Post Midterm 2 Content (Mostly Growth Theory)

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Growth Theory Introduction 1. Explain why growth theory focuses on the of average labour productivity. ● y/p = y/1 x l/p ● The relationship b/w capital and labour in an economy determine its output ● Labor productivity is a measure of economic growth within a country, it measures the real GDP produced by one hour of labour ● Helps us understand post-malthusian growth ● Helps us understand proximate and fundamental causes of growth ● Helps us understand the drivers for increasing output/person 2. Briefly explain the two classes of potential explanations for the sustained rise in average labour productivity. 1. Factor accumulation ○ Factors for production inputs ○ No labour inputs ○ Reproducible 2. Technological progress/productivity growth ○ Innovation and tech growth allows for more output with the same input factors. 3. How is growth theory related to Malthusian theories of income determination? ● Attempted to understand post-malthusian economy and related to the breakdown of the first relationship of the malthusian model ● Can someone explain this more? 4. What is meant by the term “proximate causes of growth”? ● Growth is due to technological progress. ● Cross-country income differences are due to a combination of technological differences, differences in physical and human capital per worker. ● Proximate causes of growth would be factors that immediately cause growth such as technological advances, increase in human/physical capital, etc 5. What is an aggregate production function? ● The same idea as a production function but for an economy RATHER than a firm ○ A production function is the transformation of inputs (factors of production) into output ● Representation of how inputs combine to generate outputs (PPF) 6. What is a factor of production?

● Describes the inputs used for the production of good/services in pursuit of economic profit ● They include land, labour, capital, and entrepreneurship 7. What is a marginal product? Why are marginal products often assumed to be diminishing? ● Marginal product is the slope of the production function ● The additional output produced when increasing production input by one unit, while keeping everything else constant ● It is diminishing because as an additional unit of input is added, the extra output produced from from each unit falls - results in decreasing productivity 8. What are the properties of capital? 1. Producible/productive 2. Produced 3. Rival and excludable 4. Earns a return 5. Depreciates 9. Explain why capital typically earns a return. ● When capital is producible/productive, rival and excludable, it is possible to give out capital good in return for payment (rent, adds to profit, adds to wages) ● Private capital is created in pursuit of this return 10. What is constant returns to scale? When all production variables are increased (all inputs are increased), it results in a proportional increase in output. “Doubling all of the inputs results in double the output.” zY= AF(zk. zL) 11. What is the difference between diminishing returns to scale and diminishing marginal product? Diminishing marginal product: As additional units of input are added, the extra output produced by each new unit falls. In diminishing marginal product, at least one production variable is kept constant. Diminishing returns to scale: Refers to the proportion between the increase in the total input and the resulting decrease in output. Diminishing returns to scale is a condition when ALL production variables are increased, while resulting in a less than proportional increase in output. 12. Why do early growth models not allow for increasing returns to scale?

Increasing returns to scale generally lead to a monopoly/oligopoly where production is concentrated with one producer. Oligopolists are not price takers and hence will interact strategically. This is a problem because many possible equilibria can be created. 13. Explain why early growth models cannot provide an economic theory of the determination of technological progress. Early growth theory works best with price takers (perfect competition), where the factors exhaust all outputs and there is nothing left to pay the innovators who produce such technology. Early growth models for this reason focus on capital accumulation since it is what they do best. 14. Why is it that growth can only be efficient if it is driven by factor accumulation? ● Factor accumulation and technology/productivity growth allow for sustained growth. However, technological progress requires extra capital in order to be produced. ● Factor acc ● It is not possible to have technological progress without starting off with factor accumulation as it is a resource needed for productivity growth 15. What does it mean to write the production function in intensive form? Why is this useful? y = f(k,l) ● It is useful because although the function may show constant returns to scale, individual inputs may show diminishing returns which helps us see how changing one production input can affect the total production. ● Intensive form is useful because according to CSR, output per labour is independent of capital and labour but depends on the ratio between them 16. What is a factor’s share in national income? What is special about the Cobb-Douglas production function with respect to factor shares? 17. What is the difference between a growth rate effect and a level effect? Growth rate effect: a change in a variable causes a change in the long run growth rate Level effect: a change in a variable causes a change in the income level, while leaving the long run growth rate unchanged 18. What are the two key elements to an equilibrium model? Explain. Profit maximization: firms choose input demands and output supplies Utility maximization: households choose input supplies and output demands 19. What is the difference between an equilibrium and a steady state? An equilibrium state is expected to be dynamic (if the environment suddenly changes, every member will re-optimize and the equilibrium will shift. A steady state is more restricted in

