Mathematics

# Macroeconomic Calculations

In this article we will be discussing economic calculations such as national income (C, I, G), production function (marginal product of labor, marginal product of capital K), nominal and real interest rates, inflation rates, and the unemployment rate covering job finding and separation. It is important to become aware of the different calculations in order to fully understand the context upon which news and businesses report on them. Note in the formatting does not allow symbols, therefore in explaining the examples when I use the algebraic letter with bar after it means a fixed quantity.

National Income

Macroeconomics here assumes a closed economy in which an economy does not have international trade, therefore, the GDP = C + I + G + NX is now GDP = C + I + G, where NX is no longer needed in the equation. We also assume a market-clearing model where prices adjust in order to achieve equilibrium of supply and demand. Where on the demand side it is determined by the Consumption, Investment, and Government Purchases of the closed macroeconomic GDP. For consumption “[we] define income after the payment of all taxes, Y – T, to be disposable income.” (Mankiw, 2010)

As the consumption function depends on disposable income, the equation can assume an increase or decrease in disposable income C = C(Y -T), consumption is equal to income minus taxes. “The marginal propensity to consume (MPC) is the amount by which consumption changes when disposable income increases by one dollar.” (Mankiw, 2010) Investment depends on the interest rate and will be discussed further below under nominal and real interest rates. Government purchases are determined from the level of taxes collected minus the amount of transfer payments increase household disposable income, unless an increase in taxes is equal to an increase in transfer payments leaving disposable income unchanged. “If government purchases equal taxes minus transfers, then G = T and the government has a balanced budget.” (Mankiw, 2010) However, most governments promise a budget surplus they often fail to keep their promise and ultimately lead to a budget deficit. “If G exceeds T, the government runs a budget deficit, which it funds by issuing government debt-that is, by borrowing in the financial markets.” (Mankiw, 2010) It is beneficial to have a budget surplus as it prevents creating more debts for the economy. “If G is less than T, the government runs a budget surplus, which it can use to repay some of its outstanding debt.” (Mankiw, 2010) Government purchases and taxes are considered to be exogenous variables, see my article which explains the difference in variables in more detail, here.

Where on the supply side we include only capital and labor factors of production and omit land and money holdings. Capital (K) now represents only plant and equipment. Labor (L) is physical and mental employments of workers. However, this macroeconomic model wrongly assumes that capital and labor are absolute or work as homogeneous. These two factors K and L are the determinants of output and income. Macroeconomics assumes demand (consumption) and supply (production) work as absolute where they balance to find equilibrium in the goods market and are just two stages in acting. Loanable funds market shows the “flow of resources available to finance capital accumulation.” (Mankiw, 2010)

Production Function

As we introduced above the capital K and labor L. “Capital is the set of tools that workers use: the construction worker’s crane, the accountant’s calculator, and this author’s personal computer.” (Mankiw, 2010) Labor is the workers amount of labor hours or time spent working. This model assumes a fixed amount of K and L factors of production and are fully utilized, where a bar over the letters represent a fixed value or a specific value set from the variables of K and L without bars. You could say L = L bar, here the variable value is equal to the fixed value. Capital and labor should otherwise in other economic models grow in correlation to population, technology, and investment growth.

“Production function: The mathematical relationship showing how the quantities of the factors of production determine the quantity of goods and services produced; for example, Y = F(K, L).” (Mankiw, 2010) The Y in the production function represents the maximum amount of output the economy produces from the amount of capital and labor units the economy has. “The production function reflects the available technology for turning capital and labor into output.” (Mankiw, 2010) The production function shows increased inputs correlate to the same proportion of increased outputs, called constant returns to scale.

“Mathematically, a production function has constant returns to scale if zY = F(zK, zL) for any positive number z.” (Mankiw, 2010) By multiplying both K and L by an amount z, the output is also multiplied by an amount z. Where the amount is represented as 1, Y1 = F(K1, L1). Scaling the inputs by the amount z, K2 = zK1 and L2 = zL1. We arrive at Y2 = F(K2, L2). Now we can see that a constant returns to scale is represented as Y2 = zY1. In the same way an increasing returns to scale is represented as Y2 > zY1. Alternatively, a decreasing returns to scale as Y2 < zY1.

