Basic Statistics for Economics (Correlation of Coefficient (r), Coefficient of Variation (COV), Arithmetic Mean (AM).......

Basic Statistics for Economics...... 

1. Arithmetic Mean (AM): AM or average is the ratio of the sum of the series of observations of the values of a given variable unweighted or weighted and the total no. of observations or values.

Mathematically speaking,

AM = ∑f_ix_i / ∑f_i = ∑w_ix_i ; ∑f_i = N,

This is what is called the Weighted Arithmetic Mean where w_i (=f_i/N) represents the weight of the i-th item. When w₁ = w₂ = ................ = w_n = 1/N, the formula for simple AM can be derived.

1. Coefficient of Variation (COV): COV of a series of observation of values of a given variable represents the ratio of standard deviation (SD) and arithmetic mean (AM) in percentage term.

Mathematically speaking,

COV = SD/AM x 100 , where SD is the positive square root of variance.COV is one of the relative measures of dispersion in descriptive statistics. COV is positively and negatively related with SD and AM respectively. One of the interesting features of COV is that its value is significantly small and positive.

1. Correlation of Coefficient (r): Correlation of Coefficient (r) can be adopted as a statistical measure in the case of bivariate observations of a phenomenon. The value of r lies within the close interval of -1 and +1 i.e. r[-1,+1]. It can hold the values of -1, 0 and 1 in case of perfectively negative, zero and positive correlation respectively.

Mathematically speaking,

Correlation Coefficient (r_xy) = σ(xy) / σ_x . σ_{y ;} σ(xy) is covariance

Where, σ(xy) = 1/N ∑ (x- x̄) (y-ȳ)

σ_x = { 1/N ∑ (x- x̄)² }^1/2

σ_y = { 1/N ∑ (y-ȳ)² }^1/2

 
 

Supply and Quantity Supplied, Law of supply, Market Supply Curve

Ø Supply and Quantity Supplied:

To set the stage for an understanding of this difference, take note of two related concepts:

• Quantity Supplied: Quantity supply is a specific quantity that sellers are willing and able to sell at a specific supply price. It is but ONE point on a supply curve.
• Supply: Supply is the range of quantities that sellers are willing and able to sell at a range of supply prices. It is ALL points that make up a supply curve.

• Change in Quantity Supplied: A change in quantity supplied is a change from one price-quantity pair on an existing supply curve to a new price-quantity pair on the SAME supply curve. In other words, this is a movement along the supply curve. A change in quantity supplied is caused by a change in price.

Change in Supply: A change in supply is a change in the ENTIRE supply relation. This means changing, moving, and shifting the entire supply curve. The entire set of prices and quantities is changing. In other words, this is a shift of the supply curve. A change in supply is caused by a change in the five supply determinants.

Ø Market Supply Curve:

Economists distinguish between the supply curve of an individual firm and between the market supply curve. The market supply curve is obtained by summing the quantities supplied by all suppliers at each potential price. Thus, in the graph of the supply curve, individual firms' supply curves are added horizontally to obtain the  market supply curve.

    Ø Supply curve: 

The supply curve is a graphical representation of the relationship between the price of a good or service and the quantity supplied for a given period of time. In a typical representation, the price will appear on the left vertical axis, the quantity supplied on the horizontal axis.

   

    Ø Law of supply :

The law of supply is a fundamental principle of economic theory which states that, all else equal, an increase in price results in an increase in quantity supplied.^[1] In other words, there is a direct relationship between price and quantity: quantities respond in the same direction as price changes. This means that producers are willing to offer more products for sale on the market at higher prices by increasing production as a way of increasing profits.^[2]

In short, Law of Supply is a positive relationship between quantity supplied and price and is the reason for the upward slope of the supply curve.

Key Concepts: Market, Demand Curve,Equilibrium Price, Market Demand Schedule

Ø What is a 'Market'?:

A market is a medium that allows buyers and sellers of a specific good or service to interact in order to facilitate an exchange. This type of market may either be a physical marketplace where people come together to exchange goods and services in person, as in a bazaar or shopping center, or a virtual market wherein buyers and sellers do not interact, as in an online market.

Ø Definition of 'Demand Curve':

The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis, the quantity demanded on the horizontal axis. 

 

Ø Equilibrium price:

In ordinary usage, price is the quantity of payment or compensation given by one party to another in return for goods or services at a market equilibrium determined by intersection  of  supply & demand. In modern economies, prices are generally expressed in units of some form of currency.

Ø Market demand curve;

  The market demand curve is the summation of all the individual demand curves in a given market. It shows the quantity demanded of the good by all individuals at varying price points. For example, at $10/latte, the quantity demanded by everyone in the market is 150 lattes per day.

