Macro Notes pdf - Alexander Karalis Isaac PDF

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Warning: TT: undefined function: 32 Warning: TT: undefined function: 32 Economics 1 – MacroeconomicsExponential growth: - If GDP grows at constant rate (e. 2%), the level grows exponentially – like savings interest Exponentially growing variables not very informative – a series in which %changes app...

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Economics 1 – Macroeconomics Exponential growth: - If GDP grows at constant rate (e.g. 2%), the level grows exponentially – like savings interest Exponentially growing variables not very informative – a series in which %changes appear on same scale regardless of level is more useful – giving a more linear series. - GDP, yt, grows at constant rate gy: Can be rearranged to give method for calculating rate of growth:

Constant growth is a reasonable approximation for some purposes.

Gross Domestic Product (GDP): Total expenditure on the economy’s final output of goods and services. Expenditure method (1): i = 1 … Nf is sum over all final goods and services. pi & qi price and quantity of each good. Output method (2): Na is all g+s in economy; NIR is total of intermediate goods and raw materials. E.g. bottled water. Add water, bottle, bottled water. Take away water (raw) and bottle (intermediate). Income method (3): NE all employed workers, Nc all owners of capital.

In National Accounts, should have (1) = (2) = (3). But, do not have this in practice. Everything in Macro is approximate. GDP identity: Y ≡ C + I + G +NX (see business cycles) From micro – we know that competitive markets, innovation and capital stock drive growth & prosperity. It is uncontroversial that technological change and productivity growth drive economic growth. Does it also drive business cycles? Modern macro models allow a role for productivity shocks but generally see additional market rigidities and different mechanisms for setting expectations as key to understanding business cycles and policy.

The Solow Model: Growth rates – notation: In continuous time, these are instantaneous growth rates – not compound rate of growth.

Solow Model: - Based on Cobb-Douglas production function – has constant returns to scale (x2 inputs → x2 outputs) - Growth comes from accumulation of capital and increasing population - Capital accumulates if saving > depreciation (part of investment goes on replacing old machinery as capital wears out over time) - Given constant returns to scale, there is diminishing marginal product of capital (MPK) and constant depreciation. - This results in a steady state level of capital and of output per worker. Implications of model: - Further from steady state, less capital, higher MPK, faster growth. Countries which are poor (less capital per worker), all things equal, will grow quicker than rich countries. - Technological progress is required for continued growth in output per worker. Cobb-Douglas production function: - Two factors of production: capital and labour - One output Y, standing in for GDP - Constant returns to scale - Diminishing returns to either factor A = technological level; output linear in A, the level of total factor productivity. TFP includes all reasons apart from amount of capital per worker has to work with that affect their productivity – technology in use, efficiency with which technology and capital used, and management quality. K = capital, N = labour. Parameter α is between 0 and 1 and is capital’s share of income – labour’s share is 1-α.

Output per worker: y = Y/N. Intensive production function is a function of capital per worker: k = K/N. As capital per worker (k) increases, output per worker increases at a decreasing rate. The MPK is the slope of the intensive production function. Capital accumulation: - Capital increases with investment, I = sY – savings = investment. s, the savings rate, is an exogenous parameter. This is a policy variable. - Capital depreciates at rate δ. Capital accumulates as long as saving (= investment) is greater than depreciation (i.e. if sY > δK). - There is a steady state level of capital where sY = δK (capital stock will stay at the same level) Labour input growth: - Constant, exogenous growth in labour force at rate n also assumed: (continuous proportional growth rate) - Growth in the labour force depreciates the amount of capital per worker. n can be a policy variable (e.g. immigration, 1 child policy, contraception) – but constant for now. Hence, savings needs to offset both depreciation and population growth to maintain capital stock. Fundamental Solow Equation of Motion:

This equation describes how capital per worker varies over time. The first term shows the extent to which investment is adding to the capital stock per worker. The second term shows the amount of investment needed to offset depreciation (δk ) and to equip additions to the labour force at existing levels of capital per head (nk). Hence, capital per worker grows if saving per worker is greater than depreciation of capital per worker.

