The law of diminishing returns gives us that for every unit of additional output produced, the addition to total cost increases more rapidly. Therefore, in perfect competition the supply curve is a positively sloped curve that as output increases is steeper. When we ask the firms how much they are willing to produce at different prices we derive the supply curve done in an empirical fashion. Perfect competition, monopoly, monopolistic competition, oligopoly comprise the economy and are all added up to define the short run aggregate supply curve (s.r.a.s.c.). In this essay some of the effects of changes in aggregate demand(A.D). are taken into consideration. In the long run, buildings and machinery increase but so do the wages therefore the long run aggregate supply curve is vertical at national income of full employment Y. At liquidity trap the A.D. is vertical, we prove it as this essay unfolds, resulting in sluggish economic growth or if there is asymmetry in negative economic growth and negative inflation. It is proved that all short run supply curves are valid at price equal or greater than the average variable cost (A.V.C.). Finally, we tackle economic problems of countries such as liquidity trap, inflationary pressures and try to solve them. The solutions are suggestions.
Marginal cost(M.C.) is the cost incurred in producing one additional unit of output. It is the addition to Total cost(T.C.) for producing 1 additional unit of output. The law of diminishing returns gives us that the marginal cost increases at a faster pace. Why?
When we add input to produce more goods, for example, when we add workers (labor) there comes a time that the output does not increase by the same proportion of the additional labor employed. Too many workers collide, their relative space decreases they are more disorganized. The output they produce is not proportional to the input of labor. For example, a factory building with the machines has a capacity of 100 workers if the workers are increased to 200 the output will not double. Workers are not the only variable cost. If the firms' demand for raw materials increases the price of raw materials will increase thus marginal cost progresses. Therefore, to produce one additional unit the cost (wages) is increasing at a faster pace. As output increases the cost is rising at a steeper rate: diseconomies of scale. The following diagram illustrates it:
Figure 1 As quantity produced increases the M.C. is steeper.
From the graph below we conclude the M.C. curve is the supply curve in the short run in perfect competition we explain below.
Figure 2 From figure 2 at output A, M.C. is more than the marginal revenue(M.R.) which in perfect competition is the price. M.C. is greater than the price. The firm loses money so it will produce less. At output B, M.R.is greater than M.C. For example, the price of one unit of output is $5- the M.C.=$3-. The firm gains profit and it will produce more to gain more profit until M.C.=M.R. at C (see figure 2). If it produces more than C M.C.>M.R. the firm loses money. The firm will produce at C where Price=M.C. The firm produces where the price of the product=M.C. it produces that output. Therefore the M.C. curve is the supply curve in perfect competition(pc). At a given price how much it will produce: supply curve.
Using the above technique we apply it to perfect competition(pc) and we derive the pc equation and graph by interpolation:
P=aY n+bY n-1+...+g
aY n+bY n-1+...+g>0, n integer >0, dP/dY>0, d2P/dY2>0
In monopoly, there is no unique relation between market price and quantity supplied. There is no distinct supply curve under monopoly. Yet when the demand curve shifts to the right (increases) there is a relation between increase in prices and increase in quantity supplied as the following graph shows under the assumption that the demand curve shifts parallel:
Figure 4 The monopolist produces that output where M.C.=M.R. to maximize profit as it was explained. From the graph above you can see the output determined is at the intersection of the M.C. curve (black line-) and the M.R.1, M.R.2, M.R.3 curves. The monopolist sets the price at which consumers are willing to pay at the determined output the demand curves D1, D2, D3. Where the output meets the demand curve we get the price. From the above graph you can see that the change in quantity DQ increase is less than the change in price DP (increase). The price compared to quantity increases at a larger rate.
Please see figure 5, below.
The demand curve is the average revenue(A.R.) curve.
A.R.=Total revenue/quantity = price✕quantity/quantity = Pq/q = P
Let the equation of the demand curve be PD=mq+c where m: slope, c: intersection to the y-axis or Price-axis
Marginal Revenue= d(T.R.)/dq = d(PDq)/dq = d(mq2 + cq)/dq = 2mq+c
The slope of the demand curve is m and is negative. As proved the slope of the M.R. curve is 2m it is twice as steep.
