Econ 191 2nd LE Reviewer.docx - Econ 191 2nd LE Reviewer The Solow Growth Model(Robert Solow 1956 A Contribution to the Theory of Economic Growth

# Econ 191 2nd LE Reviewer.docx - Econ 191 2nd LE Reviewer...

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Econ 191 2 nd LE Reviewer The Solow Growth Model (Robert Solow, 1956): A Contribution to the Theory of Economic Growth Assumptions o Continuous time (t) o Single good ( Y ) o Constant technology ( A ) o No government; no international trade o Full employment of all factors ( K, L ) o Labor force grows at a constant rate, η o Initial values of K and L are given at K 0 and L 0 Production Function 1. Y(t) = Y[K(t), L(t)] = AK(t)αL(t)(1-α) Where: A>0; 0 <α <1 Simplifying, by suppressing t: 2. Y = AK(α)L(1-α) Exhibits CRS: γ = α + (1-α) = 1 Inputs are Essential: 3. Y(0,0) = Y(K,0) = Y(0,L) = 0 Positive Marginal Products 4. MPK = aAKα-1L(1-α) > 0 5. MPL = (1-a)AKαL(1-α)-1 > 0 Exhibit diminishing MPs 6. ΔMPK/ΔK = (a-1)aAKα-2L(1-α) < 0 7. ΔMPL/ΔL = -a(1-a)AKαL(1-α)-2 < 0 Subscribe to view the full document.

The Per Worker Terms o Define: y = Y/L - GDP per 'capita' L grows at the 'natural' rate of the population at η Growth behavior of y: If Y grows at a faster rate than η, then y increases; If Y grows at a slower rate than η, then y decreases; If Y grows at the same rate as η, then y remains constant (does not grow) o Let k = K/L - Capital per worker (capital intensity) L grows at the 'natural' rate of the population at η Growth behavior of k: If K grows at a faster rate than η, then k increases; If K grows at a slower rate than η, then k decreases; If K grows at the same rate as η, then k remains constant. The per Worker Production Function Y = AKαL(1-α) o Y/L = y = [AKαL(1-α)]/L = AKα /Lα = A(K /L)α y(k) = Akα o Where 0 < α < 1 Capital-intensity positively contributes to growth per capita Δy/Δk = MPk = αAkα-1 > 0 y(k) exhibits diminishing marginal productivity in k. ΔMPk/Δk = (α-1) αAkα-2 < 0 The Significance of Capital-Intensity (k = K/L) in Output per Capita (y) o Given the same amount of labor input (L), investing in higher amounts of capital (K) for the given L to work with will make them (L) more productive. o Not only total output (Y) will increase; output per capita will also increase (y). The essence of increasing productivity of L. Capital Accumulation (K) 1. Simple Closed-Economy Model Income Side: a. Y = C + S b. C = C(Y) = cY - Consumption function 0 < c < 1 - the marginal propensity to consume (MPC) c. S = S(Y) = sY - Savings function 0 < s < 1 - the marginal propensity to save (MPS) Total income from economic activity goes either to Consumption (C) or to Savings (S) o The level of Consumption is always proportional to the level of Income E.g., C = 0.8Y o The level of Savings is always proportional to the level of Income E.g., S = 0.2Y Subscribe to view the full document.

Expenditure Side: d. Y = C + I Where: I – autonomous Investment expenditures Economy Equilibrium: Income = Expenditure e. C + S = Y = C + I S = Y - C = I f. S(Y) = I - Savings = Investment condition All of GDP is either Consumed (C) by households or put into Investments (I) by the business sector.  • Fall '19

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