Chapter 8 - Economic Growth Flashcards
Explain what happens in the very long run.
In the very long run, capital and labor are assumed variables. Money, price level, and nominal variables are ignored. The focus will be only on the real side of the economy. We assume that there is no government, so no G and T. The economy is always at the full employment u = un and N = L and Y = Y. To check outcomes of the very long run, we use international data. Given the different sizes of countries, we use per person variables.
Explain Absolute Convergence Theory and Conditional Convergence Theory. Draw Graph
Absolute Convergence Theory: Suppose all economies are similar in all aspects like technology, saving rate, population growth rate, depreciation rate, except the initial level of per worker capital. Poorer economies grow faster than richer economies, so they catch up, all of them converge to the same steady state equilibrium O.
Conditional Convergence Theory: Economies can be different in all or many aspects like technology, saving rate, population growth rate,.Countries only converge if they have similar conditions (like savings rates, education, institutions).Each economy converges to its own steady state equilibrium, which is determined by the parameters of the economy. Poorer economies may not necessarily growth faster.
What is the production function? Explain Constant Returns to Scale and Diminishing Returns to all production factor?
The production function shows how capital (K) and labor (L) are used to produce output (Y) using available technology: Y=F(K,L). Constant Returns to Scale: If you multiply both inputs by the same amount, output increases by that same amount. λY=F(λK,λL). Diminishing Returns to a Factor: If you increase only one input (e.g., capital), holding the other fixed, each extra unit adds less output.
How are saving, investment, and income related in the economy? What is the saving function?.
From national income accounting: Expenditure approach: Y= C + I + G. Income approach: Y= C + S + T. Combining them gives: I=S+(T−G). Investment equals national saving (private + public). If there is no government, I = S.
The saving function, S = sY, C = (1 - s)Y, I = sY. Where s is the marginal propensity to save (MPS), s = 1-MPC.
What is capital accumulation? How does it relate to steady state? What assumption is made about labor force?.
Capital accumulation shows how capital stock changes: ΔKt=It−δKt. Here It = investment (the inflow) and δKt = depreciation (the outflow). If It > δKt, capital rises. If It < δKt, capital falls. If It = δKt, is the steady state capital stays constant.
Labor Force assumption, ΔLt = n, for now assume n = 0, so Lt = L
What are the 5 key components of the Solow model in the very long run?
Production Function: Yt=F(Kt,Lt) -> yt=f(kt), Saving = Investment (no gov’t): It = St. Saving Function: St = sYt. Capital Accumulation: ΔKt=It−δKt. Labor Force (constant): Lt = L
What is the steady state in the Solow Model, and how do we know if capital is increasing or decreasing?
The Solow Model equation: kt=sf(kt)−δkt. The sf(kt), is capital inflow (savings/investment), δkt is capital outflow (depreciation).
Steady State occurs when kt = 0 -> sf(k) =δk . At this point, kt = k, no growth in capital per worker. If kt<k: inflow > outflow → kt > 0, capital and output rise. If kt<k, inflow < outflow, kt < 0, capital and output fall. This makes k a stable steady state.
How does population growth affect the Solow Model? What is the new steady-state condition?
When the labor force grows at rate n>0, capital per worker must also account for the need to equip new workers with capital.
Δkt=sf(kt)−(δ+n)kt
sf(kt) = investment per worker(δ+n)kt = effective capital loss (from depreciation and labor growth)
This is the new stable equilibrium with constant capital per worker even as population grows
sf(k)=(δ+n)k
How do you calculate the steady state in the Solow Model with population growth and depreciation? Given: Y=2K0.3L0.7, s = 0.4, n = 0.02, δ=0.08.
Find Solow Equation: Δkt=sf(kt)−(n+δ)kt
Capital inflow: sf(kt) =0.4 * 2k0.3 = 0.8kt0.3
Capital Outflow: (δ+n)kt = (0.08 + 0.02)kt = 0.1kt
Solow Equation: Δkt= 0.8kt0.3 -0.1kt
Solve for Steady State (Δkt = 0)
0.8kt0.3 =0.1kt , k* = 19.5
Compute Steady State Values
Output per worker: y* = 2k0.3 = (19.5)0.3=4.88
Investment per worker: i* = sy* = 0.4 4.88 = 1.95
Consumption per worker: c* = (1-s)y* = (1-0.4) 4.88 = 2.93
What is balanced growth in the Solow Model without technology, and what are its key implications?
Balanced growth is when all variables grow at a constant rate. In the Solow Model without technological progress: Per worker variables (like yt, kt, ct) have 0% growth. Total variables (like Yt,Kt,Ct) grow at rate n (the labor growth rate)
What happens in the Solow Model when the saving rate increases?
When saving rate s↑, in the short run, capital per worker and output per worker growth rates temporarily rise then fall back to 0, Δkt > 0. In the long run, economy reaches a new higher steady state, growth rates return to zero, but levels stay permanently higher, y* -> y, k* -> k. Graph shows a shift from sf(kt) to s’f(kt), increasing both y* and k*.
What happens in the Solow Model when the population growth rate decreases?
When population growth rate n↓. In the short run, capital and output per worker temporarily rise, then fall back to 0. In the long run, a new steady state is reached, Growth rates return to zero, but levels are permanently higher. k* -> k, y* -> y.
What happens in the Solow Model when the population growth rate decreases?
When population growth rate n↓. In the short run, capital and output per worker temporarily rise, then fall back to 0. In the long run, a new steady state is reached, Growth rates return to zero, but levels are permanently higher. k* -> k, y* -> y.
What happens in the Solow Model when a shock (like an earthquake) destroys part of the capital stock?
Capital and output fall. The growth rates of the per worker output and per worker capital temporarily increase. Economy goes back to the initial steady state equilibrium.
What is the Golden Rule level of capital in the Solow Model? How is it determined and why is it important?
The Golden Rule level of capital is the level that maximizes steady-state consumption per worker. At this point: MPK = n + δ Marginal Product of Capital = Population Growth Rate + Depreciation Rate. Graphically: It is where the vertical distance between the production function f(k) and the depreciation line (n + δ)k is the greatest (i.e., where consumption c is maximized). Mathematically: Maximize c = f(k) − (n + δ)k, Take the derivative and set it to 0.
Flashcard – Golden Rule in Solow Model (with calculation). In a Solow model with the production function Y = 2K0.3L0.7, and parameters n = 2%, δ = 8%, use the golden rule to calculate the golden rule capital per worker (k), the golden rule saving rate (s), output per worker (y), consumption per worker (c).
Differentiate the Production Function:
Y = 2K0.3L0.7
f’(k) = 0.6k-0.7
MPK = f’(k) = n + δ =0.02 + 0.08 = 0.10
-0.6k-0.7 = 0.10
k* =12.933
Savings Rate
s* = ( n + δ) k/y
Y = 2K0.3= 2(12.933)0.3 = 4.311
s* = ( 0.02 + 0.08) 12.933/4.311 = 0.30
Output per worker = 4.311
Consumption per worker: c* = (1-s) y = (1-0.30) 4.311 = 3.018
What is the effect of a one-time technological progress in the Solow Model?
This leads to a higher growth rate of per worker capital and per worker output temporarily. However, in the new SS equilibrium, the levels of per worker output and per worker capital will be higher.
