Lec 1: Scarcity and Feasibility

What is the defining feature of economics?

Scarcity

What does scarcity imply about an individuals consumption set?

The consumption set is limited, individuals cannot choose from every bundle in their consumption set. The set of feasible consumption bundles is a proper subset of the consumption set

What are some forms of scarcity?

Wealth constraints, time constraints, and technology constraints

What is the budget set?

The budget set is the set of all consumption bundles that an individual can afford given their wealth and commodity prices

Does the budget set or consumption set vary with price and wealth

Budget set

In the context of wealth, what happens to the budget set as prices and wealth change?

The budget set varies with prices and wealth, but the consumption set does not. Therefore, the budget set is a subset of the consumption set As wealth increases or prices decrease, the budget set expands, allowing for more affordable consumption bundles. Conversely, a decrease in wealth or an increase in prices contracts the budget set

How is the budget line expressed in a two-commodity world?

the line is given by the equation p1q1 + p2q2 = y, where p1 and p2 are the prices of the two commodities, and y is the individuals wealth

What is the slope of the budget line in a two-commodity world?

the slope is -p1/p2, representing the rate at which one commodity can be traded for another

What are the q1 and q2 intercepts of the budget line in a two commodity world with a slope of -p1/p2?

the q1 intercept is y/p1 and the q2 intercept is y/p2

What is the “y=mx+b” form of the budget line p1q1 + p2q2 = y?

q2 = -(p1/p2)q1 + (y/p2)

What happens when the individual is endowed with a commodity bundle instead of monetary wealth?

The budget set is based on the market value of the endowed commodity bundle, rather than monetary wealth

How does an increase in the price of a commodity affect the budget set?

An increase in the price of a commodity reduces the budget set by decreasing the number of bundles that can be afforded

what is the time constraint in the context of scarcity?

The limited amount of time available for individuals to allocate between different activities or choices in each period, impacting their decision-making regarding resource use.

What is the time constraint where there are two activities (labour and leisure)?

The time constraint is tN + tL = T, where tN is the time spent on labour and tL is the time spend on leisure

How are time and budget constraints combined when an individual has both wealth and time?

The individual faces both a budget constraint (based on monetary income and prices) and a time constraint (based on the total available time for labour and leisure). This combination determines the feasible set of choices regarding consumption and work hours.

What is the price of leisure when time is allocated between labour and leisure?

The price of leisure is the wage rate, wL, representing the foregone income when time is spent on leisure rather than labour. It reflects the opportunity cost of leisure in terms of potential earnings.

What is the two constraint equation when an individual faces two feasible constraints (the budget constraint and time constraint)?

budget: pC + wL ≤ y + wT and time: L + N = T this can be combined to pC ≤ y + wN

What is the concept of composite commodities in economics?

Composite commodities aggregate multiple goods into a single commodity, simplifying consumption choices and certain conditions. This concept allows economists to analyze consumer behavior by treating a group of related goods as one, making it easier to study demand and preferences.

Ordinary (or uncompensated, or Marshallian, or Walrasian) demand are homogenous of degree…

Zero in all prices and income. Consumer demand only varies with changes in relative price and the purchasing power of income.

What is the Hicks-Leontief “Composite Commodity Theorem”?

The theorem states that if relative prices between commodities in a set remain unchanged, those commodities can be treated as a single composite commodity with a unified price

What is the use of a price normalisation in economic models?

Price normalisation allows comparison of relative prices and simplifies analysis by fixing one commodities price (often setting it to 1) or adjusting prices so that the sum of all prices equals 1

What is the price simplex in economics?

The price simples is the set of all possible price combinations in an economy, constrained by the condition that the sum of all prices equals 1

How does the concept of ordinary demand relate to price normalisation?

Ordinary demand is homogeneous of degree zero in prices and income, meaning that consumer demand is only affected by relative prices and income, not their absolute levels

What is an alternative price normalisation using a commodity bundle?

An alternative price normalisation involves using the expenditure on a bundle consisting of one unit of each commodity as the numeraire, leading to the sum of all commodity prices being equal to 1

How does the price simplex relate to general equilibrium models?

In general equilibrium models, the price simplex represents all possible price combinations and its used to prove the existence of a competitive equilibrium.

Consumption Set Equation

C = Rn+ = {(q1, q2, …, qn): 0 ≤ q1 < ∞ A/ € {1, 2, …, n}}

Budget Set Equation

B(p, y) = {(q1, q2, …, qm) € C: ∑n I=1 (pIqI) ≤ y}

Budget set equation for only two commodities

B(p1, p2, y) = {(q1, q2) : p1q1 + p2q2 ≤ y, q1≥ 0, q2 ≥ 0}