Solow diagram: This result can be seen in the Solow diagram.

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Capital per worker (k) is on x axis, output per worker (y) is on y axis. Akα represents relationship through which capital per worker is transformed into output per worker. (n+δ)k shows what is required to keep the capital labour ratio fixed and it reflects the need to replace capital stock as it depreciates at rate δ, and the need to equip with capital new entrants to the labour force arriving at rate n.

sAkα (or sY [=I]) is a constant fraction of Akα, and so is shaped like a production function. The distance between the total capital depreciation curve and savings curve at any level of k determines k. E.g. if sAkα > (n+δ)k, capital per worker over time appreciates (k > 0) because investment per worker is greater than the reduction in capital per worker due to increasing population and depreciation. Capital per worker over time depreciates (k < 0) when sAkα < (n+δ)k. Point where two curves intersect is given by the level of capital per worker (k*) where sAkα = (n+δ)k. At this point, k = 0 and  = 0, which means that level of capital per worker and output per worker are constant. This defines a steady state in the Solow model: at k* both K and N grow at the same constant rate n. Steady state levels of output per worker (y*) and consumption per worker (c*) are shown. Steady state level of output per worker is given by: y* = A(k*)α. At this point, steady state level of consumption (c*) is constant and is a fraction of steady state income (= 1 – s)A(k*)α.

Policy experiment - increase in savings rate:

Exogenous increase in savings rate shown by upward shift of savings line – blue line represents greater proportion of income being saved. Investment is now greater than depreciation at the original capital per worker. Capital per worker starts to grow. The rate at which capital is accumulated will fall – up until the point where savings line crosses depreciation line (the new equilibrium capital per worker & output per worker). Time on x axis, output/capital/consumption per worker in y axis. At 10, savings rate increased. Capital per worker begins to grow rapidly. Output per worker also starts to grow (but rate of growth declines with diminishing marginal returns to capital, growth stops when new steady state reached. Initially, consumption falls as some consumption is given up to save more. But, as capital stock accumulates, there is more and more to consume – so path of consumption begins to increase. k and y rise unambiguously, but this does not mean it is a good policy choice. Welfare is measured as c = C/N (consumption per worker). To maximise steady state consumption (1-s)ȳ, one needs to find the savings rate that will give largest gap possible between consumption and savings at steady state. If the savings rate (and therefore capital) is low and increases, there is a big increase in output and small increase in depreciation, so in long-run consumption will increase. If the savings rate (and therefore capital) is high and increases, there is a small increase in output and large increase in depreciation, so in long-run consumption will fall. In between, where tangent line to savings line is parallel to the depreciation line, steady state consumption is maximised (marginal product capital = depreciation [MPK = n+d]). This is known as the ‘golden rule’ level of capital.

Conclusions: Income per worker and consumption per worker increase, but in the long-run they fall flat – therefore, this is only temporary growth. There is no long-run growth in this model. It is not possible to have long-run growth (per worker) just by accumulating capital – there needs to be technical progress. Convergence to steady state dictated by: n, d, s, A, α (population growth, depreciation, savings, technology level and share of capital). - Convergence: this implies that there will be convergence between countries with the same parameters, even if they start with different levels of capital (richer countries are just closer to the steady state) → a strong prediction by the model. Economic Growth: The Solow Model to Endogenous Growth: Unconditional convergence: If technology is shared across countries, all countries have access to the same steady states. Countries will have the same production function – the global production function. Countries with same savings rate and population dynamics will converge to the same GDP/capita. - Poor countries are far from steady state and grow fast - Rich countries near to steady state and grow slowly But, policy makers can influence these parameters. What is the evidence regarding convergence? Looking at all the countries in the diagram, there appears to be no negative correlation between growth and GDP – if anything, there is divergence between the rich and poor countries. Breaking up the countries into OECD and African countries, there appears to be convergence within the OECD. The poorer ‘rich’ countries have tended to grow faster than rich ‘rich’ countries. African countries have no tendency to grow faster than the rich countries. Countries within the OECD, arguably, have access to the same kind of technology (infrastructure, government stability, financial sector).