“The marginal product of labor (MPL) is the extra amount of output the firm gets from one extra unit of labor, holding the amount of capital fixed.” (Mankiw, 2010) For instance a business will hire an additional unit of labor as long as the costs do not exceed the benefit, where the cost is the real wage, and the benefit is the marginal product of labor. “We can express this using the production function: MPL = F(K, L + 1) – F(K, L).” (Mankiw, 2010) As you can see below that the marginal product of labor is the change in Y at each value of L:

L    Y   MPL

0    0   n.a.

1    11   11

2   20   9

3   25   5

To graph the MPL curve, MPL is on the vertical axis and L on the horizontal axis. To graph the production function, Y is on the vertical axis and L is on the horizontal axis, assuming a fixed value of K. The MPL is equal to the production functions slope. For every additional unit (here one unit of labor) the curve increases to the right, by the amount of which output increases. This follows that when one input is increased while others held constant, the marginal product of labor falls. If labor increased while capital is fixed, there are more workers and fewer machines, with a lower productivity. This is called diminishing returns where we can see that as the slope slows near the peak. To prove this using calculus, create the MPL expression by taking the derivative of F() with respect to L. As L increases does MPL fall, or is the derivative of MPL function with respect to L positive, zero or negative.  From the MPL above if there is a real wage of 9 = W/P, then it would be inefficient if L = 1, as the benefit of the MPL = 11 exceeds the cost if W/P = 10, so the firm should increase L. If L = 3, then the business should hire fewer workers as the 3rd worker adds only MPL = 5 units of output, while costing W/P = 10. The same logic follows for the marginal product of capital, where MPK = R/P. R/P is the real cost of renting a unit of capital for a period of time. Capital is also subject to diminishing marginal product, like labor. As K increases MPK decreases. To maximize profit the business can rent more capital to the point MPK decreases to equal the real rental price of capital. The MPK curve is a businesses demand curve for renting capital. As some businesses can own some capital, this represents an opportunity cost being the lost market rental rate. “The marginal product of capital (MPK) is the amount of extra output the firm gets from an extra unit of capital, holding the amount of labor constant: MPK = F(K + 1, L) – F(K, L).” (Mankiw, 2010) The rule of each MPL and MPK is this “The firm demands each factor of production until that factor’s marginal product falls to equal its real factor price.” (Mankiw, 2010)

Nominal and Real Interest Rates

As included above under the national income, C + I + G, the I stands for investment. “The quantity of investment goods demanded depends on the interest rate, which measures the cost of the funds used to finance investment.” (Mankiw, 2010) A higher interest rate has a less incentive to invest, while a low interest rate has a high incentive to invest. While, a high interest rate has a high incentive to save, while a low interest rate has a less incentive to save. “The nominal interest rate is the interest rate as usually reported: it is the rate of interest that investors pay to borrow money.” (Mankiw, 2010) Therefore, if the nominal interest rate (i) is 5 percent and the inflation rate is 2 percent, the real interest rate (r = i – pi) is 3 percent. “The real interest rate is the nominal interest rate corrected for the effects of inflation.” (Mankiw, 2010)

“Rearranging terms in our equation for the real interest rate, we can show that the nominal interest rate is the sum of the real interest rate and the inflation rate: i = r + [pi].” (Mankiw, 2010) The Fisher equation developed by Irving Fisher shows how an increase in inflation in turn increases the nominal interest rate by the same amount. For instance, in the example above it would be 5 + 2 = 7. “[Two] concepts of the real interest rate: the real interest rate that the borrower and lender expect when the loan is made, called the ex ante real interest rate, and the real interest rate that is actually realized, called the ex post real interest rate.” (Mankiw, 2010)

Further explained below under inflation, the money demand function, though here we can say (M / P)d = L(i, Y). Where money demand depends negatively on the interest rate, which is the opportunity cost of holding money. Depending positively on income, higher Y leads to increased spending and increased money demand. L here in the money demand function considering the interest rate, confirming that money is the most liquid asset. People can choose the amount of money holdings in their expected future opportunities against their time preference. Naturally if prices are speculated to fall, one would prefer to hold money now. Alternatively, if prices are speculated to increase, one would prefer to spend money to purchase present goods, and forgo future spending. “Next, use the Fisher equation to write the nominal interest rate as the sum of the real interest rate and expected inflation: M / P = L(r + E[pi], Y).” (Mankiw, 2010) Where M / P is the supply of real money balances, and L(rEpi, Y) is the real money demand. Where M is exogenous, r adjusts to ensure S = I, Y is Ybar = F(Kbar, Lbar), P adjusts to ensure M / P = L(i, Y).

