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## EC:250 Intermediate Macroeconomics!

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**EC:250Intermediate Macroeconomics!**By: David Cade and Luke Sinclair**Today’s Schedule**• Cover each chapter in detail • We will have examples after each concept so don’t worry if you don’t get it right away • Questions • Go over some more in-depth, comprehensive questions • Exam study tips • Additional resources**[Definitions and Ratio’s]**• Definitions: • Employed: Paid full time or part time employment • Unemployed: Available to work and has actively looked for work in the last 4 weeks • Not in the Labour Force: Not employed and under 15 years of age or has not looked for work in the past 4 weeks • Ratios • Employment = [E] • Unemployment = [U] • Labour Force = [L] = ([E] + [U]) • Unemployment Rate = [U] / [L] • Labour Force Participation Rate = [L] / population above 15**[Trends and Natural U]**• Employment Trends • Women entering the workforce • 1950’s-1990’s steady increase in employment • 2000-2005 unemployment back to lower levels • Natural Unemployment: [u*] is the average level of unemployment over a given time (usually 20+ years) • s fraction of employed [E] people who become unemployed in a given month • ffraction of unemployed [U] people who become employed in a given month • Formula: [u*] = s / (s+f)**Example**• Determine the Natural U if: • 0.3% of employed individuals become fired each month • 5% of unemployed people find work every month 0.003 = 0.0566 or 5.7% 0.003+0.05**[Frictional Unemployment]**• Frictional Unemployment: Unemployment caused by the time it takes workers to find a job • Comes from • Sector shifts • Technology change • Business failures • Individual factors • Fired / Quit • Geographic Mobility • Why it lasts • Imperfect job information (job searching takes time) • Geographic immobility (most workers cannot just pack up and move) • Policies that affect frictional unemployment • Employment Insurance raises the rate of frictional unemployment • Employment agencies can aid unemployed • Retraining programs encourage companies to retrain rather than lay off “In between jobs”**[Structural Unemployment]**• Structural Unemployment: Unemployment due to a mismatch between demand and supply of labour • This is caused by real wage rigidity and job rationing • Real wage rigidity: Failure of wages to adjust so that labour demand = labour supply • If wages are too high compared to demand Job rationing Real Wage Labour Supply Rigid Real Wage Structural Unemployment Employment Equilibrium Wage Labour Demand**[Reasons for Wage Rigidity]**• Minimum wage laws • Raise the real wage above the market equilibrium • Refundable tax credits: Better way to increase incomes for the poor (as this does not affect labour costs) • Unions • Raises wages above equilibrium through collective bargaining • Raises wages at non-unionized firms • Efficiency Wages • Higher wages = more productive workers Real Wage Labour Supply Minimum Wage Unemployment Minimum wages raise the real wage above equilibrium and create unemployment Employment Equilibrium Wage Labour Demand**[Employment Explained]**• Incidence of unemployment: The chance that a worker will become unemployed (increase in unemployment is 1/3 a result of an increase in incidence)** • Duration of unemployment: Average spell of unemployment (increase in unemployment is 2/3 a result of an increase in duration) • Upward shift in unemployment from 1950’s-1990’s: • Changing Composition: More young workers / women • Faster Sectoral Shifts: Increased pace of technological change • Skill Based Technical Change: Led to lower employment rather than lower wages**The Growth of GDP**• In chapter 3 K and L are fixed and thus determined the level of real GDP Y = F(K,L) • In reality: • K increases with capital accumulation • L grows due to population growth • If there are constant returns to scale (z), calculating Growth is simply zY = F(zK,zL) • If both K and L grow by 5%, Y will grow by 5% • What if they grow by different percentages though?