ECON 362 - Lecture notes Half of the Semester PDF

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Lecture notes for half of the Fall 2019 Semester...

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ECON 362

I. Macroeconomic Phenomena and Questions (What the course is about)! A) Economic growth and development ! 1) Facts! a)Output or Income per person across countries! b) Output per person over time - “Great Divergence” ! 2) Questions! a) Why are some countries, rich, poor?! b) Why are rich countries more productive now than in 1800?! c) Can we make poor countries rich? ! B) Inflation, Deflation ! 1) Facts ! a)People don’t like it (BUT when price goes up so do wages)! b)Varies across countries, and across time ! 2) Questions ! a) What causes it? ! b)How can we control it? ! C) Business Cycles ! 1)Facts: recessions and booms ! 2) Questions ! a) What causes them?! b) How can we avoid recessions?

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II. Macroeconomic Statistics, Mankiw Ch. 2 ! A) Intro ! 1) Prices and quantities! -In Macro, we talk about many markets at once (aggregate) ! -Supply and Demand Curves with P&Q, i.e Wages & Labor Q! 2) Real versus nominal! Quantities = Real! Prices / Wages / $ = Nominal! Price x Quality is measured in $, so it is nominal! B) Unemployment, unemployment rate ! 1) Theoretical concept! Unemployed— Not working or in school but wants to work and is willing to work at a reasonable rate! Reasonable— Wage earned by people with similar qualifications! Qualifications— Eduction & Experience! 2) Statistic: civilian unemployment rate ! a) Monthly survey! -Used to estimate / guess— representative survey. Telephone! b) Defining people as unemployed ! -No job, actively looked in last 4 weeks, currently available for work! -Looking— Job interview, talked to people, put up ads, etc. ! c) Unemployment rate ! = Number Unemployed x 100! Number Unemployed + Number Employed (Including Self)! -“Civilian Unemployment Rate”— Excludes active military ! -Administered by BLS! -Unemployment can be higher / lower for specific demographics

!

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C) Price indexes! 1) Concepts ! a) Price level— Prices of individual things changing over time. The prices going up or down. Average movement.! -Price goes up— “Price level is Rising”— Inflation! -Price goes down— “Price level is Falling”— Deflation! -“Price level is Stable”! b) Price index— Takes prices of individual goods every month or year! Year

!

Price Index

% /\

1919

74

1920

70 (70-74) 74

x 100 = -5.4% DEFLATION

1921

72 (72-70) 70

x 100 = 2.9% INFLATION

c) What goods & services are included?! Answer is different depending on Price Index! -CPI (PCE)— Consumer Price Index— Prices of goods and services purchased by households. “Cost of living”! -Households— Families / Individuals living by themselves! -Changes in CPI indicate changes in costs of living! 2) Going from levels to percent changes (inflation rates) and vice-versa! Before we did Price Index —> Percent Change. This is opposite.!

!

Year

% /\

Price Index

1933

Pick random number, 1. [a]

1934

7% 1+(.07•1) = 1.07•1 = 1.7 [b]

1935

3% 1.7-(.03•1.7) = 1.38

b = a + (.07 • 1) c = b - (.03 • b)

Common Formula: b = a + (% • a)

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3) Mathematical formulas! -We change the quantity to see significance of prices! -Things that firms sell more of count more in the price index! a) Formulas matter— Price Index will be different depending on formula used! b) Formula types ! i) Laspeyres— Use quantities in the earliest year ! ii) Paasche— Use quantities in the most recent year ! iii) Fisher— Use geometric average (Most ideal) ! c) Geometric average! -Different than arithmetic average (x+y / 2)! -Multiply together and take root.! i.e 10,12: √(10•12); 10,12,40: 3√(10•12•40)! 4) Examples (Excel spreadsheet on website)! a) Laspeyres (High inflation bias)! b) Paasche (Low inflation bias)! c) Fisher ! 5) Which is best? Fisher! a) Price index is weighted by quantities! -Inflation rate shown by Price Index will be strongly effected by percent change in price of goods with big quantities ! b) Some prices change a lot between two years, some only change a little ! c) Quantities used to weight and "bias" in a price index! -Bias— If theres big quantities on things where price changes a lot, will heavily affect inflation. Small quantities and not a lot of price changes = low inflation! d) Demand curves slope down! -When Price Increases, Quantity Decreases b/c of price curve! e) Paasche price index gives a relatively low number for inflation! -Uses latest year. ( Q↑ PL ↓ )! f) Laspeyres price index gives a relatively high number for inflation ! -Uses earliest year. ( Q↓ PL↑ )!

