Thursday, 25 July 2013

Nash Equilibrium

NASH EQUILIBRIUM

The Nash equilibrium was named after John Forbes Nash.
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash Equilibrium.
Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy. To see what this means, imagine that each player is told the strategies of the others. Suppose then that each player asks himself or herself: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?"
If any player would answer "Yes", then that set of strategies is not a Nash equilibrium. But if every player prefers not to switch (or is indifferent between switching and not) then the set of strategies is a Nash equilibrium. Thus, each strategy in a Nash equilibrium is a best response to all other strategies in that equilibrium

Game theorists use the Nash equilibrium concept to analyze the outcome of the strategic interaction of several decision makers. In other words, it provides a way of predicting what will happen if several people or several institutions are making decisions at the same time, and if the outcome depends on the decisions of the others. The simple insight underlying John Nash's idea is that one cannot predict the result of the choices of multiple decision makers if one analyzes those decisions in isolation. Instead, one must ask what each player would do, taking into account the decision-making of the others.
Things we need to know:
Players (Decision Makers)
Actions
Payoffs
Matrix and trees (not important)

Examples:
Prisoner’s Dilemma(the single nash equilibrium)
Zero Sum Games(coin tossing, the infinite)
Crossing a Street(dual solution)
The Game of Averages(stock prices)
Rock Paper Scissors(zero sum game)

Will be explaning everything with examples.

Sohoum Biswas, Presidency University

Why is price of Gold falling?

First, gold price tends to spike when the global economy faces severe economic, financial and geopolitical threats. It explains why gold price rose so high during 2009-11. Global economy is now recovering, and hence a decline in gold price. 

Secondly, gold does best when there is risk of high inflation, as gold is a traditional store of value against inflation. At present global inflation is low and falling. So, holding gold is less compelling today. 


DECREASING DEMAND

Thirdly, other assets such as equities and real estate are now giving more returns than gold. A lower return in gold is reducing the demand for gold.
(INCOME EFFECT AND SUBSTITUTION EFFECT)

Fourthly, real interest rate and gold price are highly inversely correlated. Since financial crisis in 2007-08, many countries saw slow growth in GDP (gross domestic product). Many central banks took zero-interest rate policy or ZIRP to stimulate growth. This resulted in a high price of gold until 2011. But at present central banks are exiting from ZIRP, and gold price is decreasing. 
(CONCEPT OF LIQUIDITY TRAP)

INCREASING SUPPLY

Fifthly, highly-indebted countries are selling their gold to reduce debt. Governments of these countries are encouraging investors to invest in gold as gold are less risky than government bonds. 

Sixthly, value of US dollar and gold price are inversely correlated. Currently, appreciation of dollar is reducing the price of gold.

Seventh, gold is hyped for irrational political reasons. This reason actually explains the mentality of some imprudent politicians, which led to high price of gold during 2009-11. Some extreme politically conservative gold bugs think that all government is evil, that there is a government conspiracy to expropriate most private wealth and that gold is the only hedge against this risk. This group also believes that we will return to the gold standard as central banks "debase" paper money and as hyperinflation ensues. However, inflation is falling globally and gold is not in any way a currency.

According to Roubini Global economics, the price of gold may temporarily go higher in the next few years, but it will be very volatile and trend will be lower over time as the global economy slowly mends itself. His research and consultancy firm expects gold price to go up to $1,300 by end-2013 but come down to $1,000 by 2015.


Shreyans Banthia, Presidency University





Monday, 22 July 2013

Quantity Theory of Money

Anticipations



The monetary system in the part, that was mostly stable upto a thousand years did not feature much inflation. If inflation did happen, it was a planned one. This usually mean that the government in power would direct the mint to use lesser amounts of metal to produce the same amount of coin. The result of this was that the coin would be smaller or slightly adulterated with copper or some other fairly indistinguishable metal. This was called debasement of currency and was usually done in war time in an attempt to finance war expenditure. Once the public got word of this fall in value within each coin, naturally there was inflation up till the point where the price rise matched the value debased. However there was inflation caused from other sources. And it was in this discovery that the quantity theory of money was founded.