The A.R. curve meets the q axis:
The M.R. curve meets the q-axis:
The horizontal distance from(0,0) is half for the marginal curve. When M.R. is zero it intersects the q-axis at q=-c/2m at that q the A.R.= mq+c= m(-c/2m) + c= c/2
When M.R.=0 A.R.= c/2
mc: slope of the M.C. curve
cc: intersection of the M.C. curve to the y-axis or Price-axis
x2=2mq2+c2 => Dx= 2mDq+ Dc
At the two points of intersection between M.R.s and M.C. we have: z1=mcq1+cc
z2=mcq2+cc => Dz= mcDq
M.R. curves and M.C. curve intersect at two points. The change in M.R. is the same as the change in M.C.: DM.R.=DM.C. please see figure 5.
∴mcDq= 2mDq+ Dc
∴Dc= mcDq- 2mDq -*
y1= mq1+ c1
y2= mq2+ c2
∴Dy= mDq+ Dc
From the above and from*: Dy= mDq+ mcDq- 2mDq
∴Dy= (mc -m)Dq
∴DP= (mc -m)Dq
∴DP/Dq= mc -m
∴P= (mc -m)q+ g2
∴P= b2q+ g2
b2= mc- m, mc>0 the slope of the marginal cost curve, m<0 the slope of the demand curve which is negative so -m is positive therefore b2>0, g2 is a number
Figure 5 Why the demand of a monopolist is steep, |m| is high?
Because consumers cannot switch to another brand it is monopoly. A change in price brings a small change in quantity sold and thus produced. Therefore we relax on the assumptions that the demand curve shifts and not pivots(elasticity of demand changes dramatically) and also the M.C. is a straight line (please see figure 5).
From the above calculations we have P= b'2q+ g'2
To express q units of output produced into Dollars we multiply q by price2018: output produced in Dollars. We multiply every value of q by price2018 as we did earlier in perfect competition.
We find b'2 and g'2 by interpolation we know one point P=100, p2018q2018 output of the monopoly.
P= b'2pq+ g'2
If the above monopoly(1) is 30% of the output of all monopolies then:
0.3P= 0.3b'2pq+ 0.3g'2
∴0.3P= 0.3b'2✕0.3Ym+ 0.3g'2
We add all other monopolies so Pm= b2Ym+ g2
Therefore the point 2018 will be:
p(1)2018 is the current price of 2018 of monopoly(1)
q(1) is the 2018 current output at price2018 of the monopoly(1)
In monopolistic competition there are many firms with freedom of entry and exit (competition). Yet each firm has some power over price because each sells a product that is somehow different from the firm's competitors (monopoly). The demand curve is rather elastic because there are substitute products from other firm competitors: As it was mentioned in monopoly the demand curve does not pivot because the elasticity of demand normally does not change it is a monopoly, consumers cannot switch to other goods. In monopolistic competition, however, the demand curve of a firm pivots because consumers can consume other similar products as the graph below demonstrates.
Figure 6 When the demand curve pivots from D1 to D2 there is a small change in price DP.
We showed in monopolistic competition(mc) that variation in quantity changes the price.
mc: slope of the M.C. curve
c: intersection of the A.R. & M.R. curves or y & x curves to the y-axis or Price-axis
cc: intersection of the M.C. curve or z curve to the y-axis or Price-axis
y1= m1q1 + c
y2= m2q2 + c
∴Dy= m1q1 - m2q2
z1=mcq1 + cc
z2=mcq2 + cc
∴2m1q1 - 2m2q2= mcDq -*
But Dy= m1q1 - m2q2
From the above equation and from* Dy= 1/2mcDq
∴y= 1/2mcq + g'
Pmc(1)= b'Ymc(1)+ g'
∴b'= 1/2mc, g' is a number
Consider the following more realistic case:
The demand curve moves at random that is it shifts and pivots from D1 to D2:
Figure 6.1 What we do is that we split this change in demand from D1 to D2 in 2 movements: From D1 to D1' (a parallel shift) and from D1' to D2 a pivot.
