The Binomial Distribution is one of the discrete probability distribution. It is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are appropriately labeled Successand Failure. The Binomial Distribution is used to obtain the probability of observing r successes in n trials, with the probability of success on a single trial denoted by p.
P(X = r) = nCr p r (1-p)n-r where, n = Number of events r = Number of successful events. p = Probability of success on a single trial. nCr = ( n! / (n-r)! ) / r! 1-p = Probability of failure.
Example: Toss a coin for 12 times. What is the probability of getting exactly 7 heads.
Step 1: Here, Number of trials n = 12 Number of success r = 7 since we define getting a head as success Probability of success on any single trial p = 0.5
Step 2: To Calculate nCr formula is used. nCr = ( n! / (n-r)! ) / r! …
A Pigovian tax (also spelled Pigouvian tax) is a tax levied on a market activity that generatesnegative externalities. The tax is intended to correct the market outcome. In the presence of negative externalities, the social cost of a market activity is not covered by the private cost of the activity. In such a case, the market outcome is not efficient and may lead to over-consumption of the product. A Pigovian tax equal to the negative externality is thought to correct the market outcome back to efficiency.
In the presence of positive externalities, i.e., public benefits from a market activity, those who receive the benefit do not pay for it and the market may under-supply the product. Similar logic suggests the creation of Pigovian subsidies to make the users pay for the extra benefit and spur more production.
Pigovian taxes are named after economistArthur Pigou who also developed the concept ofeconomic externalities. William Baumol was instrumental in framing Pigou'…
The Coase theorem states that where there is a conflict of property rights, the involved parties can bargain or negotiate terms that are more beneficial to both parties than the outcome of any assigned property rights. The theorem also asserts that in order for this to occur, bargaining must be costless; if there are costs associated with bargaining (such as meetings or enforcement), it will affect the outcome. The Coase theorem shows that where property rights are concerned, involved parties do not necessarily consider how the property rights are granted if they can trade to produce a mutually advantageous outcome.
This theorem was developed by Ronald Coase when considering the regulation of radio frequencies. He posited that regulating frequencies was not required because stations with the most to gain by broadcasting on a particular frequency would have an incentive to pay other broadcasters not to interfere.
The Coase Theorem: Controlling Externalities through assigning property r…
Dr Ashfaque H Khan
The present government will be presenting its fifth and the last budget on June 1, 2012. Given the persistence of political tension throughout the tenure, deterioration of security environment, unfolding of multiple epoch making events and intensification of the war on terror, presenting the fifth budget is in itself nothing short of a big achievement for the government.
Budget 2012-13 is being prepared in an inhospitable economic environment, both domestically and externally. The domestic economic environment is largely a creation of the government itself.
In fact, there is general consensus within and outside the country that the economy of Pakistan has never been in a state such as this until now. Pakistan has faced serious economic difficulties in the past, but has managed to sail through because of a strong and committed leadership and competent economic team. There is widespread scepticism as to the strength and effectiveness of…
A liquidity trap is a situation described in Keynesian economics in which injections of cash into the private banking system by a central bank fail to lower interest rates and hence to stimulate economic growth. A liquidity trap is caused when people hoard cash because they expect an adverse event such as deflation, insufficient aggregate demand, or war. Signature characteristics of a liquidity trap are short-term interest rates that are near zero and fluctuations in the monetary base that fail to translate into fluctuations in general price levels.
In its original conception, a liquidity trap refers to the phenomenon when increased money supply fails to lower interest rates. Usually central banks try to lower interest rates by buying bonds with newly created cash. In a liquidity trap, bonds pay little to no interest, which makes them nearly equivalent to cash. Under the narrow version of Keynesian theory in which this arises, it is specified that monetary policy affects the econom…
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ISLM aggregates the economy into a market for money balances, a market for goods and services, and a residual market that it ignores by invoking Walras' Law. Since part of the residual market is the labor market, and because adjustment in this market is slow, ISLM would be a better model if it could capture what is happening in the resource markets. Aggregate supply-aggregate demand analysis makes this incorporation.
The aggregate demand curve is derived from the ISLM model. In the illustration below, equilibrium income is Y1 when the price level is P1. Let the price level rise to a higher level, from P1 to P2. At the higher level, with a constant amount of money, purchasing power is cut. The fixed number of dollars no longer buys as much. The effects on the LM curve are identical to what happens when prices remain fixed and the amount of money falls. The LM curve, in either case, shifts left, interest rates rise, and income falls. The output levels at both P1 and P2 are shown i…
Most businesses charge different prices to different groups of consumers for what is more or less the same good or service! This is price discrimination and it has become widespread in nearly every market. This note looks at variations of price discrimination and evaluates who gains and who loses?
What is price discrimination?
Price discrimination or yield management occurs when a firm charges a different price to different groups of consumers for an identical good or service, for reasons not associated with costs.
It is important to stress that charging different prices for similar goods is not pure price discrimination.
We must be careful to distinguish between price discrimination and product differentiation – differentiation of the product gives the supplier greater control over price and the potential to charge consumers a premium price because of actual or perceived differences in the quality / performance of a good or service.
Conditions necessary f…