After the conquest of Persia under Alexander the Great caused a great influx of persian gold that resulted in a widespread inflation. There was a lot of gold coin depreciation (natural fall in value). Money lost its value by almost fifty times, with an inflation of 4 percent for over a century.   


In the 16th century as gold and silver coins poured in from the America into Europe, there was a massive rise in almost all prices. This brought in the idea that as the total amount of money in circulation rose, the prices rose with it. Henry Thornton in 1802, wrote about how the total volume of money circulating in the economy rose, it brought inflation with it.


The quantity theory of money had a resurgence in the 1970’s when Milton Friedman provided a strong theory and advocated monetary targeting. The hype died down by the 1980’s, but its prominence remained. As of today, most central banks do not adopt monetary targeting or attempt to focus so much on the money supply, but there is still a tendency to bring in this theory in modern economic debate.


The Quantity Theory of Money

An economic theory which states that there is a direct positive relation between the change in money supply and the level of prices and goods and services sold. According to the theory if money supply in the economy doubles, prices will also double leading to inflation. The consumer therefore pays twice as much for the same good or service.
Increase in the supply of money causes a decrease in its marginal value(buying capacity of one unit of currency). This causes inflation to compensate for the decrease in marginal value.

CALCULATIONS


where M=Money Supply,
  V=Velocity of Money,
  P=Price Level,
          T=Real value of Total Transactions,


The basic equation for the theory is,
MV=PT                                                                           (Fischer Equation)


It is based on the equation of exchange,


Amount of Money Velocity of Circulation = Total Spending


       ASSUMPTIONS

The Quantity Theory of Money is based on several assumptions. In its most basic form it states that V and T are constant.
if V and T are constant;
MV=PT,
or %dMV=%dPT
or %dM +%dV=%dP+%dT
or


change in money supply =change in price level
These assumptions have been criticised a lot.
firstly, V is the velocity of circulation of money ie the number of times money changes hands.It depends on consumer and business spending impulses and therefore cannot be constant. In reality V depends on the ease of borrowing and access to credit. When credit cards were first introduced the value of V rose, causing general price rise.
The real value of transactions T depends on labour, capital, knowledge and enterprise. The theory assumes an economy at equilibrium and at full employment. Sometimes T is written as Y or national income since national income equals national expenditure. T is assumed equal to national expenditure since the total real value of all transactions is almost equal to the expenditure on final goods and services.

Monetarist Economics

Monetarists say that a rapid increase in money supply will lead to a rapid increase in prices of goods leading to inflation. This is because money surpasses the production output of goods and there is too much money for too little output. In order to curb inflation money growth must fall below economic output growth.
Monetarists believe that the money supply should be kept within an accepted range so that inflation can be controlled. In the short run an increase in money supply can provide a quick boost to an economy in need of an increase in production levels. However its effect on the long term is still not clear. Instead of various government economic policies it is better to let non inflationary policies like gradual reduction in money supply lead an economy to full employment.
Keynes challenged the theory in 1930. He said that an increase in money supply led to a decrease in velocity of circulation.Thus velocity could change in response to changes in money supply. It was confirmed by many economists afterwards that Keynes was right.
The theory was very popular in the 1980s especially in USA and Great Britain. Leaders tried to apply the principles to their economic framework. However later it was agreed that a controlled money supply was not always the solution to economic problems regarding production output and inflation.
-Pranjal, Noyonika Presidency University


Friday, 19 July 2013

Perfect Competiton


Perfectly competitive markets are those in which all firms produce an identical product and each is so small in relation to the industry that its production decisions have no effect on the market price. New firms can enter the industry if they perceive a potential for profit, and existing firms can exit if they start losing money.

STRUCTURE OF PERFECTLY  COMPETITIVE MARKET.

The assumptions of such a market structure are as follows:

1. There are infinite number of buyers and sellers in the industry or market. 
Clearly supply quantity of an individual firm is negligible amount in respect of the total supply of the market. Hence  individual firm fails to influence market price of the product by changing its own supply quantity. Similarly demand quantity of an individual consumer is negligible amount in respect to market demand for the product. Therefore individual consumer fails to influence market price by creating excess demand or supply sufficiently through its own demand quantity. In this respect, market price is given to the individual firm and individual consumer.