“We can summarize this discussion with an equation relating investment I to the real interest rate r: I = I(r).” (Mankiw, 2010) This would show a downward sloping demand curve as the interest rate rises on the vertical axis the quantity of investment demanded decreases, called the investment function. The interest rate is determined by individual’s time preference, which asserts present goods are preferred to future goods. “When you see two different interest rates in the newspaper, you can almost always explain the difference by considering the term, the credit risk, and the tax treatment of the loan.” (Mankiw, 2010)

Aggregate demand: C = (Ybar – Tbar) + I(r) + Gbar

Aggregate supply: Ybar = F(Kbar – Lbar)

Equilibrium in the market for goods and services: Ybar = C (Ybar – Tbar) + I(r) +Gbar

The real interest rate adjusts to equate demand with supply. In the equation for the equilibrium in the market for goods and services, note that the real interest rate is the only variable that doesn’t have a bar above it, being the only endogenous variable in the equation, it adjusts to equate the market. The interest rate in the equilibrium of the one asset loanable funds in the financial markets, also uses the supply (savings) and demand (investment) model, in this case for funds. Where the real interest rate is the price of the loanable funds. Each public, private and government savings become a part of the supply of loanable funds in the financial system:

Private Saving =    (Y – T ) – C    Public savings, equation interpretation: public saving is tax revenue minus government spending.

Public Saving =    T  –  G     Private savings, equation interpretation: private saving is disposable income minus consumption spending.

National Saving, S or Y – C – G  = private saving (Y – T) -C + public saving T – G    National savings, equation interpretation: national saving is disposable income minus consumption minus government purchases.

Inflation Rates

“Inflation is always and everywhere a monetary phenomenon.” (Friedman & Schwartz in Mankiw, 2010) The inflation rate is a measure of the increase in asset prices, measuring the percentage change in the average price level from the previous year. “The quantity equation, written in percentage-change form, is % Change in M + % Change in V = % Change in P + % Change in Y.” (Mankiw, 2010) This equation shows the % change in quantity of money, then % change in velocity of money which is zero if constant, then the % change in price level which is the rate of inflation, and lastly the % change in output. As the inflation theory is similar to the theory of the price level, inflation rates are just the percentage change in the price level. The inflation rate is denoted as the Greek letter “pi”, therefore, pi = the % change in M / M – the % change in Y / Y .”Thus, the quantity theory of money states that the central bank, which controls the money supply, has ultimate control over the rate of inflation.” (Mankiw, 2010) Where a positive inflation rate means rising prices, a negative interest rate means falling prices, and a declining positive interest rate means rising prices at a slow rate. “Periods of falling prices, called deflation, were almost as common as periods of rising prices.” (Mankiw, 2010)

“The link between transactions and money is expressed in the following equation, called the quantity equation [or quantity theory of money:] Money x Velocity = Price x Transactions M x V = P x T.” (Mankiw, 2010) This theory links price increases to the money supply growth rate. Where, if the money stock M increases more than output, prices rise. P is the price of transaction, number of notes exchanged. “The product of the price of a transaction and the number of transactions, PT, equals the number of dollars exchanged in a year.” (Mankiw, 2010) However, the quantity theory of money overlooks the fact that all money does not go into consumer prices, as some may go into asset prices causing asset price bubbles. Maybe some money is accounted in the changes in money demand, or ofset by a natural fall in prices resulting from technological advancements or increased productivity. Microeconomic data is overridden by macroeconomic statistics.

“Velocity theory of money: The value of a firm’s output minus the value of the intermediate goods the firm purchased.” (Mankiw, 2010) Velocity means the rate at which money circulates, or the amount of times a note exchanges hands in a period. Say there is 100 billion notes in transactions, and the money supply is 50 billion, then a note can be said to have exchanged hands in a certain period by two times. 100 / 50 = 2, so velocity = 2. Therefore, V = T / M, where V = velocity, T = total magnitude of transactions, and M = money supply.

