<h5 id="preliminary-notations-and-assumptions">Preliminary Notations and Assumptions</h5> <ul> <li>A consumer’s choice problem is simplified to the consideration of two goods: bananas and mangoes.</li> <li>The quantity of bananas is denoted as $x_{1}$ and mangoes as $x_{2}$.</li> <li>Both $x_{1}$ and $x_{2}$ can be positive or zero.</li> <li>$\left(x_{1}, x_{2}\right)$ represents a bundle consisting of $x_{1}$ quantity of bananas and $x_{2}$ quantity of mangoes.</li> <li>Specific bundles are represented by particular values of $x_{1}$ and $x_{2}$, for example, $(5,10)$ represents a bundle of 5 bananas and 10 mangoes.</li> </ul> <p>======</p> <h5 id="21-utility">2.1 UTILITY</h5> <ul> <li>Utility is the want-satisfying capacity of a commodity.</li> <li>The more the need or desire for a commodity, the greater the utility derived.</li> <li>Utility is subjective, varying from person to person based on their preferences.</li> <li>An individual’s utility from a commodity can also change with place and time.</li> <li>For example, the utility of a room heater would be higher for someone in Ladakh in winter than for someone in Chennai in summer.</li> </ul> <p>======</p> <h5 id="211-cardinal-utility-analysis">2.1.1 Cardinal Utility Analysis</h5> <ul> <li>The text discusses the Law of Diminishing Marginal Utility, which states that marginal utility from consuming each additional unit of a commodity declines as its consumption increases.</li> <li>Marginal utility becomes zero at a level when total utility remains constant, and thereafter, total utility starts falling and marginal utility becomes negative.</li> <li>Cardinal utility analysis can be used to derive demand curve for a commodity, which is a graphical presentation of various quantities of a commodity that a consumer is willing to buy at different prices.</li> <li>Demand for a commodity depends on factors such as prices of other commodities, income of the consumer, and tastes and preferences of the consumers.</li> <li>The downward sloping demand curve shows that at lower prices, the individual is willing to buy more of the commodity, and at higher prices, she is willing to buy less of it, reflecting the Law of Demand. The law of diminishing marginal utility explains this negative slope.</li> </ul> <p>======</p> <h5 id="212-ordinal-utility-analysis">2.1.2 Ordinal Utility Analysis</h5> <ul> <li>The text discusses the concept of indifference curves in economics.</li> <li>Combinations of bananas and mangoes, A, B, and C, with the same quantity of mangoes but different quantities of bananas, are presented.</li> <li>Based on the quantity of bananas, B and C offer higher satisfaction than A, and C offers higher satisfaction than B, represented by higher indifference curves.</li> <li>Higher indifference curves represent combinations that give higher levels of satisfaction.</li> <li>Two indifference curves never intersect each other to avoid conflicting results. If they did, it would imply that a higher quantity of mangoes provides the same level of satisfaction as a lower quantity, which is absurd.</li> </ul> <p>======</p> <h5 id="22-the-consumers-budget">2.2 The Consumer’s Budget</h5> <ul> <li>The Consumer’s Budget is based on a consumer’s fixed income and the prices of goods in the market.</li> <li>The consumer cannot buy any and every combination of the two goods.</li> <li>The consumption bundles available to the consumer depend on the prices of the goods and the consumer’s income.</li> <li>The consumer can only buy those bundles which cost her less than or equal to her income.</li> <li>The set of all affordable bundles is called the consumer’s budget set.</li> </ul> <p>======</p> <h5 id="221-budget-set-and-budget-line">2.2.1 Budget Set and Budget Line</h5> <ul> <li>The budget set is the collection of all bundles that the consumer can buy with her income at the prevailing market prices, represented by the inequality $p_{1} x_{1} + p_{2} x_{2} \leq M$.</li> <li>The budget line is the line that consists of all bundles which cost exactly equal to M, represented by the equation $p_{1} x_{1} + p_{2} x_{2} = M$.</li> <li>The slope of the budget line is $-\frac{p_{1}}{p_{2}}$, representing the rate at which the consumer can substitute bananas for mangoes when she spends her entire budget.