2. There is free entry and exit. Free entry and exit implies that there is no cost to the newcomers or to leave the industry. This assumption is necessary for the infinite number of buyers and sellers. If entry is blocked and initially there is only one firm then we cannot have infinite number of buyers and sellers. Perfect competition breaks down. If number of firms is not infinitely large then supply quantity of an individual firm can create excess supply or demand significantly by changing its own supply and hence individual firm can influence the market price.

3. Products are homogeneous among the firms in both real and apparent sense.  Products are homogeneous in the real sense implies that there is no quantitative difference of the product among the firms. Products are homogeneous in apparent sense implies that there is no selling activity (i.e. brandname, goodwill, advertising etc).  Hence there is no apparent qualitative difference of the products among the firms. Hence consumers fail to distinguish products among the firms. Hence none of the firms operate as a single seller of a product and has no monopoly power in this respect and therefore individual firm fails to influence market price in this respect.
If there is qualitative difference of the products among the firms in real sense then individual firm has some degree of monopoly power as a supplier of a particular quality of the product.
Thus perfect competition is inconsistent if there is selling activity such as brand name, goodwill, and advertising expenditure. Thus we can also infer that there is no selling cost or advertising cost to the firm in perfect competition.

4.There is perfect knowledge or complete information.  
If there is complete information then none of the firms can create product differentiation by suppressing information. Hence none of the firms can influence market price in this respect.

5. Firm’s objective is to maximise profit.
A market structure characterised by the above assumptions is called a pure competition. The above assumptions are sufficient for the firms to be a price taker and have an infinitely elastic demand curve.
Market price is given to the individual firm. Hence demand curve to the individual firm is horizontal as the firm can sell any quantity at this existing price. However the market demand curve is downward sloping as market price is not constant in the industry.




Total revenue is defined as TR = P.q. Hence average revenue is given by AR = TR / q = P. q /q = P.

Change in TR due to one unit change in q is known as marginal revenue (MR).

Here MR = dTR / dq = d (P.q) / dq = P.

Hence AR = MR = P >0 and constant.

So demand curve to the individual firm is the MR as well as AR curve which is a horizontal straight line. Intuition is that as q increases one unit, TR increases by P units. So MR = P as P is given to the individual firm.
6. Factors are homogeneous and perfectly mobile.

Factor prices are given to the individual firm (not in the market) i.e. w and r are fixed to the individual firm. The factors of production are free to move from one firm to another throughout the economy.

7. Production is such that output (q) is rising function of inputs and quasi-concave. Hence isoquants are convex to the origin.

Implication of the last two assumptions: When input prices w and r are given to the firm and production function is quasi-concave and rising function of input, so cost is rising function of output and it is strictly convex. Hence MC = d C /dq > 0 and d(MC)/ dq> 0 . MC is positive and upward sloping. 



SHORT RUN EQUILIBRIUM OF THE FIRM and DERIVATION OF SHORT RUN SUPPLY CURVE.


Short run profit function of individual firm is given by:

Π = TR – TC = P.q + ø (q) – F   ..................... (a)

Where TR = P.q and TC = ø (q) + F

F is the fixed cost. Therefore it is given to the firm. P is also given to the individual firm as individual firm is price taker. Clearly firm maximises profit by choosing q. Then from F.O.C. of profit maximisation we get,
dπ / dq = P – ø’(q) = 0

From this equation one can determine optimum output supply in terms of the parameter P ; q = q(P) ...............(c)

S.O.C.  for π maximisation requires,

d ^ 2 π / d q ^2 = - d ø’(q) / dq < 0 which requires

d ø’ / dq = d(MC) / dq > 0 , i.e. at the point of P= MC. MC must be rising which is satisfied by the assumptions that production function is quasi concave and input prices are given to the firm.

Therefore equation (c) represents output supply  function of individual firm.

