Comprehensive Study Notes on Market Equilibrium, Firm Theory, Production, and Consumer Behaviour

Market Equilibrium: Foundations and Definitions

• Conceptual Foundation: Market equilibrium is built on the behavior of consumers (price takers, Chapter 2) and firms (price takers, Chapter 4). It combines demand (what consumers are willing to buy at various prices) and supply (what profit-maximizing firms wish to sell at various prices) to determine the equilibrium price ($p^*$) and equilibrium quantity ($q^*$).

• Equilibrium Definition: A situation where the plans of all consumers and firms in the market match and the market clears. At this point, the aggregate quantity firms wish to sell equals the aggregate quantity consumers wish to buy.     * Algebraic Condition: $(p^*, q^*)$ is an equilibrium if $qD(p^*) = qS(p^*)$.     * $p^*$ denotes equilibrium price and $q^*$ denotes equilibrium quantity.

• Excess Demand: If at a given price, the market demand exceeds market supply (qD > qS). This creates upward pressure on prices as consumers compete for limited goods.

• Excess Supply: If at a given price, the market supply exceeds market demand (qS > qD). This creates downward pressure on prices as firms lower prices to clear surplus inventory.

• The ‘Invisible Hand’: Derived from Adam Smith ($1723-1790$), this intuition suggests that market forces automatically adjust prices in response to imbalances (raising them for excess demand and lowering them for excess supply) until equilibrium is reached.

Market Equilibrium with a Fixed Number of Firms

• Graphic Representation: Equilibrium occurs at the intersection of the market demand curve ($DD$) and the market supply curve ($SS$).

• Out-of-Equilibrium Dynamics:     * At Price p_1 < p^*: Market demand ($q_1$) is greater than market supply ($q'_1$). There is excess demand equal to $q_1 - q'_1$. Price rises because consumers are willing to pay more to obtain the commodity.     * At Price p_2 > p^*: Market supply ($q_2$) is greater than market demand ($q'_2$). There is excess supply equal to $q_2 - q'_2$. Price falls as firms lower prices to sell their desired output.

• Example 5.1 Analysis:     * Demand function: $qD = 200 - p$ (for $0 \leq p \leq 200$).     * Supply function: $qS = 120 + p$ (for $p \geq 10$).     * To find $p^*$: $200 - p^* = 120 + p^* \rightarrow 2p^* = 80 \rightarrow p^* = 40$.     * To find $q^*$: Substitute $p^* = 40$ into demand: $200 - 40 = 160$. Equilibrium quantity = $160\,kg$.     * Excess Demand algebraic form: $ED(p) = qD - qS = 80 - 2p$.     * Excess Supply algebraic form: $ES(p) = qS - qD = 2p - 80$.

Wage Determination in a Perfectly Competitive Labour Market

• Market Roles: In the labour market, households are suppliers and firms are the source of demand. "Labour" refers to hours of work provided.

• Demand for Labour: A profit-maximizing firm hires labour up to the point where the cost of the last unit of labour (Wage, $w$) equals the benefit derived from it (Marginal Revenue Product of Labour, $MRP_L$).     * Formula: $w = MRP_L$.     * $MRP_L = MR \times MP_L$.     * In perfect competition, $MR = P$, so $MRP_L = VMP_L$ (Value of Marginal Product of Labour).     * Equation: $w = P \times MP_L$.     * Because of the Law of Diminishing Marginal Product, the labour demand curve is downward sloping.

• Supply of Labour: This is a trade-off between income and leisure.     * Two Effects of Wage Increase:         1. Substitution Effect: Leisure becomes more expensive (utility cost), inducing the individual to work more.         2. Income Effect: Higher wages increase purchasing power, inducing the individual to spend more on leisure activities.     * Individual Curve: Often backward bending (at low wages, substitution effect dominates; at very high wages, income effect may dominate).     * Market Curve: Generally upward sloping as higher wages attract more people into the labour force from outside the market.

• Equilibrium Wage ($w^*$): Determined where the labour demand curve and labour supply curve intersect.

Impact of Demand and Supply Shifts on Equilibrium

• Demand Shifts (Number of firms fixed):     * Rightward Shift: Caused by factors like increased income (for normal goods) or increased consumers. Results in higher price ($p$) and higher quantity ($q$).     * Leftward Shift: Results in lower price ($p$) and lower quantity ($q$).

• Supply Shifts (Number of firms fixed):     * Rightward Shift: Caused by improved technology or decreased input prices. Results in lower price ($p$) and higher quantity ($q$).     * Leftward Shift: Caused by increased input prices or a decrease in the number of firms. Results in higher price ($p$) and lower quantity ($q$).