**The Growth Accounting Eq’n**• The Growth Accounting Equation • α is the elasticity of Y with respect to an increase in K • 1-α is the elasticity of Y with respect to an increase in L • This equation makes no sense. Explain! • The growth rate of output can’t be more than the growth rate of either K or L as it is a function of the two • Its growth needs to be a balance of the two L K**Growth Accounting: Example**• Let’s take Canada: • We have lots of really old people leaving the workforce • Growth rate of labour is low: 0.5% • Elasticity in Canada is low: 1/3 • On the other hand we have a lot of capital accumulation • Growth rate of capital is strong: 6% • What is the growth rate of output (Y)? • %∆Y = (1/3)*0.06 + (2/3)*0.005 • = 0.02 + 0.0033 • = 2.33%**Useful Metrics**• Growth Per Capita (y) • Determined (intuitively) by dividing output (Y) by the number of units of labour (L) • y = Y/L • Increases when your output is growing faster than your labour force • It means your labour is getting more efficient, not just more numerous • ∆y = ∆Y/Y - ∆L/L • Capital Per Worker (k) • Same deal: k = K/L • Technological Progress (A) • An index of the productivity of capital and labour represented by A • Growth rate of A or ∆A/A is the rate of technological progress • So Growth accounting equation becomes: • ∆Y/Y = ∆A/A + α*∆K/K + (1- α)*∆L/L • Single most important source of Canadian growth in Y and y**Solow Growth Model**• This model shows how the long-run equilibrium growth is determined by three factors: • The rate of savings • The rate of population growth • The rate of technological progress • Start Simple: No population growth or technology • We assume constant returns to scale • zY = F(zK, zL) • Because of this output per worker is a function of only capital per worker • Why…? We can now substitute z for 1/L to find y • Y/L = F(K/L,L/L) y = F(k, 1) y = f(k) • This is called the per capita production function • y = f(k)**Solow: No pop. Or tech.**• y=f(k) • It has a positive slope but diminishing returns • If you invest more capital into better equipment you are going to get a better return but this is not constant • The slope = marginal product of capital (MPK) y (output per worker) k (capital investment per worker) f(k): per capita production function MPK**Solow: No pop. Or tech.**• Investment per worker (i) • Need investment in order to get capital accumulation • Determined solely by the savings (s) per worker • i = sy i = sf(k) • Once again, diminishing returns y f(k) k ∂k sf(k) • Depreciation (∂) wears machinery down ∂k**Solow: No pop. Or tech.**• Steady-State (k*) • As worker investment growth increases, output per capita increases • However, depreciation also increases because there is more depreciable capital • This lowers capital per worker • So: ∆k = sf(k) - ∂k • When worker investment is equal to the rate of depreciation (∆k=0) this is called the “steady-state” level of capital stock per worker • It is denoted by k***Solow: No pop. Or tech.**• The actual level of capital per worker will always increase or decrease to equal to the steady state in the long run • If the rate of investment is greater than the depreciation then k will continue to increase but by diminishing returns • This increase in k will result in an increase to the amount that is depreciated until sf(k)=∂k and k = k* y k* f(k) ∂k k sf(k)**Example 1**• We start with a basic economy at steady-state equilibrium y s1f(k) k1 f(k) ∂k k**Example 1**• Suppose savings rate increases from s1 to s2 • s2f(k1) > ∂k1 y s1f(k) k1 f(k) ∂k k s2f(k)**Example 1 cont.**• Suppose savings rate increases from s1 to s2 • s2f(k1) > ∂k1 • The rate of investment is greater than the rate of depreciation so capital stock is increasing faster than it is depreciating. • k increases • As k increases, more is being depreciated • Eventually k increases to the point where the rate of depreciation and the rate of savings are equal (k2) y s1f(k) k1 k2 f(k) ∂k k s2f(k)**The Golden Rule**• Based on the previous example, we see that for every level of savings there is a steady state that will result over time • Is there a steady state that is better than the others? • There is and it is called the Golden Rule level of capital • Denoted by k*gold Pictured: Wrong Golden Rule**The Golden Rule**• The Golden Rule level of capital is not determined by output or capital, we care about buying more stuff! • So we look at maximizing consumption per capita (c): • Consumption per capita at the steady state (c*) is equal to the the vertical distance between the per capita production function and the depreciation line • In other words, c* = f(k*) - ∂k* y f(k) k ∂k c* sf(k)**The Golden Rule**• We want to maximize c* • c* is greatest where the slope of the per capita production (MPK) function equals the slope of the depreciation line • In order to increase consumption per capita, the economy should increase or decrease the savings rate y slope f(k) k ∂k c*gold k*gold**Example**• We want to maximize c* • c* is greatest where the slope of the per capita production (MPK) function equals the slope of the depreciation line • We are not at the Golden Rule level of k*. What do we do? y f(k) k ∂k k***The Golden Rule**• Increase the level of savings! • The economy increases the savings rate • This will result in less per capita consumption (y) in the short term • But greater per capita consumption in the long term y f(k) k ∂k k* k*gold**Solow: Adding Population**• We now assume that