Graphically:

Equilibrium of the individual firm is shown in the following figure. From assumption 1 to 5 we can say that P is given to the individual firm. AR is a horizontal straight line which is equal to the MR curve. Here MC is positive and upward sloping from the assumption 6 and 7. Thus at the point of interaction between MC curve and MR curve we have P = MC at which MC is increasing, so for the corresponding output q, π is maximised. Thus q is the equilibrium output supplied by the individual firm which depends on the parameter P. thus output function of individual firm is defined by equation (c).           

                   

Economic Interpretation:

We have already explained that d TR / dq = MR = P > 0 and constant to the individual firm and d TC / dq = MC > 0. Therefore P and MC represent rise in TR and TC due to one unit rise in q respectively. Consider any output say q0 in the above figure where P>MC holds, i.e., for any unit rise in q increase in TR is larger than increase in TC. Thus (π = TR – TC) increases, so profit maximising firm will induce to rise q in further. As q increases further 1 unit, P does not change as it is given to the firm. But MC rises as d (MC) / dq > 0 by assumptions 6 and 7. So gap between P and MC decreases. If some gap exists then by similar logic it will keep on decreasing until P = MC holds. At this point for one unit rise in q rise in TR is just offset by rise in TC. So profit does not rise furthermore. Hence it reaches its maximum level. If initially P < MC holds then by reverse logic as q decreases , profit increases and gap between P and MC decreases as MC is rising. Clearly profit is maximised when P = MC holds at which MC is rising.

If MC is not rising , i.e. , suppose MC is falling, then at P = MC , profit is not maximised since , if initially P > MC holds as q increases, π increases , so π maximising firm will rise q further for which MC decreases, as MC is falling. P is given to the firm so P becomes far larger than MC. So π again increases and so on. This process will continue and gap between P and MC becomes larger and larger and π is ever rising, it can’t be maximise. So when MC is not rising i.e. production function is not quasi-concave i.e. convex then perfect competition is incompatible.

At equilibrium P = MC holds, we have marginal cost pricing. If P is not equal to MC i.e. if we deviate from marginal cost pricing then market is not perfectly competitive.

Concept of normal and supernormal profit.


r.k. is the normal return to the capital which is known as Normal Price. 
                   TC = w.l + r.k

Therefore TC includes normal profit if π = TR – TC = 0 then TR = TC. Then firm must earn (r.k) after paying labour cost (w.l). Hence firm earns just normal profit. If π = (TR – TC) > 0, then TR > TC holds. So after paying labour cost (w.l) and recovering (r.k) i.e. normal profit, firm retains something more. This is the additional profit of the firm, over the normal profit level which is known as supernormal or pure economical profit whose magnitude is π = ( TR – TC ) < 0 , then TR < TC holds. Firms fail to recover normal profit and hence firm incurs loss.


COMPETITION IN THE LABOUR MARKET


 Many people believe that perfect competition doesn’t actually happen in the real world, that it is merely a theoretical idea used to illustrate points in economics textbooks.

Examples of perfect competition typically used in textbooks like wheat, soybean etc. Are not really ideal examples because they are provided with public support in the form of subsidies or protective tariffs.

In fact, few if any goods are sold in perfectly competitive markets and firms seek to limit the pressure of competition in any way they can.

One market however in which perfect competition reigns supreme, where quality of one seller’s product is essentially identical to that of any other seller and number of sellers is very large. Competition forces price right down to the good’s marginal cost, every time. Not only have that – this market is really important – the fundamental building block of the economy – marketed for unskilled labour. Unskilled labourers are those workers who are selling their labour time, without any resources that would improve their bargaining power such as union membership, government regulation or professional license.

In a perfectly competitive market, π is maximised when P = MC.
What could this mean in the case of labour? What is labour’s marginal cost?
Labour’s marginal cost is essentially working another day instead of not working – the unskilled labour has no better alternative. So while it is true that workers engage in “profit maximising” behaviour, we must not forget that for most of them “profit maximising” means working instead of starving.

Any wage higher than mere subsistence will always be undercut by some other worker who is just a bit more desperate. Marginal cost of unskilled labour is equal to subsistence, which is the market clearing price.



-Riddhi Mazumdar, Presidency University, Kolkata.