From D1 to D1' as already proved in monopoly:
P= (mc -m)q + g'
From D1' to D2 as already proved in monopolistic competition:
P= 1/2mcq + g
In order to find the full effect we add them up:
P= (11/2mc -m)q + g1'
Where mc is the slope of the marginal cost curve, m is the slope of D1 and D1'.
If the demand curve pivots to the left and not to the right, as we took into consideration just above, we subtract 1/2mcq + g from (mc -m)q + g' in the equation P= (mc -m)q + g' to find the full effect.
What if the demand curve moves a third time randomly and the new point(Price, quantity) is not on the supply curve. We do either regression analysis (best line through the points) or interpolation (best equation that describes the points) and we find the best possible equation of Price and quantity. We know one point P=100, p2018q2018. We can take real, actual monopolies and observe the Price and the corresponding quantity produced. We do this for different prices in the same monopoly and find if there is correlation between Price and quantity produced.
Subsequently, we do the same analysis as done in technical information 1 and monopoly, the principle is the same, and we derive the equation of the monopolistic competition:, b3>0, g3 is a number
In oligopoly few firms compete with each other. Each firm has enough power so that it cannot be a price taker(take price as given), but it is subject to enough inter-firm rivalry that it cannot consider the market demand curve as its own. This is probably the dominant market structure outside agriculture and basic industrial materials.Figure 7
In the figure above the oligopolistic firm is assumed to be selling q1 units at a price of p1. It then considers altering its price and it makes two key assumptions. First, it assumes that if it cuts its price, all of its competitors will match its price cut. Its demand will then expand along the relatively steep curve below a, which indicates the effect of the firm's price cut when its share of the market is unchanged. Second, it assumes that if it raises its price, above p1, none of its competitors will raise theirs. Its demand for prices above p1 thus contracts along the relatively flat curve indicating the effects of raising prices with a declining market share. To summarize, above price p1 the competitors will not increase the price thus the firm loses a lot of demand: a small increase in price leads to a large decrease in demand the demand curve is flatter. At price below p1 the competitors will also reduce the price there will be no change in the firm's demand, competitors follow suit therefore the demand curve is steep a change in price brings a small change in output. Therefore, changes in the (M.C.) do not alter the price: see figure 7 M.C.1, M.C.2.
Figure 8 As demand increases the demand curve shifts from D1 to D2 the quantity changes from q1 to q2 but the equilibrium price remains the same p1
In oligopoly price is constant.
To conclude, we add up all markets of the economy as displayed above to derive the short run aggregate supply curve (s.r.a.s.c.) of the economy. We assume that perfect competition= 10% of the economy, oligopoly= 50%, monopoly=10% and monopolistic competition= 30%. Therefore, Ypc= 0.1Y=> Ypcn= 0.1nYn and Ym= 0.1Y. We integrate the analysis done separately before and the just previous assumptions and we have:
0.1P= 0.1a1✕0.1nY n+...+0.1✕0.1b1Y+0.1g1
0.1P= 0.1✕0.1b2Y+ 0.1g2
0.3P= 0.3✕0.3b3Y+ 0.3g3
Overall the s.r.a.s.c is a positively sloped curve which becomes steeper as national output increases because in the short run firms have a specified capacity leading to a s.r.a.s.c. which has a vertical asymptote at a large national output, please see figure 3.
Below there is an example of a s.r.a.s.c.:
The given equations are not the real US GDP they are just an example which resemble reality more realistic equations can be obtained from empirical evidence that is at given prices how much the producers are willing to produce as explained before.
The equation for perfect competition(pc):
According to the above equation the graph is as follows:
Figure pc Now, as explained before Ypc=0.1Y we substitute 0.1Y for Ypc to express the above equation in terms of Y, national output:
The above Ppc to express it in terms of Price, P for the whole economy we multiply the above equation by 0.1 because this is the share of pc in the economy to derive the weighted average for the whole economy:
With the same thinking we have:
0.1P= 0.03Y + 9.385
0.3P= 0.045Y + 29.0775
Please, see the graph below.
