ECON 112 Template.pdf

eoclassical Model “Monetarist.” If resources are allowed to be fully employed, economies can correct themselves. k is endogenized - it develops (something) internally, especially a parameter within an economic model. y = Af(k) f’(x) >0 f’’(x) < 0 Three assumptions: 1. Savings rate is constant 2. n =...

eoclassical Model “Monetarist.” If resources are allowed to be fully employed, economies can correct themselves. k is endogenized - it develops (something) internally, especially a parameter within an economic model. y = Af(k) f’(x) >0 f’’(x) < 0 Three assumptions: 1. Savings rate is constant 2. n = 𝑑𝑁 𝑁 = Population Growth Rate is constant So 𝐾 𝑁 → 𝐾 𝑁+𝑛𝑁. If the population grows by 1.9%, capital has to grow by 1.9% per year. So laborers are equipped with the same number of tools. 3. S = Depreciation is constant 𝐾 𝑁. There is a natural decrease in the capital labor ratio and therefore you need to invest to maintain the capital Therefore for the second and third assumption you would need (N + S)*K to keep the capital labor ratio constant - the breakeven investment. *Refer to the linear curve in graph above for the breakeven investment. *Y/N = y Steady State https://sites.middlebury.edu/econ0428/neocl assical-growth-model/ When: S/N = (m+d)*k/N ; k is constant We are maintaining our capital, maintaining the capital labor ratio. This is the steady state. S/N > (m+d)*k/N ; k is increasing We save more than we need, resulting in a surplus. Leading to a higher capital labor ratio. S/N < (m+d)*K/N ; k is decreasing Here we are unable to maintain our machinery. This leads to a lower capital labor ratio. When you have natural disasters or terrorism, infrastructure and capital get destroyed. Lower things to maintain, it will return to the (k/N)*or the steady state. more capital means 2% growth in the entire economy. When you have unconditional foreign aid, due to the law of diminishing marginal productivity wrought by the maintenance of the capital, you will return to the steady state. If we change capital labor ratio only we go back to (k/N)*. So how do we change (k/N)*? There is no way to change the steady state with capital - you will have to employ other factors like population control. In the poorest region of the country, they cannot save. No savings, no investment. No investment, no income. No income, no savings. It’s a loop, a vicious cycle or perpetual shit. That is the origin point in the graph. This is where external help comes from. It’s not private investment that will help. It’s missionary work of the government. A minor irrigation project results in a small increase in savings, investment, and income. A small maintenance. The capital labor ratio increases slowly and eventually it will start to make a dent. That is how regions in extreme poverty eventually get out of the shithole. We would want a bigger proportion of income saved. You would have excess savings, more investment, capital labor ratio increases - moving the equilibrium capital labor ratio to the right and up. GDP Growth or ∆𝑌/𝑌 is always growing by small n - growing at the same level as the population growth rate. Balanced Growth Path 𝑑𝑁 𝑁 = 𝑑𝐾 𝐾 = 𝑑𝑌 𝑌 =𝑛 At steady state, we say that k (capital labor ratio) is constant, K/N is constant. If the population is growing by “n” therefore the aggregate capital is also growing by “n”. What affects the economy is population growth. 2% more population means 2% In order to increase the savings rate however is tricky. Many of these evidences are: 1. Correlation, not causality. Maybe the reason people are able to save is because they have higher income. They have higher income because they can save. 2. Time - Generational Wealth The period between 0 and 1 is roughly 25 years. A generation. If you have nothing at the start, you can only save very little, little return. With GW behind you, you can save so much and have a huge return in the next generation. 