</li> <li>The horizontal intercept of the budget line represents the bundle that the consumer can buy if she spends her entire income on bananas, and the vertical intercept represents the bundle that the consumer can buy if she spends her entire income on mangoes.</li> <li>The budget set can be represented in a diagram as the collection of all bundles that are on or below the budget line, with quantity of bananas measured along the horizontal axis and quantity of mangoes measured along the vertical axis.</li> </ul> <p>======</p> <h5 id="222-changes-in-the-budget-set">2.2.2 Changes in the Budget Set</h5> <ul> <li>The set of available bundles depends on the prices of goods and consumer’s income.</li> <li>When income changes from M to M’, the consumer can afford bundles with the equation p1x1+p2x2 ≤ M'.</li> <li>If income increases, there is a parallel outward shift of the budget line, and if income decreases, there is a parallel inward shift.</li> <li>When the price of one good changes, the vertical intercept remains the same, but the slope and horizontal intercept change.</li> <li>An increase in the price of one good makes the budget line steeper, and a decrease makes it flatter.</li> </ul> <p>======</p> <h5 id="23-optimal-choice-of-the-consumer">2.3 Optimal Choice of the Consumer</h5> <ul> <li>The consumer’s budget set consists of all bundles that are available to her. She chooses her consumption bundle from the budget set based on her tastes and preferences.</li> <li>The optimum bundle of the consumer is located at the point where the budget line is tangent to an indifference curve. This is the point where the absolute value of the slope of the indifference curve (MRS) and that of the budget line (price ratio) are the same.</li> <li>A rational consumer always chooses the bundle which gives her maximum satisfaction from the bundles available to her.</li> <li>If the consumer’s preferences are monotonic, the optimum (most preferred) bundle of the consumer would be on the budget line where the budget line is tangent to an indifference curve.</li> <li>The point at which the budget line just touches (is tangent to), one of the indifference curves would be the optimum as any other point on the budget line lies on a lower indifference curve and hence is inferior.</li> </ul> <p>======</p> <h5 id="24-demand">2.4 Demand</h5> <ul> <li>Demand is the quantity of a commodity that a consumer is willing to buy and can afford, given prices of goods and consumer’s tastes and preferences.</li> <li>It is dependent on the price of the good, prices of other goods, consumer’s income, and tastes and preferences.</li> <li>A change in any of these variables can result in a change in the amount of the good chosen by the consumer.</li> <li>The relationship between the quantity of the good chosen by the consumer and each of these variables will be studied individually.</li> <li>The amount of a good that a consumer chooses optimally is called the consumer’s demand for the commodity.</li> </ul> <p>======</p> <h5 id="241-demand-curve-and-the-law-of-demand">2.4.1 Demand Curve and the Law of Demand</h5> <ul> <li>The demand curve is a relation between the quantity of a good chosen by a consumer and the price of the good.</li> <li>A function is a relation between two variables where for each value of the independent variable, there is an unique value of the dependent variable.</li> <li>An increasing function is one where the value of the dependent variable does not decrease with an increase in the independent variable.</li> <li>A decreasing function is one where the value of the dependent variable does not increase with an increase in the independent variable.</li> <li>The demand curve can be represented graphically as the function X=f(P), where X is the quantity and P is the price of the good. The graph of this function is known as the demand curve.</li> </ul> <p>======</p> <h5 id="242-deriving-a-demand-curve-from-indifference-curves-and-budget">2.4.2 Deriving a Demand Curve from Indifference Curves and Budget</h5> <ul> <li>The demand curve for a commodity is negatively sloped, meaning that as the price of the commodity decreases, the demand for it increases, and vice versa, given other factors remaining constant.</li> <li>This negative relationship is explained by the substitution effect and the income effect that come into play when the price of a commodity changes.