Giffen’s paradox is an economic term named after the British economist and statistician Robert Giffen. The law of demand states that when the price of a commodity falls, the demand for it rises. However Giffen’s Paradox is an exception to this law. This is, Giffen goods are those goods whose demand moves in the same direction as the price variation. In other words, raising the price of the good will increase its demand. Consequently any Giffen good has an upward-sloping demand curve.

Alfred Marshall coined this term in his third edition of his “Principles of Economics”, 1895, where he wrote:

“As Mr. Giffen has pointed out, a rise in the price of bread makes so large a drain on the resources of the poorer labouring families and raises so much the marginal utility of money to them, that they are forced to curtail their consumption of meat and the more expensive farinaceous foods: and, bread being still the cheapest food which they can get and will take, they consume more, and not less of it.”

The Lagrange function is used to solve optimization problems in the field of economics. It is named after the Italian-French mathematician and astronomer, Joseph Louis Lagrange. Lagrange’s method of multipliers is used to derive the local maxima and minima in a function subject to equality constraints.

The existence of constraints in optimization problems affects the optimal value of the function since it implies a reduction of the feasible solutions space. Lagrange’s method multiplier is precisely used to measure how the correspondent restriction affects the optimal value of the objective function. In other words, they measure the degree of responsiveness of the problem’s optimal value due to changes in the constraints.

Mathematically, it is equal to the objective function’s first partial derivative regarding its constraint, and multiplying this last one by a lambda scalar (λ), which is an additional variable that helps to sort out the equation.

Let’s consider the following optimization problem:

The objective is to maximize (or minimize) a function with several variables 

subject to the equality constraints

And we introduce the Lagrangian function,

Constrained optimisation plays a central role in Economics. For example, the consumer’s choice problem can be represented by either fixing a budget and obtaining its maximum utility (primal demand), or by setting a level of utility we want to achieve and minimise cost (dual demand). Other examples include profit maximization, along with various macroeconomic applications. Similarly to the previous example, the firm’s input decision has a dual nature. This is, it should find the optimal level of output given the resources available (minimising cost) or,  having a budget constraint, solve the inputs allocation that results in  the highest output (maximising production).

Economic science makes a distinction between normative and positive economics. Positive economics is the branch of economics that focuses in the description and explanation of economic phenomena, while normative is concerned with the application of positive economics with the purpose of giving advice on practical problems including those regarding public policy.

We can easily make the distinction between positive and normative economics by asking two very different questions: “What is?” and “What ought to be?”. As stated before, positive economics focuses on analysing economic phenomena, on answering the question “What is?”. Normative economics wants to answer the question “What ought to be?”. In other words, how can I apply something I found out (positive economics) to the real world (normative economics)? Thus, we can think of positive economics as being the purely scientific part of the economic discipline being objective and fact-based, while normative economics is more subjective to values and hence considered non-scientific.

Normative economics analyses can be found both at a microeconomic and macroeconomic level. For instance, welfare economics has a purely normative branch, which aims at finding better ways of arriving to optimum conditions and equilibriums to benefit a greater amount of people. Also, at the macro level, all related to policymaking is considered to be part of the normative economics branch.

Economic science makes a distinction between positive and normative economics. While the former is the branch of economics that focuses in the description and explanation of economic phenomena, the latter is concerned with the application of positive economics with the purpose of giving advice on practical problems including those regarding public policy.

We can easily make the distinction between positive and normative economics by asking two very different questions: “What is?” and “What ought to be?”. As stated before, positive economics focuses on analysing economic phenomena, on answering the question “What is?”. Normative economics wants to answer the question “What ought to be?”. In other words, how can I apply something I found out (positive economics) to the real world (normative economics).

The distinction was first made during the nineteenth century, by some of the most renowned economists of the classical school, such as John Stuart Mill or John Neville Keynes (John M. Keynes’ father). In their analysis, these economists first observed an economic phenomenon, and then postulated a hypothesis aiming at explaining the phenomenon. This hypothesis would then tested against factual observations of economic behaviour, in order to determine the theories’ scope of applicability.

Thus, we can think of positive economics as being the purely scientific part of the economic discipline being objective and fact-based, while normative economics is more subjective to values and hence considered non-scientific. As a result, only positive economic statements can be tested and accepted or disregarded, however as normative economics statements are opinion based they can neither be right nor wrong.

Elasticity is a concept introduced by British economist Alfred Marshall, and is used in order to measure the variation that a variable suffers when another variable is changed. We can distinguish between different types of elasticity depending on the variables we are using.

Probably the most common example is price elasticity of demand, which measures changes in the demand of a good or service when its price is increased or decreased. It’s important to note that only price should be modified; this is, ceteris paribus, as in the contrary our measurement would be affected by changes in other variables. Depending on the type of good we analyse, we will see different relations between price changes and demand variation. For example, in the case of ordinary goods, an increase (decrease) of price will result in a decrease (increase) of demand, and thus will follow a negative relation. However, with Giffen goods the contrary will be true, an increase (decrease) of price will result in an increase (decrease) of demand, which this time implies a positive relation between both variables. Regarding elasticity, apart from the direction or the sign of the relation we also look at the degree of responsiveness. This way, we distinguish between inelastic goods (or relative inelasticity) and elastic goods (or relative elasticity). When, in absolute terms, the value of price elasticity of demand is lower than one, we’ll have inelasticity and, if it is higher than one, we’ll have elasticity.

Another example of elasticity that is frequently found in Economics textbooks is income elasticity of demand. It measures variation in demand due to changes in the consumers’ income. Normal goods are those whose demand increases due to a rise in income levels, having therefore a positive correlation, which implies that the elasticity of this kind of goods is always higher than 0. On the other hand, inferior goods are those whose demand moves in opposite direction to the income variation of consumers.

Similarly to price elasticity of demand, crossed elasticity measures the variation in demand but in this case as a result of changes in other goods’ prices. In the case of normal goods, an increase in the price of substitutive goods will imply a higher demand for the other substitutive goods.

Concerning firms, the Lerner index can capture the relationship between price elasticity of demand and market power. It does this by measuring the firm’s level of market power by relating the selling price to marginal cost. Therefore, the extent to which a firm can take advantage of its monopolistic power will highly depend on the elasticity of its demand curve. If it is more rigid (steeper), it will only have to reduce its production in order to achieve a higher price. However the more flexible (flatter) the demand curve is, the less market power the firm has to increase prices.

The Big Mac index was invented in 1986 by the magazine The Economist, and considers the Big Mac hamburger sold in McDonald’s as its basket of reference. This index is based on the purchasing power parity theory. When analysing exchange rates through this theory, we compare an homogeneous basket of goods (a Big Mac) available in the analysed countries.

Since Big Macs are sold all around the world and can be considered to be homogeneous, it allows us to make simple calculations. For example, if the price of a Big Mac in the US is $1.2 and in Brussels €1, the exchange rate should be 0.83 euros per dollar. By dividing the domestic currency price in each country by the price in dollars, we can calculate the purchasing-power parity, and comparing it with the current exchange rates test whether the currency is under or overvalued.

The results are not exact because there are other factors that influence them, for instance, the local preferences of the consumers. However, they give a reasonable approximation with a very simple calculation.

More on the Big Mac index in The Economist website.