When aggregate demand, A.D. increases: shifts to the right, the increase in price is enough at low values of output. For example, in the graph from A.D.red to A.D.green the price went from 99 to 128: change 29. Then by the same amount of increase in A.D. from A.D.green to A.D.blue the price went from 128 to 176: 48. This is because the supply curve as output increases becomes steeper. At full employment output (supply curve is vertical) an increase in A.D. causes high inflation and zero economic growth(annual percentage increase of real National Output, Y). The shift of A.D.red to A.D.green Y increased (in trillions) from 20 to 27: 7. From A.D.green to A.D.blue Y increased from 27 to 32: 5. The above paragraph is merely an example to demonstrate the effects of changes in A.D. This is what is happening to the US economy right now: inflation is increased, economic growth is reduced.
As output increases costs are rising at a faster pace. As output increases labor and raw materials become scarce so the wages, costs rise. Costs are also rising from diseconomies of scale and diminishing returns as previously explained. In all markets perfect competition, monopoly, monopolistic competition, oligopoly, the marginal cost curve leads to finding the output produced and the price. For example, if the M.C. curve turns upwards: the equilibrium output q is restrained while the price increases. Thus, as output increases the price increases at a faster pace giving us a short run aggregate supply curve which is upward sloping. At very high output the economy's potential is reached: full employment, full capacity the output remains constant while price escalates. The assumption in deriving the s.r.a.s.c. is that the factory buildings, heavy equipment remain the same. In the long run factory buildings, machinery increase. Thus the s.r.a.s.c. shifts to the right:
Figure 10 At equilibrium the economy is at its natural level of output (potential output) Y and the s.r.a.s.c. meets aggregate demand curve at point A. When buildings, machinery increase the s.r.a.s.c. shifts to the right s.r.a.s.c.2. At point B the actual output Y2 exceeds the potential output workers are scarce thus wages rise and s.r.a.s.c. shifts to the left to s.r.a.s.c.1. Therefore, at point A after the shift we have more factories and machinery and higher wages. In reality this is what happens.
At liquidity trap the money demand curve (Md) is flat as money demand changes the rate of interest is the same r1. The money supply curve MS does not change with interest rate changes in fact the rate of interest does not have an effect on money supply it remains the same: 40. Suppose we have an increase in prices the real money supply decreases because real money supply= M/P= 40 where P is the price. If prices double then real money supply= M/2P= 20.
A change in prices does not change real money demand because the higher the prices the more money people will demand canceling each other out. Money demand= (M/P)d after doubling the price: (2M/2P)d= (M/p)d real money demand is the same.
From the previous graph the rate of interest is constant thus the LM curve is flat. Therefore, national income does not change it remains the same Y1 as in the graph below.
Figure 12 Because the Y1 remains the same we have a vertical national income or aggregate demand curve. As price changes A.D. is the same:
In the short run a firm should produce if and only if total revenue is equal or greater than total variable cost. A firm to make a profit its total revenues must be greater than its total costs: T.R.>T.C. Profit= Total revenues- Total costs
Total costs= Fixed costs + variable costs
Fixed costs: interest, rent, depreciation
Variable costs: labor, raw materials for the product
The fixed costs are there even if the output is zero the fixed costs exist.
In the short run the firm produces if the total revenues are equal or greater than the variable costs. Why? Even if: Total revenues- variable costs= $1- the firm subtracts this one dollar from the fixed costs. The fixed costs will be $1- less. The fixed costs always exist. Except when the firm closes down.
Therefore the firm to reduce its fixed costs produces where the total revenue is equal to or greater than the variable cost. At that point Total revenues= Total variable costs and at values where the total revenues are greater the firm produces and at that point onwards the marginal cost curve is the supply curve in perfect competition. Please bear in mind that
total revenues= price✕quantity produced
total variable cost= average variable cost✕quantity produced
total revenues= total variable cost
Therefore price✕quantity produced= average variable cost✕quantity produced
Therefore price= average variable cost(A.V.C.)