Conditional convergence: So far, it has been assumed that rich and poor countries have the same Cobb-Douglas production function – in other words, they can produce the same amount of output from a given amount of labour and capital. This may not necessarily be true – richer economies could have more efficient production processes (i.e. the technology, A, is not the same). Conditional convergence states that countries have their own steady states, and more similar economies have steady states closer to one another (e.g. the OECD countries). This is arguably because, after the Second World War, richer countries began to import from the US – making cars, planes and tanks with US production line technology. 2 countries, marked red and blue, have the same savings rate, the same depreciation rate, the same share of capital and output, but different technologies. The red country has a higher efficiency – i.e. a greater ability to turn capital per worker into output per worker. Hence, its output line is above the output line of the blue economy. Thus, they converge to different steady states – but no convergence between red and blue.

Introducing 9 Asian countries (‘tiger’ countries), it can be seen that there is evidence of convergence between the industrialising Asian nations (Hong Kong, S. Korea, Singapore, Taiwan, Indonesia – and later India and China) and earlier industrialised European countries, Japan and the US. Asia diverged from Europe before the 1950s, but since then there is some evidence of convergence – even if the rate of convergence is slower than the Solow model would predict.

Summary: - There has been sustained economic growth for c.200 years in countries with competitive markets - Capital accumulation is important – but technological progress is required for sustained, long-run growth - Poorer countries with good technology grow quickly – there is convergence between countries with similar technology levels - There is divergence between the leading ‘convergence club’ and the poorest countries with lowest levels of total factor productivity (primarily African countries)

Exogenous technical progress in the Solow Model: In the original Solow equation, A (level of technology) is fixed. With technical progress, A grows exponentially at rate x: Technical progress is associated with labour productivity, so it is given the same exponent: It is now not total factor productivity but labour augmenting productivity. I.e. as the state of technology improves, it makes each worker more productive by ‘augmenting’ their labour. Capital (k) and output (y) per worker y now grow at rate x. There is a steady state in ‘capital per efficiency unit’ (rather than capital per worker) – i.e. in capital per technology-augmented worker:

Living standards rise at the rate of x (technological progress). ŷt and kt reach steady state values. The economy is in steady state when there is no change in capital per efficiency unit. Technological progress shifts the depreciation curve inwards – as the value of x increases. This reduces capital per efficiency worker – each technology augmented worker does not need as much capital as efficiency units are being added into the economy as a result of the technological growth – labour productivity has increased due to the increased technology level of capital Endogenous technical progress – research & development: In the Solow model, improvements in productivity appear at no resource cost, and access to new technology is non-excludable. Economists visualise the ideas that result in innovation as blueprints – once blueprints are available (e.g. how to build the latest plane), anyone can use it. Hence, ideas in the context of innovation are non-rivalrous. The non-rivalrous nature of ideas promises social benefits, as everyone can benefit from them without diminishing the availability to others. However, at least for some time period, ideas are excludable. Patents is one method that allows firms to earn supernormal profits. Paul Romer: Long-run growth comes from effort directed at productive research. - Output produced by workers using physical capital, labour and the stock of ideas (the ‘blueprints’ for goods and machines) - Such ideas are produced by a second type of worker in the R&D sector (though such workers do not contribute directly to output and GDP in their day to day work, their output is the rate of technological progress) - There are constant returns to scale in production of ideas – diminishing marginal returns, as with the production of physical output, are not experienced. The growth rate of technology is a function of the number of workers employed in R&D. - The are some positive spill-overs in the R&D sector to justify this scaling. - Model is quite mechanical, simple and internally logical. But, correlation between R&D investment and economic growth is not particularly strong (though not completely rejected), according to the data.