population and labour force grow at a constant annual rate (n) • Now, if k is to increase it needs to outpace both the depreciation, and also the growth in the number of workers • Need to equip more workers • So we add the growth rate to the depreciation line y f(k) (∂ + n)k k As before, the steady state is where the change in k is 0. So, where: (∂ + n)k – sf(k) = 0 sf(k)**Example**• Start off in steady state of an economy with population growth • Suppose the rate of population growth decreases • So n↓ changing the slope • No longer in steady state • Rate of saving is greater than depreciation and population growth rates y y y1 k*1 f(k) f(k) (∂ + n1)k (∂ + n1)k k k (∂ + n2)k sf(k) sf(k) y2 y1 k*1**Example**• k* increases in the longterm • Output per worker (y) increases as well y y (∂ + n2)k k*1 k*2 f(k) f(k) (∂ + n1)k (∂ + n1)k k k (∂ + n2)k sf(k) sf(k) y2 y1 k*1 k*2**Solow: Adding Technology**• The result: • Labour input is improved by increases to the efficiency of workers • So we now measure Labour in terms of “effective workers” • Equal to the number of workers (L) multiplied by worker efficiency (E) • Y = F(K, L*E) • E grows at a constant annual rate (g) • If we include the rate that the population increases (n) then we can say that the effective number of workers (L*E) is growing at a rate of n+g We have the technology!**Solow: Adding Technology**• Now when we look at per capita production, we are looking at production per effective worker • y = Y/L*E and k = K/L*E • Steady State with technological progress • ∆k = sf(k) – (∂+n+g)k = 0 • So NOW we need enough savings to meet: • The depreciation in capital • The cost of equipping new workers • AND the cost of equipping the new effectiveness of workers that is being created by technological progress**Solow: Adding Technology**• Here is what the graph looks like now y f(k) (∂ + n + g)k k sf(k)**Empirical Growth Studies**• Prediction of balanced growth • Solow predicts that total output will grow at the same rate as the total capital stock and output per actual worker • Prediction of convergence • Similar economies that start at different levels of capital accumulation will converge in the long run. Dissimilar economies will exhibit conditional convergence where they converge on their own steady states.**Policies to Promote Growth**• Increase the Canadian Saving Rate • Run a budget surplus • Raise private savings • Reduce investment taxes • Emphasize sales tax instead of income tax • Tax-free savings initiatives • Promoting Investment • Eg. Investment tax credits, R&D credits • Policies on allocating investment • Government can invest in forms of capital with positive externalities (social return) • Eg. Infrastructure, human capital etc. • Policies to encourage technological progress**[Chapter 9: Intro to Economic Fluctuations]**Cycle of economic stock fluctuations**[Intro to Short Run and Long Run]**• Short Run • Prices and/or wages are sticky • Business Cycle significant part of short run economics • The business cycle is unpredictable (expansion followed by recession) • Long Run • Prices are fully flexible • Assume full employment of labour and capital**[Long Run AD-AS Model]**• Aggregate Demand Curve [AD Curve] • The AD curve shows how [Y] (quantity of output) varies with [P] (price level) for given values of [M] (money supply) and [V] (velocity) P Aggregate Demand Curve Y**[Complete Long Run AD-AS Model]**LR Impact of a Increase in M P LRAS P1 Y P0**[Short Run AD-AS Model]**• Aggregate Supply Curve [AS Curve] • The AS Curve shows how [y] (supply of output) varies with [P] (price level) in the short run P Aggregate Supply Curve Y SRAS**[Complete AD-AS Model]**SR Impact of a Increase in M P SRAS Y y0 y1**[Summary of a Demand Shock]**• M or V • SR • Y P • LR • Y P • M or V • SR • Y P • LR • Y P IN THE LR MONEY OR VELOCITY HAVE NO IMPACT**[Planned Expenditure Curve]**• Assumptions based on Keynesian-Cross Model: • E = C + I + G • C = MPC(Y-T) • I = I G = G T= T E E0 Y C0 Planned Expenditure Curve y0 What is the slope of the PE Curve???**[Equilibrium of the Economy]**• Output adjusts so that Y = E • If E-Y < 0 Output will decrease • If E-Y > 0 Output will increase E EE Y 45◦ yE**[Equilibrium Example]**• A decrease in G • Unplanned inventory buildup • Firms produce less E E0 Y E1 45◦ Y1 Y0**[Government Purchases Multiplier]**• Definition: The amount by which equilibrium Y changes following a one unit change in G: • Example: • MPC = 0.75 • Purchase Multiplier Thus a $1.00 decrease in government spending will reduce equilibrium Y by $4.00**[Tax Multiplier]**• Definition: The amount by which equilibrium Y changes following a one unity change in T: • Example: • MPC = 0.75 • Purchase Multiplier Thus a $1.00 increase in taxes will reduce equilibrium Y by $3.00