</li> <li>The substitution effect results in an increase in demand for bananas as they become cheaper, leading to a substitution of bananas for mangoes to maintain the same level of satisfaction.</li> <li>The income effect results in an increase in purchasing power as the price of bananas drops, further increasing demand for bananas and mangoes.</li> <li>The Law of Demand states that there is a negative relationship between the price of a commodity and its demand, with demand increasing as the price decreases and vice versa, other factors remaining constant.</li> <li>A linear demand curve can be represented by the equation d(p) = a - bp, where a is the horizontal intercept, b is the slope of the demand curve, and the slope measures the rate at which demand changes with respect to its price.</li> </ul> <p>======</p> <h5 id="243-normal-and-inferior-goods">2.4.3 Normal and Inferior Goods</h5> <ul> <li> <p>Demand function is a relation between the consumer’s demand for a good and its price, but it can also be studied in relation to the consumer’s income.</p> </li> <li> <p>Normal goods are those for which the quantity demanded increases as consumer income increases and decreases as consumer income decreases.</p> </li> <li> <p>Inferior goods are those for which the demand moves in the opposite direction of the consumer’s income. As income increases, the demand for an inferior good falls, and as income decreases, the demand for an inferior good rises.</p> </li> <li> <p>A good can be a normal good at some levels of income and an inferior good at other levels of income.</p> </li> <li> <p>A Giffen good is a specific type of inferior good where a rise in the purchasing power (income) can induce the consumer to reduce the consumption of the good, and the demand for such a good can be inversely or positively related to its price depending on the relative strengths of the substitution and income effects.</p> </li> </ul> <p>======</p> <h5 id="244-substitutes-and-complements">2.4.4 Substitutes and Complements</h5> <ul> <li>The relation between the quantity of a good chosen by a consumer and the price of a related good can be studied.</li> <li>If two goods are consumed together, they are called complementary goods (e.g. tea and sugar, shoes and socks). The demand for a complementary good moves in the opposite direction of the price of its complementary goods.</li> <li>If the price of a complementary good increases, the demand for the other good is likely to decrease, and vice versa. This is because they are consumed together.</li> <li>Goods that can be used in place of each other are called substitutes (e.g. tea and coffee). The demand for a good moves in the direction of the price of its substitutes.</li> <li>If the price of a substitute good increases, the demand for the other good is likely to increase, and vice versa. This is because consumers can shift to the other good.</li> </ul> <p>======</p> <h5 id="245-shifts-in-the-demand-curve">2.4.5 Shifts in the Demand Curve</h5> <ul> <li>The demand curve can shift due to changes in consumer income, prices of related goods, and tastes/preferences.</li> <li>For normal goods, an increase in consumer income results in a rightward shift of the demand curve, while for inferior goods, it results in a leftward shift.</li> <li>A change in the price of a substitute good will shift the demand curve rightward if the price increases, and leftward if the price decreases.</li> <li>A change in the price of a complementary good will shift the demand curve leftward if the price increases, and rightward if the price decreases.</li> <li>A change in consumer preferences towards/against a good will shift the demand curve rightward/leftward, respectively.</li> </ul> <p>======</p> <h5 id="246-movements-along-the-demand-curve-and-shifts-in-the-demand-curve">2.4.6 Movements along the Demand Curve and Shifts in the Demand Curve</h5> <ul> <li>The demand function is a relation between the amount of a good and its price, keeping other factors constant.</li> <li>The demand curve is a graphical representation of the demand function, with higher prices corresponding to less demand and lower prices to more demand.</li> <li>Changes in price result in movements along the demand curve, while changes in other factors (prices of other goods, income, tastes, and preferences) cause shifts in the demand curve.