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that quantities are assumed to be constant in the long run. Once we reach a steady state, nothing will change. Solow Growth Model 1. Outline the theory of savings behaviour used in the Solow model. What are the advantages and disadvantages of this approach to modelling savings? ● Solow model assumes that savings rate is constant (a). i=a*y ● This way, given y, capital supplied for the next year is pinned down (independently of r). ● Market clearing condition requires capital supplied (Ks) to equal capital demanded (Kd) ● Therefore, we don’t have to solve the firm's problem to find equilibrium quantities (i.e. we don’t need to solve for r - the cost of capital) Capital is accumulated as a result of savings behaviour 2. Outline the theory of labour supply used in the Solow model. Why is this approach to modelling labour supply commonly used in growth theoretic models? ● Labour is supplied inelastically ● Labour grows exogenously through population growth ● Labour is constant and does not depend on the wage rate (w) ● Market clearing condition (Ls=Ld) pins down the labour demanded. So we don’t need to solve firm’s problem to find the wage rate ● Also inelastic labour supply allows us to ignore the labour/population (L/P) distinction 3. Write out the equations of the Solow growth model. Explain each one. y = f(k): y is a measure of output per worker and k is capital per worker. Shows the relationship between capital and output y = gf(k): Investment is output per worker multiplied by the savings rate y = dk: this function assumes proportional depreciation, as we increase capital there is an increase in depreciation. These two are proportional. K is capital per worker Y is output per worker 4. Write out the law of motion of aggregate capital. Use this to derive the law of motion of capital per worker. Aggregate: Kt+1 - Kt = aF(Kt,Lt) - dKt ; where a - savings rate and d- depreciation Per worker: (divide top equation by L)

kt+1 - kt = af(kt) - dkt ; where k = K/L shouldnt it be dkt ? -yes 5. “ solves the Solow model.” Discuss. 𝑘∗ ● At k*, capital stock doesn’t change ● Investment equals depreciation, steady state level of k* (not an equilibrium) ● Suppose k0 is where the economy’s capital stock is, where k0 < k* ○ Investment exceeds depreciation - capital stock will grow until reaches k* ○ Change in k decreases as the economy approaches k* (diminishing marginal product of capital) 6. Explain, using both the diagram and a written explanation, why capital per worker converges to steady state in the Solow growth model. Because of DIMINISHING MARGINAL PRODUCTIVITY OF CAPITAL (K). When investment is greater than depreciation, capital stock will grow. Likewise, when depreciation is above investment, capital stock will fall. The point on the graph where the function for depreciation and investment converge is known as the steady state. Investment = Depreciation 7. What are the two main results of the Solow growth model?

1. Capital per worker converges to a steady state level k* → implies that output and consumption per worker also converge to a steady state and there is no long-run growth ● Capital consumption (itself) cannot explain sustained, long-term growth 2. Conditional convergence → countries further from their steady state grow faster Those results are due to diminishing marginal product of capital per worker 8. Explain why the Solow growth model is often interpreted to mean that capital accumulation cannot generate long run growth? What is the key assumption that drives this result? Explain. The assumption is ‘Diminishing Marginal productivity of capital per worker (k)’. As k increases, MPk falls, i.e get less output per worker. But depreciation increases linearly with k. So eventually, net capital only generates enough to replace itself. 9. “The implications of the Malthusian and Solow models are essentially the same because in both models output per worker converges to a steady state level.” Discuss. Both models conclude that there is no long run growth and that Y/L converges to a steady state. However they are not the same. Malthusian model: y* is determined by fertility and subsistence factors and is independent of economic activity; e.g. productivity, savings, etc. Solow model: y* responds to economic factors such as productivity and savings In both the Malthusian and Solow model, output per worker converges to a steady state. However, in the Malthusian model, y* is independent of the economic side of the model. In contrary, Solow y* responds to economic factors. 10. Discuss the effect of a decrease in the depreciation rate on the path of capital and output per worker in the Solow growth model. Include both a diagram and a written explanation. A decrease in the depreciation rate results in investment being higher than depreciation compared to the initial state of k. As a result the steady state will be reached later and output per worker will increase as well. The slope of the depreciation curve decreases. 11. Suppose the savings rate of a country increased. Discuss the implications for output per worker, the growth rate of output per worker, and welfare using the Solow model as a framework. A higher saving rate does not permanently affect the growth rate in the Solow model. A higher saving rate does result in a higher steady-state capital stock and a higher level of output per worker. The shift from a lower to a higher steady-state level of output causes a temporary increase in the growth rate. I think it’s because it increases the investment function since it is the product of the saving rate and output per worker. Thoughts ?

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● Yes, it does increase the investment function (shifts upwards) and this causes the steady state k* to increase, which also causes y* to increase. This causes a level effect; i.e a short term growth rate. 12. Suppose you were to consider an equilibrium model of capital accumulation (i.e. replace the Solow model’s behavioural rules with optimal choices), how would that impact your answer to question 11? The answer would still be the same. Because of optimal savings. Using an equilibrium model means that consumers will choose savings rate. So increasing the savings rate will increase investments and will increase k. As k increases, MPk decrease. In perfect competition, MPk=r (interest rate), so r decreases. So eventually, even as savings increase, there won’t be enough output to increase k (investments will eventually < depreciation) 13. Explain why some economists view capital accumulation as a potential explanation of relative income levels, but not relative growth rates. Because capital accumulation causes shifts in the output curve, but do not affect the slope. And so amount of capital can tell us why countries are at different levels, even if it doesn’t say much about growth rates. Capital accumulation causes level effects. 14. What is conditional convergence? Once we control for observable differences between countries (differences that affect the steady-state level such as investment, population growth, financial development, etc.), then the lower the initial capital stock (K), the faster the growth is. This is because there is so much space for growth as steady-state level is far from the initial amount of capital invested. Therefore, countries further away from their steady states grow faster than countries close to their steady states due to being further away from reaching the point where diminishing marginal product per worker kicks into effect. BUT: this does mean that poor countries grow faster mostly because they may not know how to increase development (lack of knowledge, education, or health, etc). Steady states are endogenous. ● Countries further from their steady states grow faster conditional on steady state. ● Why? Diminishing marginal product of capital ● But... Different countries have different steady states so not all countries will converge to the same levels 15. Explain how the notion of conditional convergence differs from the statement that poor countries grow faster than rich countries. Conditional convergence is only true if both countries have the same steady state. However, if a poor country has a lower steady state than a richer country, it won’t be expected to grow as rapidly as it would if it had a high steady state like a rich country.

