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Growth Facts and Solow Growth Model
## Economic Development & Construction 0008 ###
Dr. Kumar Aniket
### Lecture 1 --- ## Evaluating an intervention A society is in situation `\(A\)` Policy intervention `\(P_B\)` would lead to situation `\(B\)` .thebox[ `\begin{align} {A} \stackrel{P_{B}}{\longrightarrow} {B} \end{align}` ] **Policy `\(P_B\)`** could be *constructing a new highway* or a *new train line* .emab[Winners] and .emab[losers] from the intervention How can we **objectively** compare situation `\(A\)` with situation `\(B\)`? How do we avoid **subjective** judgements in comparing situation `\(A\)` and `\(B\)` --- ### Pareto Improvement .thebox[ An intervention that makes some people better off without making anyone worse off is called a **Pareto improvement**. ] **Winners** but *no losers* .emgr[in the society] -- ### Pareto Efficiency .thebox[ **Pareto efficiency** situations are one where you cannot make anyone better-off without making anyone worse off. ] **Winners** and **losers** .emgr[in the society] --- ## Development economics .thebox[ The primary role of **Development economics** is to find interventions that increase the size of the pie, so that everyone gets a bigger slice of pie than they were getting before the intervention. ] .mybox[ `\begin{align} \text{Pie} = \text{Aggregate Output} = \text{Aggregate Income} \end{align}` ] .footnote[ `\(\text{Aggregate Output} = \text{Aggregate Income}\)` follows from National Income Accounting ] --- ## GDP Per-capita Livings standards of the citizens related to average income .thebox[ `\begin{align} \text{GDP per-capita} = \frac{\text{Aggregate Output}}{\text{Total population}} \end{align}` ] -- ## GDP Per-worker Productivity of workers in the economy .thebox[ `\begin{align} \text{GDP per-worker} = \frac{\text{Aggregate Output}}{\text{Total number of workers}} \end{align}` ] --- ## Life Expectancy versus GDP per-capita <img src="images/lec1/ch1_lifeexp-1.svg" width="72%" style="display: block; margin: auto;" /> --- <img src="images/lec1/ch1_lifeexp-1.svg" width="85%" style="display: block; margin: auto;" /> --- <img src="images/lec1/ch1_panel_lifeexp-1.svg" width="85%" style="display: block; margin: auto;" /> --- ## Life Expectancy versus GDP per-capita .ema[Countries with **low** GDP per-capita:] small gains in GDP per-capita leads to large gains in life expectancy] .emb[Countries with **high** GDP per-capita:] large gains in GDP per-capita leads to small gains in life expectancy] Increase in life expectancy creates **winners** but *no losers* .mybox[ Scope for .emg[**Pareto improvement**] for low GDP per-capita countries through policies that encourage economic growth ] --- <img src="images/lec1/ch1_ypp_panel-1.svg" width="85%" style="display: block; margin: auto;" /> --- # Living Standards **Living standards** are associated with a country's per-capita income.<sup>1</sup> High income per-capita is simply **accumulated growth** from the past Increasing a country's future living standards requires increasing it current growth rate of per-capita income/output -- .emab[Dasgupta & Weale 1992]<sup>1</sup>: **per-capita income** highly correlated with measures of **living standards** like *political* and *civil rights*, *infant mortality*, *life expectancy* and *per-capita income*. .footnote[ 1. National income should equal national output. 2. P. Dasgupta and M. Weale. On measuring the quality of life. World development, 20(1):119–131, 1992. ] --- # Dasgupta & Weale 1992 Table: Correlation Matrix of living Standard rankings from Dasgupta & Weale | |Life expectancy |Infant Mortality |Literacy rate |Political rights |Civil rights | |:-----------------|:---------------|:----------------|:-------------|:----------------|:------------| |Per-capita income |0.78 | | | | | |Life expectancy |0.69 |0.92 | | | | |Infant Mortality |0.59 |0.8 |0.79 | | | |Literacy rate |0.49 |0.41 |0.41 |0.24 | | |Political rights |0.51 |0.43 |0.38 |0.27 |0.79 | --- class: center, middle # Production Function --- # Production Function A firm uses range of factor inputs and turns it into output. A firm's production function: $$Y = F(K, L) $$ where `\(Y\)` is the output, `\(K\)` the capital, `\(L\)` the labour used by the worker An economy also has .emab[range of different types of firms] that turn factor inputs into outputs Does .emab[economy's production function] look different from a .emab[firm's production function]? - the distinction between the two is absolutely critical --- # Returns to Scale .emcb[Constant returns to scale] *production function:* If factors inputs increase by a certain proportion, output also increase by the *same proportion* -- .emcb[Increasing returns to scale] ... output increase by a *greater proportion* .emcb[Decreasing returns to scale] ... output increase by a *lesser proportion* --- # Economy's Production Function If firms in the economy have .emcb[constant returns to scale], then economy's production function can be estimated by a **representative firm**'s production function.