3. Golden Rule of Accumulation. The slope of the breakeven investment is exactly the same as the slope of the production function. Find the point where the slopes are the same using derivatives. The slope gets flatter, you have a higher capital labor ratio permanently, higher per capita income permanently, more welfare. The graph shows that at lower rates of population growth, the long run standard of living will be higher Increasing the savings rate increases income, but that’s not the end. Income allows you to consume. Savings does not infinitely increase welfare. That said, negative population growth will cause GDP to decrease. Making an “L” shaped function. Consumption = y - sy. The end goal is to consume so savings is probably not worth it… Effect of n Let’s see what happens when you control the population. Lack of education leads to increased fertility rate because there is no clear understanding of the risks and responsibilities. Lack of education leads to less opportunities resulting in a poorer life. Note: An average individual in Japan has a better life than the average individual in China. But China as a whole has a bigger economy than Japan and therefore has bigger dictate and sway in international relations. A positive shock, it would lead you to Y4 which is a stable equilibrium. The solution is technology and education. You can never have too much technology or education as it raises your ceiling. Malthusian Population Trap Women cannot get pregnant at 0 per capita income as they would be too hungry and even if they did, kids would die young due to hunger Technology changes the steady state, makes it so GDP grows at a higher rate permanently. There is a threshold where the GDP will grow slower than the population growth. With the equation Y/N, Population grows when N grows and Income grows when Y grows. Y2 is an equilibrium. But it is unstable as a negative shock, population drops, per capita income increased, that would lead you to Y1. Y1 is a stable equilibrium. If you do have something good happen, couples have more babies, the population grows again, per capita income does not change and you are stuck at Y1. Hence, the trap. This is different from savings as with savings, the growth after period 1 returns to former levels. There is a level effect. Whereas with technology imbues a growth effect that permanently makes it so that there is growth permanently in the economy. In macroeconomics, autoregressive models are commonly used to analyze the behavior of key economic indicators over time. For instance, an AR(1) model might be used to study how GDP growth in the current quarter is related to GDP growth in the previous quarter, while an AR(2) model might capture not only the immediate past GDP growth but also the growth rate from two quarters ago. E is the negative shocks like war or natural disaster. Autoregressive models are especially useful for forecasting purposes since they allow analysts to use past data to predict future values of economic variables. These models can provide insights into the persistence of shocks in the economy, the dynamics of business cycles, and the effectiveness of policy interventions over time. Foreign Investment Foreign Investment will not come in unless there is potential. It will not come in if you are not growing. Once it comes in, it will lead to a level effect. It is not necessarily chicken and egg. Level Effect Growth increases but after one period it simmers and becomes constant. Does not raise the ceiling. Slope is n. Growth Effect Growth increases permanently and raises the ceiling. Slope is n + g. Where g is ∆𝐴/𝐴 RBC (Real Business Cycle) Autoregressive Model (AR) AR 1 | 𝑦𝑡 = 𝑎0 + 𝑎1𝑦𝑡−1 + 𝑒𝑡 AR 2 | 𝑦𝑡 = 𝑎0 + 𝑎1𝑦𝑡−1 + 𝑎2𝑦𝑡−2+ 𝑒𝑡 AR 3 |𝑦 AR m 𝑡 |𝑦 𝑡 = 𝑎0 + 𝑎1𝑦𝑡−1 + 𝑎2𝑦𝑡−2+ 𝑎3𝑦𝑡−3 + 𝑒 𝑡 = 𝑎0 + 𝑎1𝑦𝑡−1 +....... + 𝑎𝑚𝑦𝑡−𝑚 + 𝑒 *Where a is constant and e is the error term 𝑡 However, it's important to note that autoregressive models have limitations, such as their assumption of linearity and stationarity. Extensions like ARIMA (Autoregressive Integrated Moving Average) models are often used to address these limitations by incorporating differencing and moving average components. Additionally, the presence of structural breaks or regime shifts in the data can complicate the analysis and require more sophisticated modeling techniques. Effect of 𝑦𝑡−𝑛 |𝑎1|=1 |𝑎1|1 Effect of 𝑦𝑡−1 1 0.5 2 Effect of 𝑦𝑡−2 1 0.25 4 Effect of 𝑦𝑡−3 1 Effect of 𝑦𝑡−∞ 1 Verdict Constant 0.125 8 So the final RBC… 𝑦𝑡 = 𝑎0 + 𝑎1𝑦𝑡−1 + 𝑎2𝑦𝑡−2 + 𝑒𝑡 0 ∞ 0 < 𝑎1 < 1 − 1 < 𝑎2 < 0 Transitional Explosive *The result is to raise it by the year What happened 30 years ago in terms of the economy almost does not affect us anymore. What does affect our economy the most is what happened last year, then the year before, then the year before the year before in that priority. In Macroeconomics, it is therefore more transitional. If the values of a are negative, it leads to an oscillating effect on the verdicts. Effect of 𝑦𝑡−𝑛 𝑎1=-1 0>𝑎1>-1 𝑎1 |𝑎2| 𝑦𝑡 = 𝑎0 + 𝑎1𝑦𝑡−1 − 𝑎2𝑦𝑡−2 𝑦𝑡 = 0. 02 + 0. 75𝑦𝑡−1 − 0. 3𝑦𝑡−2 𝑦24𝑄1 = 2% + 0. 75(5. 6%) − 0. 3(6%) 𝑦24𝑄2 = 2% + 0. 75(4. 4%) − 0. 3(5. 6%) 𝑦24𝑄3 = 2% + 0. 75(3. 6%) − 0. 3(4. 4%) 𝑦24𝑄4 = 2% + 0. 75(3. 4%) − 0. 3(3. 6%) 𝑦25𝑄1 = 2% + 0. 75(3. 5%) − 0. 3(3. 4%)