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g) Fisher price index is in between ! 6) US price indexes ! a) CPI— Goods and services that households buy.! Formula: Mix of Laspeyre’s and Fisher’s! Recorded monthly ! b) PCE price index— Personal consumption expenditure. Covers same as CPI ! Formula: Entirely Fisher! Recorded quarterly, not monthly! c) GDP price index! Covers everything. ALL goods and services.! Formula: Fisher. Released quarterly! D) GDP! 1) Concepts ! a) Output of goods and services! -NOT prices (nominal will combine this)! b) Final versus intermediate goods and services! -Lots of goods and services produced and sold are just used as inputs of further productions of other goods and services. i.e Raw cotton, Landscaping a hotel ! c) Domestic output of final goods and services! -Within borders of U.S. Anything produced abroad doesn't count ! d) Depreciation! -Cost of replacing worn out equipment. Can apply to country or business.! e) Gross versus net of depreciation! -Gross— Not subtracting cost of depreciation! -Net— After subtracting cost of depreciation! 2) Definition of GDP! a) Gross domestic product— The output of final goods and services produced within the borders of the United States, gross of depreciation. ! -Intermediate goods vs. Capital! -Capital— Computers, factory machines, roads, etc. -Capital DOES count in GDP!

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-Capital is used again and again, unlike intermediate! b) Nominal GDP ! -Price • Quantity. Current dollar value of GDP! c) Real GDP! -Just quantities added together! 3) How we measure nominal GDP: value-added ! a) Establishment— A producing unit in one place controlled by a firm. i.e Factory, office, shop, university! b) Value-added by an establishment! -VA = $ Value of Output - Intermediate Goods & Services! i.e Fuel, Business Services, Raw Materials! c) Total VA equals nominal GDP (example on website) ! -Only add what hasn't been used before (intermediate)! 4) How we measure real GDP! a) Review: Fisher price index! b) Quantity index ("chain-weighted real GDP")! -Do exact same thing as Fisher, but instead of changing quantities, change prices and keep quantities the same! -Uses price as weights! -Calculated by Bureau of Economic Analysis! c) Chained-dollar real GDP estimate! -Take real GDP quantity index (base year value 100). Rebase it, so that value in base year is NOT 100, but another number. Instead, make it equal to nominal GDP in that year. ! -Take Nominal GDP ÷ 100, and multiply it by real GDP! -People just want to make real GDP look like dollars! -**Don’t really have to know how to calculate it, just know its how we calculate Real GDP**! E) GDP and income of Americans ! 1) Definition: "factor income" (wages, profits, rents)! -Factors of Production: Land (resources), Labor (Workers & Management), Capital (Infrastructure).! -Factor Income— Income paid to owners of factors of production for use of factors by establishments.! -Including: Waged Salaries, Rent paid for establishments, Profits !

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-Employees are owners of labor! 2) Review: value-added of an establishment! 3) Value-added equals total factor income paid out by an establishment! -Value of Output - Cost of Intermediate Input = Value Added = Factor Income! 4) Does GDP equal total income of Americans? No. ! -But almost. Why not exactly? Some American establishments make payments to foreigners. A lot of Value-Added doesn't go to Americans, we also get income FROM foreigners. ! F) GNP (or GNI, gross national income) ! 1) Definition— GDP - Factor Income paid by U.S establishments to foreign residents + Factor Income paid by foreign establishments to U.S residents! 2) GNP (GNI) equals total income of Americans! -In U.S GDP & GNP are very similar, but in smaller countries numbers are further apart.! G) How unemployment rate, real GDP and inflation move over time ! 1) Long-term trends ! 2) Business cycles III) Capital, Labor and Output Mankiw Ch. 3-1, 3-2 Intro! -Models are used to think about how much stuff an economy can produce! B) Factors of production (whats used in the models)! 1) Labor! L = Labor Input / Quantity of Labor used in an economy! L = # of Employees • Hours per employee! Ł = A particular quantity of labor (particular country at a particular time)! Ł = Labor Force • (1 - Ú÷100)! Ú = “Normal” unemployment rate! If U = 6%, then Ł = Labor Force • 0.94! If theres a bar over a letter, we don't mess around with its value! 2) Capital! -Goods and services that are used to produce other goods, and are