Ø Market demand schedule:

 Market demand schedule  refers to a tabular statement showing various quantities of a commodity that all the consumers are willing to buy at various levels of price, during a given period of time. It is the sum of all individual demand schedules at each and every price.

Economic goods, free goods, Public Good, Private Good

Ø Economic goods and free goods:

·        The vast majority of goods and services are what economists call economic goods. An economic good is one which takes resources to produce it. As a result, its production involves an opportunity cost. Thus the possession of those goods require financial payments.

·        Free goods are abundant in nature. They do not involve the use of resources to produce them and so they do not have an opportunity cost. Thus the possession of those goods require no financial payments as  such. Examples include sunlight and air.

Ø What is a 'Public Good'?

A public good is a product that one individual can consume without reducing its availability to another individual, and from which no one is excluded. Economists refer to public goods as "nonrivalrous" and "nonexcludable." National defense, sewer systems, public parks and other basic societal goods can all be considered public goods.

   Ø Characteristics of public goods:

There are two specific characteristics of a public good.

·        It must be non-excludable. This means that once the good has been provided for one consumer, it is impossible to stop all other consumers from benefitting from the good.

    Ø It must also be non-rival. As more and more people consume the good, the benefit to those already consuming the product must not be diminished.

Ø What is a 'Private Good'?

A private good is a product that must be purchased to be consumed, and its consumption by one individual prevents another individual from consuming it. Economists refer to private goods as rivalrous and excludable. A good is considered to be a private good if there is competition between individuals to obtain the good and if consuming the good prevents someone else from consuming it.

MRT or Marginal rate of transformation i.e. Slope of PPC/PPF

Ø Marginal rate of transformation:

The slope of the production–possibility frontier (PPF) at any given point is called the marginal rate of transformation (MRT). The slope defines the rate at which production of one good can be redirected (by reallocation of productive resources) into production of the other. It is also called the (marginal) "opportunity cost" of a commodity, that is, it is the opportunity cost of X in terms of Y at the margin. It measures how much of good Y is given up for one more unit of good X or vice versa. The shape of a PPF is commonly drawn as concave to the origin to represent increasing opportunity cost with increased output of a good. Thus, MRT increases in absolute size as one moves from the top left of the PPF to the bottom right of the PPF

Ø Explanation of PPC/PPF:

Economists also use the PPF model to illustrate two categories of goods, both consumer goods and capital goods. So here is what that PPF curve looks like. aaaEvery point along the curve is efficient; points outside the curve are unobtainable or inefficient.

Why are most production possibility curves outward bowed (concave)? and Limitations of PPC

Ø Why are most production possibility curves outward bowed (concave)?

Production Possibility Curve is concave to the origin because to produce each additional unit of good X, more and more unit of good Y is to be sacrificed. Opportunity cost of producing every additional unit of good A tends to increase in terms of the loss of production of good Y. It is so because factors of production are not perfect substitute of each other.

Ø Limitations of PPC:

• Preferences: Production possibilities analysis is designed to analyze production capabilities. It can answer questions about the quantity of one good produced, given the production of another good. This analysis does not say if anyone actually wants the goods produced. Production possibilities says nothing about which goods people want and which provide the most satisfaction. It only indicates the available options.

Economic Efficiency: Because production possibilities is unrelated to preferences, it provides no indication of economic efficiency. While production possibilities might indicate what quantities can be produced, it does NOT indicate if this is an efficient use of resources. It does not indicate if this combination of goods provides the most satisfaction possible

Assumptions of PPC and Different Shapes of PPC/PPF

Ø Assumptions of PPC:

The four key assumptions underlying production possibilities analysis are: 

(1) resources are used to produce one or both of only two goods, (2) the quantities of the resources do not change, (3) technology and production techniques do not change, and (4) resources are used in a technically efficient way.

Ø What happens if the production possibilities curve is a straight line?

If the production possibility frontier is straight, it means that the resources released by producing one fewer unit of peanut butter are just sufficient to allow the economy to produce the same added amount of jelly, regardless of how much of each item is currently being produced. In economic terminology, we say that the marginal rate of substitution between the two items in question is constant. That’s very unlikely to be the case if more than one input is used in the production process of either.

One implication is that if the economy is producing both peanut butter and jelly, the price of peanut butter must be three times the price of jelly. That outcome is most likely if the economy is isolated from international trade.

On the other hand, if the country is exposed to international trade, a straight-line PPF will normally imply that the country will fully specialize in the production of one good or the other: if the world price of peanut butter is more than three times the price of jelly, this country will produce only peanut butter and no jelly; and conversely if the world price of peanut butter is less than three times the price of jelly. This kind of specialization is a familiar result from the Ricardian theory of comparative advantage.