16. Explain how the conditional convergence result is sensitive to the Solow model’s behavioural rule assumptions. Sensitive to savings rate. Savings rate could be different at different income levels, this could result in identical countries having different steady states. So, poor countries get stuck in a poverty trap; they have a lower steady state because of unfavourable initial conditions. They will need policy to increase savings to get to the higher steady state. Solow Variants 1. Explain how capital dilution works in the Solow model extended to allow for population growth. Negative effect of population growth on capital per worker. If a country has a rapidly growing population, and the quantity of capital is held constant, then population growth would result in less capital being available for each worker. A country in which population is growing rapidly could maintain a constant level of capital per worker only by investing a large fraction of its output in building new capital. 2. Explain how the population growth rate affects the steady state level of income in the Solow model extended to allow for population growth. Raising the rate of population growth leads to a lower steady state level of output. Thus, the Solow model, modified to include population growth, provides a potential explanation for why countries with high population growth rates are poorer than countries with low population growth rates. Specifically, higher population growth dilutes the per-worker capital stock more quickly and so lowers the steady-state level of output per worker. 3. What is the growth rate of Y in the Solow model extended to allow for population growth? Explain. At the steady state, Y grows at the same rate as population (n). Because y*=Y/L, if L grows at n, Y must grow at n. Along the transition path, y is increasing (y<y*) and so Y grows at a rate faster than n. 4. Why don’t we get the Malthusian results in the Solow model extended to allow for population growth? ● CRS and non-labour inputs reproducible ● In the long-run, it doesn’t matter how many people there are as long as there is new capital

● In the LR, can just increase capital and air new workers with capital so that Marginal product of labour doesn’t fall. ● 5. What is the theory of productivity growth in the extended Solow model? Discuss. Adding exogenous productivity growth to the model is possible. It doesn’t explain growth, but rather shows how capital accumulation is affected by productivity. Long run productivity growth has to be labour augmenting in order to reach a steady state. 6. Is it possible to have capital augmenting technological progress in the Solow model? Discuss. Yes, it is possible to have capital augmenting tech progress in solow model so long as it can be written as labour augmenting. E.g. Cobb douglas: Y=AK^a*CL^(1-a)8 Let B= A^(a/1-a)*C^(1-a) Then Y = K^a*BL^(1-a) ← pretty much manipulated capital augmenting to look like labour augmenting. - wtf is this question? 7. Does k converge to a steady state in the Solow model extended to allow for technological progress? Explain. K does not converge to steady state. Rather, k/A (K/AL) converges to a steady state. In this steady state, k grows at the same rate as productivity growth (x). 8. Explain how capital can grow indefinitely in the Solow model extended to allow for technological progress. Same as above, K/AL converges to a steady state, at this steady state, k (K/L) grows at a rate x and so capital accumulation is ongoing and responsible for part of the measured growth . 9. What role does the diminishing marginal product of capital play in the Solow model extended to allow for technological progress? Diminishing marginal product of capital has no tendency in the steady state, since new capital is always paired up with effective labour. But in the transition path, diminishing marginal product of capital still matters. When converging to the steady state, capital is being added faster than AL is increasing. Thanks for deleting the non-tested stuff. GOOD LUCK! FUCK SOLOWWWWWWWW < I stand with you - Thank you very much, let us all clench our butts

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45 mins before exam and i still dont get it - me too ive kind of stopped giving a shet Pretty sure imma forget everything the moment that paper gets laid out in front of me :) lol RT! Lets go my dudes ^ ^^ I like turtles About to SwOLLOW my pride and just take the fucking exam - i literally have a SWOLLOWED eye rn, can barely see out of my left lmaooo Thank mr goose To sum it up, this was all bs because all these models are based on assumptions and in real life these assumptions don't work. This class is point-less. < I wouldnt mind a pointless class if it had decent powerpoints- amen, he doesnt even know how to use to the power of on office I thought this course was going to be a breeze. This is legit the hardest easy course i have ever taken I dont even know my mark as i have never attended class, and that book report was such bs lol If i was an equation in this course i would be y=f(k) because fk my life R we still here

Post Midterm 2 Content (Mostly Growth Theory)

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