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used over and over again! i.e Machines, shovels, Xerox machines, buildings, roads, software! -Need to aggregate these things into 1 number! -“K”— Index number that measures quantity of capital in an economy! -K — Particular quantity of capital at a particular time! 3) Inputs we’re ignoring ! a) Land & other natural resources! -If you look at rich countries, land does matter much ! (Output in Japan = Output in U.S)! b) Skills of workforce (i.e Literacy)! -Only ignoring for simplicity! C) Aggregate production function ! 1) General definition! Y= Output (Real GDP), K= Capital Index Number, L= Labor Input! There is a relationship between these 3! Y = F(K+ , L+) = Aggregate production function! The + means if you make K or L bigger, you get higher GDP! i.e My Fatness = G(Martinis+ , Pork+, Miles Ran Per Week-)! Ÿ = F(K, Ł)— There always needs to be positive relationship between K and L! Y = 2K + 3L OK! Y = 30 + 2K + 3L OK! Y = 2K + 3÷L NOT OK (Negative relation between Y and L)! Y = K^2 + L^3 OK! Y = K • L OK! Y = K^(1/2) • L^(1/2) OK! -If technology changes, production function changes! 2) Constant returns to scale (we want this)! a) What we observe across countries! -No relationship btwn size of country & output per person! b) CRS: definition ! -A property of some production function. If you double all inputs, you get exactly twice as much output. (Double, triple, half, etc.)! -If inputs are doubled, output doubles (exactly proportional)!

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-On aggregate scale, all countries should have CRS! z = some number like 2 or 1/2! zY = zK • zL. Holds only if CRS! -Relies on fact that size of country doesn't affect output! 2 Ways to check if theres Constant Return to Scale:! 1) Compare zF(K,L) with F(zK,zL) algebraically! 2) Compare Y = F (2,2) with F (4,4)! Example

Method 1 (Algebra)

Method 2 (Good way to check)

CRS?

Y = 2K + 3L

z(2K + 3L) = 2zK + 3zL! 2zK + 3zL = 2zK + 3zL

F(2,2) = 10! F(4,4) = 20

YES

Y = 30 + 2K + 3L

z(30 + 2K + 3L) = ! 30 + 2zK + 3zL 30z + 2zK + 3zL ≠! 30 + 2zK + 3zL

F(2,2) = 40! F(4,4) = 50

NO:! Decreased! Return to! Scale

!

Y = 2K + 3÷L

NO:! Not Production Function

Y = K^2 + L^3

z(K^2 + L^3) = (zK)^2 + (zL)^3! zK^2 + zL^3 ≠ (z^2)(K^2) + (z^3)(L^3)

F(2,2) = 12! F(4,4) = 80

NO:! Increased Return to Scale

Y = K•L

z(KL) = zK • zL! zKL ≠ zK • zL

F(2,2) = 4! F(4,4) = 16

NO:! Increased Return to Scale

Y = K^1/2 • L^1.2

z(K^1/2 • L^1.2) = zK^1/2 • zL^1/2! zK^1/2 • zL^1/2 = zK^1/2 • zL^1/2

F(2,2) = 2! F(4,4) = 4

YES

3) Marginal product! -We want relationship between Marginal Product & National Income— This is the third condition ! -The one that will do this looks like a variation of of ! K^(1/2) + L^(1/2). This is the only kind of Aggregate Production Function that satisfies this third condition! a) General definition— Relationship between inputs and outputs. What happens if you increase 1 input and keep others the same?!

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i.e Adding 1 labor to same capital or 1 capital to same labor!