T number of transactions can be represented as Y total output. Uses nominal GDP as an approximation for total transactions, excluding intermediate stages in production that use money transactions. Here, V = P x Y / M, or M x V = P x Y. P = price of output, Y = quantity of output, and P ‘Y = value of output. P can stand for GDP deflator, Y can stand for real GDP, and P ‘Y can stand for nominal GDP.

“A money demand function is an equation that shows the determinants of the quantity of real money balances people wish to hold.” (Mankiw, 2010) Where the real money balance equation is M / P, the money demand function is (M / P)d = kY. K is exogenous as K is the amount of money people hold to each dollar of income. The connection between the demand for money and the quantity equation is represented in the equation K = 1 / V. “When people want to hold a lot of money for each dollar of income (K is large), money changes hands infrequently (V is small).” (Mankiw, 2010) Therefore, showing the relationship between the demand for money and the velocity of money. “Conversely, when people want to hold only a little money (k is small), money changes hands frequently (V is large).” (Mankiw, 2010)

“For example, when automatic teller machines were introduced, people could reduce their average money holdings, which meant a fall in money demand parameter k and an increase in velocity V.” (Mankiw, 2010) With this assumption we can assume V = Vbar which is constant and an exogenous variable. Now, in this instance the quantity equation becomes M x Vbar = P x Y. “Therefore, a change in the quantity of money (M) must cause a proportionate change in nominal GDP (PY).” (Mankiw, 2010) Showing how the price level is determined. Real GDP would be determined by the supply of K and L in the production function explained above. Now the price level would be P = (nominal GDP / real GDP). The overall price level is determined by the following three conditions:

1. The factors of production and the production function determine the level of output Y. […]
2. The money supply M determines the nominal value of output PY. This conclusion follows form the quantity equation and the assumption that the velocity of money is fixed.
3. The price level P is then the ratio of the nominal value of output PY to the level of output Y. (Mankiw, 2010)

It is wrong to assume inflation reduces or increases real wages. As in the long run, the real wage is determined from MPL not the price level or inflation rate. Here, in the short run nominal wages are fixed, and may not adjust immediately. The social costs of inflation include transaction and adjustment costs and redistributive effects. “The inconvenience of reducing money holding is metaphorically called the shoeleather cost of inflation, because walking to the bank more often causes one’s shoes to wear out more quickly.” (Mankiw, 2010) However, nowadays ATMs and online banking cause little shoeleather costs. This is one of the social costs of inflation, where the second results from changing prices. “These costs are called menu costs, because the higher the rate of inflation, the more often restaurants have to print new menus.” (Mankiw, 2010) However, businesses change prices at different times in the year, causing relative price distortions and mis-allocation of resources.

Also, in the adjustment costs to inflation, there can be unfair tax treatment. For instance, the capital gains tax does not account for inflation.You purchase a house for \$300,000 and then decide to sell it after a year for \$330,000. The nominal capital gain is \$30,000. However, inflation or price rises are 10%, making the gain really zero dollars as other goods and wages increase to this 10% also. Now, the government taxes the gain of \$30,000 when in reality you earned zero dollars, causing you to be out of pocket by how much you get taxed on the \$30,000 nominal gain. “The problem is that the tax code measures income as the nominal rather than the real capital gain.” (Mankiw, 2010) Income tax and bracket creep are other forms of unfair tax treatment. Here nominal interest earnings are taxed, whereas real interest earning are not. General inconvenience can also be another problem to the adjustment for inflation, and can complicate long-term planning, as it makes it difficult to compare nominal values from different time periods.

Cantillon effect considers the redistribution effects of inflation. If everyone added or subtracted a nought on each dollar of money in the economy everyone would be the same amount richer or poorer had this not of happened. The only part that would have to change is adjustment to the new money supply. However, inflation benefits those at the core of the financial system first, this is called the Cantillon effect. This in affect takes wealth from one part of society and gives it to some other part of society. Furthermore, it’s impossible to predict when inflation will turn out higher than expected, when it will be lower, and how big the difference will be. So, these redistribution’s of purchasing power are arbitrary and random.