Consequently, in the short run, the firm produces where the price= average variable cost or at a greater price. This applies to all the markets in the economy: perfect competition, monopoly, monopolistic competition, oligopoly.
Figure 14 As it was previously explained the supply curve is the red line-curve (please see figure above). At price-output less than point B (less than A.V.C.) the firms close down. The supply curve is a vertical line along the vertical-axis, price-axis at output 0 until point A. Then the supply curve is the curve from point B onwards.
Figure 15 When wages, costs, prices fall: Supply curve shifts to the right, down (please, see the figure above). There is a vertical movement from A to B the supply curve moves vertically down from A to B the new supply curve is the red line curve. Please, note that at price less than B the supply curve moves from B to C. There is a horizontal movement from B to C.
At the above graph there is an asymmetry: point A the s.r.a.s.c. does not meet the A.D. curve. There is excess supply. When there is excess supply the prices fall. When prices fall below A the supply curve moves from point A to point B. What that means is that supply moves to zero, firms not having at least their average variable costs covered stop production they are closing down there is a movement: a arrow (please, see figure below). When firms are closing down unemployment increases demand for raw materials decrease. Wages and prices decrease therefore the supply curve falls there is a movement: b arrow. The result is a diagonal movement of the s.r.a.s.c. from point A to point C. At point C prices fell and output fell. This is what happened during the Great Depression in U.S.A. and to a lesser effect in Germany and Japan in 2009.
The problem with liquidity trap is that individuals do not deposit their money in the banks. The European Central Bank (ECB) injects money into the economy individuals take the money out of the economy by holding money as cash, money demand is flat please figure 11. Why is this happening? Europeans do not feel safe by depositing their money in the banks because the banks may default. What the ECB, Bank of England and Bank of Japan should do is to guarantee all bank deposits: in case a bank goes bankrupt the central bank will pay for the deposits and be legally bound to keep their word. Central banks have an unlimited supply of money. Secondly, even if all bank deposits are guaranteed individuals are indifferent of depositing their money because the rate of interest is very low. They do not forego any interest so they keep money as cash. Therefore, the interest rates should be increased this can be achieved by increasing the discount rate (the interest rate central banks charge the commercial banks for lending the commercial banks) and by increasing the funds rate (the interest rate banks charge each other). When banks need money they will sell bonds that they hold they will not borrow from the central bank or other banks because the rate of interest is higher. By selling bonds the price of bonds will go down the rate of interest will go up. There is the paradox how interest rates can increase (and they should be increased) and the economy and inflation grow? At a higher interest rate the opportunity cost of holding money increases individuals will deposit their cash injecting thus money into the economy. This will lead to banks using and/or lending money because they will have more cash from depositors and because the lending rate will increase. Banks will trade off between risk of loan and higher interest. I suggest the interest rate on deposits be driven to 3% even if selling bonds is required. As US interest rate rose there is an upward pressure on the interest rates in the rest of the world. Do not fight these upward pressures let the interest rates rise. Thus, evading the liquidity trap. The above hold true for the Eurozone, United Kingdom and Japan. Also, with E.U. citizens leaving the U.K. there has to be a way of increasing the labor force. I think this could be achieved if a tax is imposed on couples who live in the same house and only one is working and they do not have child/ren below 6 years of age. The tax should be an additional tax of 10% on the income of the person who is working. If both people work this tax does not apply. The money received could be given to married couples who both work for example in the form of increased marriage allowance (allowance: a sum to be deducted from gross income in the calculation of taxable income). This is an incentive for people to work and be married. It will increase the British labour force participation rate. British housewives will displace E.U. citizens in U.K. The classic measure in eliminating liquidity trap is a generous fiscal policy please see figure 12 IS curve shifts to the right. It proved to work in USA but not in Japan which ran generous fiscal policies. Also, if the government wants to reduce the expenses to achieve budget surplus the generous fiscal policy measure cannot be used.