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b) MP of labor! -MPL = F(K, L+1) - F(K, L)! i.e Y = 2K + 3L! MPL = 2K + 3(L+1) - (2K + 3L) = 2K +3L + 3 - 2K - 3L = 3! Y = K^1/2 • L^1/2! MPL = K^1/2 • (L+1)^1/2 - (K^1/2 • L^1/2)! -In order to know exact MPL, we must know value of K & L! c) MP of capital! -MPK = F(K+1, L) - F(F,L)! d) MP and calculus (partial derivatives)! Y = K^(1/2)•L^(1/2)! DY/DK = MPK = 1/2•K^(-1/2)•L^(1/2) = 1/2•(K/L)^(-1/2)! DY/DL = MPL = 1/2•K^(1/2)•L(-1/2) = 1/2•(L/K)^(-1/2)! Y = 3K + 3L! MPK = 3 MPL = 3! e) Diminishing MP ! i) Defn! -Factor x (L or K) has diminishing MP if MP of x falls as you add more x to production while holding fixed quantities of other factors.! -F(K+2, L) - F(K+1, L) < F(K+1,L) - F(K,L)! -Extra Y from K+1 to K+2 is less than extra Y from K to K+1! -True for some Production Functions, but not others!

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ii) In a graph ! Constant MPL

Diminishing MPL !

! ! !

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-Slope of the line is the MPL! -In Diminishing MPL, slope is getting smaller as we get more labor.! iii) Examples ! -A Production Function that does NOT have Diminishing MP or L or K:! Y = 2K + 3L. MPL = 3. Slope always 3. K shifts line! MPK = 2. Slope always 2. L shifts line! -A Production Function that does NOT have Diminishing MP or L or K:! Y = K^(1/2)•L^(1/2) MPK = DY/DK = 1/2(K/L)^-1/2! MPL = DY/DL = 1/2(L/K)^-1/2! More K or L respectively = smaller slope! -Constant Return to Scale and Marginal Product are completely different things. Return to scale is the effect of changing the quantities of all factors in same proportion. MP only changes one quantity at a time. PF’s can have any combination of the 2.!

ECON 362 !

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D) Factor Prices, Factor Demand and Incomes ! 1) Simplifying assumptions (in model economy)! a) Homogenous K & L! -All units of L exact same productivity (labor hours all same). All units of K are exactly the same and can be used for anything by any firm.! b) Employers maximize profit! -Usual assumption for economic models. Should be fairly realistic.! c) All labor, capital and product markets perfectly competitive ! -Not true, does matter a lot. Still need to assume this. ! -Very unrealistic! i.e No Unions! $W = Wages = Earnings of employees & Cost of labor to employees! $R = (Rental) cost of capital. Assumes all K is owned by people and rented to firms.! -Income of owners of K & Cost to firm of using K! Profit? In perfectly competitive market, there is no economic (supernormal) profit! -All firms are getting “normal profit” which isn't really profit. All either ($R)— payment to capital owners, which would look like economic profit if the owner of the firm is the owner of the capital OR ($W) manager of firm’s income. ! -All income paid out by establishment is either W•L (Labor Income) or R•K (Capital Income)! 2) Real factor prices! $W— Wage! $R— Rent for capital! $P — Price Level— Price of a unit of output Y! Real Wage— W÷P — How much stuff an employee can buy with wages from an hours labor! Real Rental Price— R÷P!

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3) MP and factor demand ! a) General principle! -Firms (profit-maximizing) always hire the quantity of labor so that the MP of labor is = to the real wage. (MPL = W÷P)! -Same applies for capital so that MPK = R÷P! b) Labor! -On average, price of output is price level (PL)! -P•MPL = Amount of extra revenue firm will get if it hires one more unit of labor! -Must compare that number with wage (cost of hiring unit)! -If P•MPL > W, then hire more labor! -If P•MPL < W, the fire some labor! -If firm is maximizing profit, P•MPL = W! -P•MPL = MPL = W÷P (When maximum profit)! P!

W

= P•MPL

= L!

= MPL

= L!

! OR ! ! W/P ! Same concept for capital

!

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c) Capital ! -Firm compares MPK•P with R! -To maximize profit, P•MPK = R, MPK = R÷P! 4) Division of national income ! -Total income means GNP = Wages + Salaries! Total Income! -Only agg production function that will give us this constant for Labor’s share of national income is Cobb-Douglas!