Many long-term contracts not indexed, but based on Epi. If p turns out different from Ep, then some gain at others’ expense. If pi is different from Epi some people will gain at some others’ expense. If pi > Epi then (i – pi) < (i – Epi), here purchasing power will be transferred from lenders to borrowers. If pi < Epi, here purchasing power will be transferred from borrowers to lenders. High inflation pi varies larger from Epi with uncertainty in the market, and people with credit risk worse off.

“All variables measured in physical units, such as quantities and relative prices, are called real variables.” (Mankiw, 2010) Such real variables include GDP and employment levels. “[Nominal] variables-variables expressed in terms of money.” (Mankiw, 2010) Such nominal variables include the inflation rate and the dollar wage. In order to explain real variable and nominal variable separation, the use of the classical dichotomy is employed. “Economists call this theoretical separation of real and nominal variables the classical dichotomy.” (Mankiw, 2010) In this classical model nominal variables do not affect real variables in any way. In order to explain real variables and omitting for nominal variables, the use of money neutrality is employed. “This irrelevance of money for real variables is called monetary neutrality.” (Mankiw, 2010) Where aggregated real variables are not affected by a change in the money supply, and over the long term money is neutral in macroeconomics.

Unemployment Rates, Job Finding & Separation

Notation:

L = # of workers in labor force

E = # of employed workers

U = # of unemployed

U/L  = unemployment rate

s = rate of job separations

f = rate of job finding

Where, (s and f  are exogenous)

Unemployment rate = # of employed x 100 / labour force. “Unemployment rate: The percentage of those in the labor force who do not have jobs.” (Mankiw, 2010) Unemployment occurs when nominal wages are above equilibrium level. Inflation discussed above allow real wages to decrease and achieve equilibrium, minus the nominal wage cuts. It is inefficient to direct capital through justified credit expansion from employments satisfying more urgent wants to correct for unsold services of employments whose wages asked for are currently too high. (Mises, 1949) One could not adjust asking prices where wage laws set wages too high causing unsold labour purposefully benefiting labor unions. Where job seekers place a downward pressure on nominal wages. Unions of employed advocate for higher minimum wages to keep out unskilled workers through not hiring or laying off unproductive workers as are prevented from competing on price and forced to compete on skill, union wages would increase now rather than decrease.

“The wages of unionized workers are determined not by the equilibrium of supply and demand but by bargaining between union leaders and firm management.” (Mankiw, 2010) The inefficiency of not being able to achieve equilibrium is explained further down, and is called wage rigidity. Another argument that follows from this logic is that immigrants steal jobs. Though an interesting article to read is on Immigrants Won’t Reduce Wage Rates: Here’s Why, by Keith Weiner. Explaining the assumption that increased supply of labor lowers the equilibrium price in a fixed assumption, though employers don’t calculate it on the quantity they calculate it on profit. Where if not held constant everything but the increase in workers, an increase in immigrants can create new businesses and new jobs increasing productivity, with more specialization and an increasing returns on labor. “Efficiency-wage theories propose a third cause of wage rigidity in addition to minimum-wage laws and unionization.” (Mankiw, 2010)