</li> <li>Figure 2.17 illustrates movements along the demand curve (panel a) and shifts of the demand curve (panel b).</li> <li>In panel (a), a movement along the demand curve occurs due to a change in price, while in panel (b), a shift in the demand curve is caused by a change in other factors.</li> </ul> <p>======</p> <h5 id="25-market-demand">2.5 Market Demand</h5> <ul> <li>Market demand for a good is the total demand of all consumers in a market for that good.</li> <li>It can be derived from individual demand curves through horizontal summation.</li> <li>At a specific price, market demand is the sum of individual demands at that price.</li> <li>The market demand curve can also be derived graphically by adding up individual demand curves horizontally.</li> <li>In the example provided, the market demand for a market with two consumers and their linear demand curves was derived.</li> </ul> <p>======</p> <h5 id="26-elasticity-of-demand">2.6 Elasticity of Demand</h5> <ul> <li>The initial price (P1) and quantity (Q1) of a good are 5$ and 15, respectively. The new price (P2) and quantity (Q2) are 7$ and 12.</li> <li>The percentage change in quantity demanded is -20% and the percentage change in market price is 40%.</li> <li>This indicates that as the price of the good increases, the demand for it decreases, with a price elasticity of demand of 0.5.</li> <li>The demand for this good is inelastic, as the percentage change in quantity demanded is less than the percentage change in market price.</li> <li>This is typical for essential goods, where the demand is not very responsive to changes in price.</li> </ul> <p>======</p> <h5 id="261-elasticity-along-a-linear-demand-curve">2.6.1 Elasticity along a Linear Demand Curve</h5> <ul> <li>The elasticity of demand along a linear demand curve is given by the formula $e_D = -\frac{b p}{a-b p}$, where $p$ is the price and $q$ is the quantity demanded.</li> <li>The elasticity of demand is zero at $p=0$, infinite at $q=0$, and 1 at $p=\frac{a}{2 b}$. It is less than 1 at prices greater than 0 and less than $\frac{a}{2 b}$, and greater than 1 at prices greater than $\frac{a}{2 b}$.</li> <li>The elasticity of demand can be geometrically measured as the ratio of the lower segment and the upper segment of the demand curve at any point.</li> <li>A vertical demand curve has an elasticity of 0, making it perfectly inelastic, while a horizontal demand curve has an elasticity of $\infty$, making it perfectly elastic.</li> <li>A demand curve with the shape of a rectangular hyperbola has a constant elasticity of 1, making it a unitary elastic demand curve.</li> </ul> <p>======</p> <h5 id="262-factors-determining-price-elasticity-of-demand-for-a-good">2.6.2 Factors Determining Price Elasticity of Demand for a Good</h5> <ul> <li>The price elasticity of demand for a good is influenced by its nature and the availability of close substitutes.</li> <li>Necessities like food have inelastic demand, as they are essential for life and less responsive to price changes.</li> <li>Luxuries, however, have elastic demand, as they are more responsive to price changes.</li> <li>For specific food items, demand can be more elastic due to the availability of close substitutes.</li> <li>The demand for a good is likely to be elastic if close substitutes are easily available, and inelastic if close substitutes are not readily available.</li> </ul> <p>======</p> <h5 id="263-elasticity-and-expenditure">2.6.3 Elasticity and Expenditure</h5> <ul> <li>The text discusses the relationship between price elasticity and the change in expenditure on a good.</li> <li>A rectangular hyperbola is an equation of the form xy = c, where x and y are variables and c is a constant, resulting in a downward sloping curve in the x-y plane.</li> <li>If the equation of a demand curve takes the form pq = e, where e is a constant, it will be a rectangular hyperbola, where price (p) times quantity (q) is a constant.</li> <li>The total expenditure on a good at price p is pq, and at price p + Δp, it is (p+Δp)(q+Δq).</li> <li>The approximate change in expenditure on the good is given by ΔE = Δp[q(1+eD)], where eD is the price elasticity of demand. The sign of ΔE depends on the value of eD.</li> </ul> <p>======</p>