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a) Income and MP’s ! Y = Total output (Real GDP), about = to real income! Y = F(K,L)! PY = Nominal GDP! wL = Total Labor Income in $ (How much they're paid)! (W÷P)L = Total real income of workers (Real stuff workers can buy)! RK = Total Income paid to capital workers! (R÷P)K = Total real income received by K owners! (W÷P)•L = MPL•L = Share of national income going ! Y Y to labor! = Real Income Going To Labor! All Income! (R÷P)•K = MPK•K = Share of national income going ! Y Y to capital! = Real Income Going To Capital! All Income!

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When firms maximize profit, W = MPL! b) Zero economic profit and Euler’s theorem (calculus) ! Y = (MPL•L)+(MPK•K) aka (W÷P • L) + (R÷P • K)! Total Real Income = Labor Income + Capital Income! Divide both sides of equation by Y: ! (MPL•L)+(MPK•K) OR MPK•K = 1 - MPL•L! Y Y Y Y! OR MPL•L = 1 - MPK•K! Y Y! F(K,L) = [F(K,L+1) - F(K,L)]L + [F(K+1,L) - F(K,L)]K! dY/dL + dY/dK! Is this possible mathematically?! Euler’s Theorem— This can be true if aggregate production function has constant returns to scale

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E) Cobb-Douglas production function ! 1) What it is! -Any production function that looks like ! F(K,L) = A•K^α •L^(1-a)! -One example: A=1, α = 1/2, F(K,L) = A•K^(1/2) •L^(1/2)! -A = parameter used to describe things like changes in technology! 2) Always has CRS (calculus)! Is A•(zK)^α • (zL)^(1-α) = z(AK^α•L^α-1)?! zY = z(AK^αL^1-α) = A•(zK)^α • (zL)^(1-α)! zAK^αL^α-1 = zAK^αL^α-1! 3) Allows constant income shares ! a) Fact! -K÷L varies from decade to decade, but almost no change in! (W÷P)L = ~.7 or 70% (R÷P)K = ~.3 or 30%! Y Y! -As K÷L increases, MPK decreases (Diminishing MPK) =! Decrease in R÷P (Real Rental Rate) tends to reduce capital’s share of income and raise labor’s share of income! -But, increase in K÷L tends to increase capital’s share of income! -In reality, these 2 forces seem to balance out! b) How CD allows constant income shares! -MPL = dY/dL = W÷P! -MPK = dY/dK = R÷P ! -(Both consequences of profit maximization)! -Z(x/x) or Xxx^-1 = Z! Labor’s Share of Income:! (W÷P)L = dY/dL ! Y = F(K,L)=AK^αL^α-1! MPL = AK^α • (1-α)L^([1-α]-1) (the partial derivative)! Multiply by L^1•L^-1 [=1]! = (1-α)AK^α•L^-α • [L^1•L^-1] = (1-α)AK^α•L^(1-a)•L^-1! MPL = (1-α)•Y•L^-1! Labor’s Share of Income = MPL•L = (1-α)•Y•L^-1 •L = 1-α! Y Y ! 1-α is a constant, which is ~0.3. Therefore, α is 0.7!

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Capitals’s Share of Income:! (R÷P)K = dY/dK ! Y = F(K,L)=AK^αL^α-1! MPK = αAK^(α-1)L^(1-α) (the partial derivative)! Multiply by K^1•K^-1 [=1]! *Go though same steps here as MPL*! MPK= αY = α! Y! Labor’s Share of Income = MPL•L = (1-α)•Y•L^-1 •L = 1-α! Y Y ! 1-α is a constant, which is ~0.3. Therefore, α is 0.7! -i.e Y = AK^(1/3)L^(2/3), you can just tell that Labor’s share of income is 2/3 and Capital’s is 1/3! 4) What we think aggregate production is ! Y = AK^.3•L^.7! A is growing at a rate relative to K or L! F) Growth accounting Mankiw Ch. 9 appendix ! 1) Question ! Y = AK^.3•L^.7! Take aggregate production function with value for α! Get data in %Δ in __ over past __ years! %Δ in Y (Real GDP)! %Δ in K (Capital stock)! %Δ in L (Labor input)! How much %Δ was caused by ΔK? ΔL? ΔA?! ΔA = Improvement in efficiency / technology! 2) A Math trick (calculus)! Z = X1...