A minimum wage (price floor) is set above the market clearing wage, and a surplus of labor occurs. Where labor demanded (jobs available) is lower than labor supplied (willing laborers) is higher. Unemployment increases for unskilled workers and are now forced to compete with skilled workers. A labour market that is prevented from clearing leads to unemployment. Or when indirectly affected by a recession, the unemployment rate also increases above the natural rate, until wages are able or allowed to adjust to new conditions. Alternatively, the unemployment rate can decline below the natural level in a boom, until wages adjust to new conditions. If you get confused as to where you draw the line for a price floor or ceiling and whether its binding or unbinding then here is a good way to remember them, refer to the picture below. For an unbinding price ceiling and floor, picture a house with a floor and a ceiling, now lay the supply and demand graph over it. The unbinding price floor is below the equilibrium as you would assume the floor to be on the floor. The unbinding price ceiling is above equilibrium as you would assume the ceiling to be on the ceiling. For a binding price floor or ceiling, picture them as the opposite, picture a house with a floor and a ceiling, now the lay the supply and demand graph over it. The binding price floor is not below equilibrium as you would assume it is above, so the opposite. The binding price ceiling is not above equilibrium as you would assume it is below, so the opposite. “Unemployment represents wasted resources.” (Mankiw, 2010) The common argument arises that government can easily create jobs, but this only misdirects labor to factors of product that do not best serve customer needs. Watch this YouTube video on Does the government create jobs?, here Source: (Horwitz, 2013). Labour force participation rate = labour force / adult population   x 100. The labour force participation rate: the percentage of the adult population that is in the labour force. The rate of unemployment is U / L. If L represents the labour force, E represents # employed workers, and U # of unemployed workers. “Because every worker is either employed or unemployed, the labor force is the sum of the employed and the unemployed: L = E + U.” (Mankiw, 2010) For job separation let it be denoted by S, which means the amount of employed workers who get laid off or leave their jobs over a monthly period. “Let f denote the rate of job finding, the fraction of unemployed individuals who find a job each month.” (Mankiw, 2010) Both job finding and separation can help in determining the unemployment rate. “If the unemployment rate is neither rising nor falling-that is, if the labor market is in a steady state-then the number of people finding jobs fU must equal the number of people losing jobs sE.” (Mankiw, 2010) The steady-state can determine the unemployment rate. “We can write the steady-state condition as fU = sE.” (Mankiw, 2010) This means job finding x # of unemployed is equal to job separation z # of employed. The steady-state condition is: s x E (# of people who lose jobs) = f x U (# of people who find work). We can say the total of students to none students remain the same when the same # of new students entering first year is equal to the # of students graduating. Assuming the labor market is always fixed. “From our definition of the labor force, we know that E = L – U; that is, the number of employed equals the labor force minus the number of unemployed.” (Mankiw, 2010) Next we minus the labor force from the # of unemployed to arrive at the # of employed. “If we substitute (L – U) for E in the steady-state condition, we find f U = s(L – U).” (Mankiw, 2010) Then we find that job finding x # of unemployed is equal to job separation; which is then multiplied by the labor force minus # of unemployed. “Next, we divide both sides of this equation by L to obtain f U/L = s(1-U/L).” (Mankiw, 2010) Here we are taking both sides of the equation and just diving both sides by the labor force. Job finding is multiplied to the number after we divide # of unemployed by the labor force. This will be equal to job separation once job separation is multiplied by the number after we divide the # of unemployed by the labor force and minus the division by 1. Alternatively, you could do S x L – S x U to achieve the unemployment rate. “Now we can solve for U/L to find U/L = s/s+f.” (Mankiw, 2010) To solve for the unemployment rate: # of unemployed divided by the labor force. We find the unemployment rate U/L is equal to job separation divided by job separation that is added to job finding. “This can also be written as U/L = 1/1+f/s.” (Mankiw, 2010) Or written as (f + s) x U = S x L.

Example 1, using the following data calculate: (i) the labor force, (ii) the # of people not in the labor force, (iii) the labor force participation rate, (iv) the unemployment rate. Population as 2016: # Employed = 150.68 million, # Unemployed = 15.62 million, Adult population = 267.85 million

(i) the labor force: L = #E + #U => 150.68 + 15.62 = 166.30

(ii) the # of people not in the labor force: NILF = P – L => 267.85 – 166.30 = 101.55

(iii) the labor force participation rate: L/P x 100% => (166.30/267.85) x 100% = 62.08%

(iv) the unemployment rate: U/L x 100% => (15.62/166.30) x 100% = 9.39%

Example 2, compute percentage changes in the labor force participation and unemployment rates, using the following data. Population increases 2%, labor force increases 4%, and # of unemployed increases 3%. Note LFPR and U-rate are represented as % of initial values, such as a 2% increase in 60% LFPR equals 61.2% as 2% of 60 equals 1.2.

(i) The labor force participation rate: LFPR = L/P, where L increases 4%, P increases 2%, then LFPR increases 4% – 2% = 2%.

(ii) The unemployment rate: U = U/L, U increases 3%, L increases 4%, then U-rate increases 3% – 4% = -1%.

Example 3, compute the steady-state rate of unemployment, using the following data. Job separation is 2% (s=0.02), job finding is 30% (f=0.30).

(i) The steady-state rate of unemployment: U/L = s / s+f, where 0.02 / 0.02+0.30 = 0.0625

(ii) To find the rate of unemployment from 0.0625 just multiply by 100, that is 6.25%.

