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...

This preview shows page 1 - 5 out of 38 pages.

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
Image of page 1

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
Image of page 2
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
Image of page 3

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.
Image of page 4
Image of page 5
  • Fall '19

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes