during period t: 1 1 1 1 1 - = - = = - - - - t t t t t t t X X X X X X X X X Percent change during period t: X X X = 100 % 5) Example. b) Continuous growth. 1) Continuous time-dependent variables are observable at any instant of time t. For example, temperature is known and recordable at any time during a day. 2) Let X(t) = value of X at instant of time t, for 0 < t < +∞. X(0) = starting value (at t = 0) Notation X t , t = 0,1,2,… Time-dep. variable (discrete) X(t), t > 0 Time-dep. variable (contin.) Q(t) Real GDP Y(t) Nominal GDP P(t) Aggregate price level C(t), S(t) Consumption, Saving N(t) Population L(t) Labor force K(t) Capital stock I(t) Gross capital investment Discrete Example t X t ΔX t %ΔX t 0 1. 2 1 2. 6 1.4 116.67% 2 4. 1 1.5 57.69% 3 4. 4 0.3 7.32%
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Ec 117 MATH OF GROWTH THEORY p. 2 3) Rate of change (absolute rate of growth) at time t: X t X dt t dX = = ) ( ' ) ( 4) Proportional and percent rates of growth: X X X X t X t X 100 ; ) ( ) ( ' = 5) Example.
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