Example 4, suppose that legislation is passed making it difficult for businesses to fire workers, for instance severance pay. (i) if the law reduces job separation would it affect the rate of unemployment? (ii) do you think the legislation would not affect job finding?

(i) Any policy that affects the rate of job separation or job finding also changes the natural rate of unemployment.

(ii) No, as hiring firms would hire less (decreasing job finding) if they now have to pay to fire workers, therefore, (decreasing job separation).

Example 5, The natural rate of unemployment in China is lower than the U.K. Chinese businesses have wages which increase with seniority at the business. (i) If job finding is the same in both China and the U.K., can wages which increase with seniority explain the natural rate of unemployment in both countries.

(i) As workers stay with Japanese firms longer for the incentive of increased wage correlated to seniority, Japan has a rate of less job separation compared to the fixed job finding the unemployment rate is low compared to the U.S.

However, job finding and separation does not in itself explain why there is unemployment. Where, f=1 it represents job finding is instant, the natural rate in this case would be close to 0. Where, f<1 job finding is less instant, to explore this we will consider two underlying causes of unemployment which are job search and wage rigidity. It takes time for workers to find employers, though workers are not all equally suited to a job making it difficult and timely to find work. Such things which cause wage rigidity are minimum wage laws, labor unions, and efficiency wages. If job finding were perfect then it would have no problem in aligning to equilibrium quickly, which is explained in the following paragraph.

We know that wages are just the same as any other price. Every price tends towards equilibrium. An unsold surplus shows a price higher than equilibrium. A shortage shows a price lower than equilibrium. Both can be corrected by either increasing or decreasing prices, where a surplus of goods or services requires decreases in price, and a shortage of goods or services requires increases in prices. Only when prices are fixed does the surplus or shortage continue. However, equilibrium is not an accurate term, therefore natural rate of unemployment or the average rate of unemployment variations in the economy are called the normal rate.

The natural rate of unemployment in assuming L is exogenous and fixed, and can be during any given month can detract from the real economy. Where in a free market, buyers can cooperate with sellers and the market tends to clear to the adjustment process. Employers cooperate with employees. Competition occurs within the labor market, where buyers compete with other buyers and sellers compete with other sellers. Workers compete with other workers, and employers compete with other employers. This competition results from the fact that either employers or employees want to be able to cooperate with each other.

Considering wages are flexible and there are plenty of jobs available, what is it that is allowing frictional unemployment to occur. “The unemployment caused by the time it takes workers to search for a job is called frictional unemployment.” (Mankiw, 2010) To address frictional unemployment consider (sectoral shift) trying to align changes in the differing wages and skills demanded among industries or regions in a state of imperfect information. “Economists call a change in the composition of demand among industries or regions a sectoral shift.” (Mankiw, 2010) An example of this would be technological innovations that improve the factors of production, create new industries, and therefore direct jobs from old industries to the new more efficient industries that. “In addition, workers find themselves unexpectedly out of work when their firms fail, when their job performance is deemed unacceptable, or when their particular skills are no longer needed.” (Mankiw, 2010) Where jobs require different skill and qualification requirements, it is hard for market information to direct the right workers and employers to each other. The reason can be found in the fact that workers have differing capabilities and preferences spanning geographically, where relocation of workers are required. “Because sectoral shifts are always occurring, and because it takes time for workers to change sectors, there is always frictional unemployment.” (Mankiw, 2010)

“The unemployment resulting from wage rigidity and job rationing is sometimes called structural unemployment.” (Mankiw, 2010) To address structural unemployment consider (wage rigidity) comparing the number of people who are willing to work to the number of jobs available. “A second reason for unemployment is wage rigidity-the failure of wages to adjust to a level at which labor supply equals labor demand.” (Mankiw, 2010) When one speaks of wage rigidity being the failure of wages to adjust to equilibrium at which labor supply equals labor demand, as explained above is often aggravated by wrong polices and arguments.

Reference List (American Psychological Association)

Mankiw, G. (2010). Macroeconomics. (International 3rd ed.). New York, United States of America: Worth Publishers.

Mises, M. 1949 (2010). Human Action, Scholar’s ed. United States: Yale University Press, Ludwig Von Mises Institute.

Featured image supplied from Unsplash.