<sup>1</sup> Economy's production function: $$Y = F(K, L) $$ where `\(Y\)` is economy's output, `\(K\)` and `\(L\)` are that total available capital and labour in the economy --- # Per-worker Production Function Economy constant returns to scale production function: `$$\lambda{Y} = F(\lambda{K}, \lambda{L})$$` Set `\(\lambda\)` such that `\(\lambda=\frac{1}{L}\)` $$\frac{Y}{L} = f \left(\frac{K}{L} \right) $$ .pull-left[ .emci[Left hand side:] Output per-worker Country's livings standard ] .pull-right[ .emc[RHS:] function of capital per-worker how much capital does an average worker get to work with in the country ] Implies, **accumulating capital** at a rate faster than population growth is key to increasing living standards --- ## Decreasing Marginal Product of Capital .thebox[ The more capital is added, the less productive it is at the margin ] The average worker experiences a smaller and smaller productivity increase at the margin as capital gets accumulated. --- ## Growth Potential Low GDP per-capita countries can experience exponential economic growth through capital accumulation Capital accumulation makes workers more productive As countries accumulate capital, the growth slows down. Why are developed countries still growing? --- .center[.emg[This shows how UK's output capital ratio has evolved over time]] <img src="images/lec1/uk_prodfn1.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[UK's Output capital ratio in 1969 was 2.55]] <img src="images/lec1/uk_prodfn4.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[UK's Output capital ratio in 1994 was 1.93]] <img src="images/lec1/uk_prodfn3.svg" width="75%" style="display: block; margin: auto;" /> .center[.emg[This shows how France's output capital ratio has evolved over time]] <img src="images/lec1/fr_prodfn1.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[France's Output capital ratio was 2.29 was 1979]] <img src="images/lec1/fr_prodfn3.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[France's Output capital ratio was 2.48 in 2002]] <img src="images/lec1/fr_prodfn4.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.emg[This shows how China's output capital ratio has evolved over time]] <img src="images/lec1/ch_prodfn1.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[China's Output capital ratio was 14.35 in 2008]] <img src="images/lec1/ch_prodfn3.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[China's Output capital ratio was 12.24 in 2008]] <img src="images/lec1/ch_prodfn4.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.emg[This shows how US's *output-capital* ratio has evolved over time]] <img src="images/lec1/us_prodfn1.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[US's Output capital ratio was 17.64 in 1987]] <img src="images/lec1/us_prodfn3.svg" width="75%" style="display: block; margin: auto;" /> --- .center[.ema[US's Output capital ratio was 16.69 in 2003]] <img src="images/lec1/us_prodfn4.svg" width="75%" style="display: block; margin: auto;" /> --- <img src="figs/unnamed-chunk-24-1.svg" style="display: block; margin: auto;" /> --- <img src="figs/unnamed-chunk-25-1.svg" style="display: block; margin: auto;" /> <style> h1, h2, h3 { color: #EC5800; } p { line-height: 1.5em; } rr { color: #002E63; } a { color: #002E63; } .inverse { background-color: #D2691E; } .tab { display:inline-block; margin-left: 15px; } .ema {color: rgb(43,106,108);} .emb {color: rgb(184,13,72); } .emc {color: #1034A6; } .emd {color: rgb(64,64,64); } .eme {color: #614051; } .emo {color: #CC5500; } .emg {color: #6D351A; } .emgr {color: #696969; } .emab {color: rgb(43,106,108);font-weight: bold;} .embb {color: rgb(184,13,72); font-weight: bold;} .emcb {color: #1034A6; font-weight: bold;} .emdb {color: rgb(64,64,64); font-weight: bold;} .emai {color: rgb(43,106,108);font-style: italic;} .embi {color: rgb(184,13,72); font-style: italic;} .emci {color: #1034A6; font-style: italic;} .emdi {color: rgb(64,64,64); font-style: italic;} .footnote {color: gray;} .red { color: red; } .mybox { color:#3D2B1F; background-color:#3D2B1F10; margin:1em; padding: 1em; border-radius: 10px; } .thebox { color:#704214; background-color: #F5DEB320; margin: 0.1em 0.5em 0.1em 0.5em; padding: 0.1em 1em 0.1em 1em; border-radius: 10px; border-color: #704214; border-style: solid; border-width: 2px; } </style> <!-- rgb(184,13,72) #plum rgb(242,151,36) #orange rgb(43,106,108) #dark-teal rgb(64,64,64) #dark-grey --> <!-- #386890 #A40000 #FFB347 -->