Aghion and Howitt (after Schumpeter): Creative destruction. - Schumpeter identified the entrepreneur as the key agent in the process of innovation – they implement new discoveries and bring them successfully to the market - Innovations may include developing a new route using existing FoP; a new product or improving quality of an existing product; or a completely new market. - ‘Creative destruction’ captures the dual nature of technological progress: the ‘creation’ is entrepreneurs introducing new products or processes in the hope of temporary monopoly profits (innovation rents) as they capture markets. The ‘destruction’ comes as a result, as old technologies or products become obsolete. - Entrepreneurs have an incentive to make risky investments in order to make temporary profit. Imitation can be prevented through patents, trade secrets and being a first mover. - The greater the scale of the economy, the bigger the market for innovations

The Business Cycle: Aggregate Demand and the IS Curve: Business cycle fluctuations are not just a supply side phenomena – demand shocks will play a crucial role. Aggregate Demand: yD = C + I + G (closed economy)

Simplified consumption function - Taxes T = ty are a constant fraction of output (or a fixed proportion of income) - Consumption is a function of disposable income y – T (T is total taxes net of transfers) c0 being autonomous consumption, c1 a positive number less than one. (2) relates total consumption C to aggregate output in economy (y). - This defines the Marginal Propensity to Consume out of disposable income:

Substituting model of household consumption,

Exogenous part of AD (not being modelled): - Autonomous consumption, c0 - At this stage: firms’ demand for investment, I, and government purchases, G AD also depends on aggregate output through C1(1 – t)y. Output is exogenous – this gives rise to the multiplier effect.

Output and Aggregate Demand: The ‘Keynesian cross’: The same quantity of output, y, is produced and purchased when y = yD. There is goods market equilibrium where the 45° line crosses the AD curve. The point where the two intersect shows the level of output where planned expenditure by firms, households and government is exactly equal to the level of goods being supplied in the economy.

What happens if there is increase in aggregate demand (e.g. government spends money): Initially, the AD curve shifts upwards, taking into account the increase from G to G1. Aggregate demand now exceeds output (at point B). As government increases purchases of goods (e.g. office equipment) the stocks of these goods in warehouses decline. Inventory management triggers an increase in production, and output rises. This is the movement from B to C. This higher output in turn raises incomes (wages of additional workers employed and profits of owners of firms making higher sales). Some proportion of the higher incomes is spent on goods and services in the economy, raising AD further. This process continues, iterating until there is convergence of yD and y. Output has increased more than the initial change in government spending. Quantity Equilibrium in the Goods Market: Quantity equilibrium between output produced, y, and demanded, yD: y = yD Demand depends on C, exogenous I and G. Hence:

(4) uses (3) to give an equation in terms of output, investment and government purchases. Output (endogenous) is determined by the parameters c0 (autonomous consumption), c1 (mpc) and t, and the exogenous I and G components of AD (which at this stage have not been modelled). From (4), the level of output where supply and demand match can be found:

Output is equal to a multiple of the exogenous spending plans of consumers, c0, firms, I, and government, G. The multiplier, k, describes the conclusion of the iterative process which determines the effect of the demand shock. Because c0 and t are between 0 and 1, this implies that the multiplier is greater than 1. Hence, a 1% ↑G will lead to an increase in output of more than 1%. This is the short-run multiplier, as the interest rate and all other policy responses are held constant. The multiplier increases as the mpc increases or as the tax rate decreases.

Aggregate Demand to the IS curve: Output and the interest rate - ↑i rate: - ↑mortgage rates → ↓spending on new housing, ↓consumer durables, ↓income to spend on other consumption - Households postpone consumption as ↑returns to saving - ↓income of debtor households - Putting these together, these outweigh the +ve income effect for creditor households - Higher borrowing costs reduce firm investment in new equipment as it increases the level of profitability required for such investment to pay off The IS (Investment/Saving) curve: Shifts of IS curve: - Changes in income growth expectations - Changes in degree of uncertainty - Changes in the collateral value of firm and household assets (collectively known as changes in ‘autonomous’ consumption/investment) - Changes in government purchases Movement along the IS curve: - Change in the interest rate (e.g. base rate set by CB)

There is a strong correlation between interest rate and investment changes – higher interest rates are associated with lower growth in future investment, The investment...