In conclusion, the s.r.a.s.c. is a diagonal curve starting from low price and low national output (Y) and as Y increases it becomes steeper, at large Y there is a vertical asymptote because in the short run firms have a maximum capacity and because of diminishing returns and diseconomies of scale. The s.r.a.s.c is derived empirically and perfect competition, monopoly, monopolistic competition, oligopoly are taken into account. Some effects of changes in A.D. are examined. In the long run the s.r.a.s.c. shifts to the right because more buildings and machinery are used but the s.r.a.s.c. shifts back to the left because wages increase therefore the long run aggregate supply curve is vertical. At liquidity trap the A.D. is vertical and if it is low the s.r.a.s.c. does not intersect it leading to a reduction in both prices and Y. The short run supply curves hold true for price equal or greater than the average variable cost as previously thoroughly explained. Now, if s.r.a.s.c. shifts to the right and long run supply curve shifts to the right because natural level of output increases then prices fall and Y is increased, please see figure below. This can be achieved if the labor is increased if the number of workers increases. The US government can increase labor if it taxes couples living in the same house and only one is working and they do not have child/ren below 6 years of age by decreasing the tax deduction from their adjusted gross income. The US government can increase the tax deduction of couples who both work and are married with a church wedding and are husband and wife. This measure will increase the US labor force participation rate increasing the natural level of output Y decreasing the prices, please see figure below. How can productivity increase? The US government can introduce a measure that when an employer dismisses an employee the salary of the employee is deducted from the net profit before tax of the employer, the maximum duration of this is for a year and can apply if no other person is employed in a similar job of the dismissed employee. When a new employee takes the similar job this measure stops. This measure cannot be used if the period of the dismissal and employment is less than 3 months. This measure will reduce the number of unproductive employees and compel the employees to work more productively in order not to be dismissed.
Is there a way to reduce inflation and simultaneously reduce interest rates? Yes, there is. If the government runs a tight fiscal policy for example if government expenses are reduced:
Figure 19 A tight fiscal policy shifts the IS curve down because National income Y is reduced. Government spending is one of the components of Y.
Figure 20 Government spending is reduced consequently aggregate demand is reduced, shifts down reducing Y to Y3.
In the above two graphs interest rate is reduced from r1 to r2 and price level is reduced from P1 to P2.
We all want lower taxes and a generous government. How can we achieve this without causing inflation to rise?
As Professor William H. Branson says in his book Macroeconomic Theory and Policy there are 5 ways for a government to finance its deficit:
1. The US government can sell bonds to the nonbank public. It is rather inflationary.
2. The US government can sell bonds to the commercial banks. Thus, the banks pay the US government and reduce lending to the private sector. It is rather inflationary.
3. The US government reduces its demand deposits(money it has in the commercial banks) at the commercial banks. It is inflationary.
4. The US government issues and sell bonds to the Federal Reserve System. It is highly inflationary.
5. The US government takes money from the Fed. It is highly inflationary.
What the US government can do is to sell bonds only to US people and institutions inside U.S.A. By doing this it takes money out of the economy and when it spends it, it puts the money back into the economy. When the US government sells bonds to foreigners there is an injection of money into the economy from outside. The US government must not sell its bonds to foreigners because the foreigners flood the US economy with US dollars overheating the already hot US economy. Another way to see it is that the US government does not take money out of the US economy but from abroad, which is inflationary.
I mentioned 4 measures to combat US inflation the fifth and most important is please pray that inflation is reduced and you may prosper.
Christmas is a time when kids tell Santa what they want and adults pay for it. Deficits are when adults tell the government what they want and their kids pay for it.
Macroeconomics, N. Gregory Mankiw
Macroeconomics, Rudiger Dornbusch, Stanley Fischer, Richard Startz
Macroeconomic Theory and Policy, William H. Branson
Macroeconomics, Dernburg, McDougall
An introduction to Positive Economics, Richard G. Lipsey
Economics, David Begg, Stanley Fischer, Rudiger Dornbusch
Price theory and applications, Jack Hirshleifer
The author is a graduate from City.
Lord our God, our all-powerful Father, You who gave birth to wisdom let all the words in this essay be Yours and not mine. In Jesus' name. Amen.