• Simultaneous Shifts:     * If both shift Rightward: Quantity increases; Price change depends on the magnitude of shifts.     * If both shift Leftward: Quantity decreases; Price change depends on the magnitude of shifts.     * If Demand Right / Supply Left: Price increases; Quantity change depends on magnitude.     * If Demand Left / Supply Right: Price decreases; Quantity change depends on magnitude.

Market Equilibrium: Free Entry and Exit

• The Zero-Profit Condition: With free entry and exit, firms enter if there is supernormal profit and exit if there is a loss. Equilibrium is reached when all firms earn exactly normal profit.     * Condition: $p = \min(AC)$.     * If p > \min(AC), firms enter, market supply shifts right, price falls.     * If p < \min(AC), firms exit, market supply shifts left, price rises.

• Determination of equilibrium number of firms ($n_0$):     * $n_0 = \frac{q_0}{q^f_0}$, where $q_0$ is the market equilibrium quantity and $q^f_0$ is the quantity supplied by a single firm at $p = \min(AC)$.

• Shift Dynamics under Free Entry/Exit:     * A demand shift changes only the equilibrium quantity and the number of firms, but the price remains unchanged at $p = \min(AC)$.     * The effect on quantity is more pronounced compared to the fixed-firm case.

Applications: Government Intervention

• Price Ceiling: Maximum allowable price set below equilibrium (e.g., for wheat, sugar, kerosene).     * Consequences: Excess demand (shortage). Leads to rationing (fair price shops) and potential black markets.     * Consumer Problems: Long queues and insufficient quantities.

• Price Floor: Minimum allowable price set above equilibrium (e.g., agricultural support prices, minimum wage).     * Consequences: Excess supply (surplus). To maintain the floor, the government must often buy the surplus.

Theory of the Firm: Revenue and Profit

• Perfect Competition Features: Large number of buyers/sellers, homogeneous product, free entry/exit, perfect information. Firms are price-takers.

• Revenue Functions:     * Total Revenue ($TR$): $TR = p \times q$. The $TR$ curve is an upward-sloping straight line starting from the origin with slope $p$.     * Average Revenue ($AR$): $AR = \frac{TR}{q} = p$.     * Marginal Revenue ($MR$): $MR = \frac{\Delta TR}{\Delta q}$. For a price-taking firm, $MR = p$.

• Profit Maximization Conditions:     1. $p = MC$.     2. $MC$ must be non-decreasing at the output level.     3. Short Run: $p \geq AVC$. Long Run: $p \geq AC$.

• Supply Curves:     * Short Run: The rising part of the $SMC$ curve at or above the minimum $AVC$. For prices below minimum $AVC$, output is zero.     * Long Run: The rising part of the $LRMC$ curve at or above the minimum $LRAC$. For prices below minimum $LRAC$, output is zero.     * Market Supply: Derived by the horizontal summation of individual firm supply curves.

Production and Costs

• Production Function: The relationship between inputs (Labour $L$, Capital $K$) and the maximum obtainable output ($q$). $q = f(L, K)$.

• Product Concepts:     * Total Product ($TP$): Output produced by a variable input given fixed amounts of other inputs.     * Average Product ($AP_L$): $AP_L = \frac{TP}{L}$.     * Marginal Product ($MP_L$): $MP_L = \frac{\Delta TP}{\Delta L}$.

• Laws of Production:     * Law of Variable Proportions: As more of a variable input is added to fixed inputs, $MP$ initially rises and then eventually falls.     * Returns to Scale (Long Run):         * Constant (CRS): Output increases by the same proportion as inputs.         * Increasing (IRS): Output increases by more than the proportion of inputs.         * Decreasing (DRS): Output increases by less than the proportion of inputs.

• Costs Break-down:     * $TC = TFC + TVC$.     * Average Fixed Cost ($AFC$): $AFC = \frac{TFC}{q}$ (Graphically a rectangular hyperbola).     * Average Variable Cost ($AVC$): $AVC = \frac{TVC}{q}$.     * Short Run Average Cost ($SAC$): $SAC = \frac{TC}{q} = AFC + AVC$.     * Marginal Cost ($MC$): Change in total cost per unit increase in output ($MC = \frac{\Delta TC}{\Delta q}$).

Theory of Consumer Behaviour

• Utility: The want-satisfying capacity of a commodity.     * Cardinal Utilities: Total Utility ($TU$) and Marginal Utility ($MU$). $MU_n = TU_n - TU_{n-1}$.     * Law of Diminishing Marginal Utility: As consumption of a good increases, the marginal utility from each additional unit declines.

• Indifference Curves (IC): The locus of points representing bundles among which the consumer is indifferent.     * Features: Downward sloping, convex to the origin (due to diminishing MRS), higher ICs represent higher utility, ICs never intersect.     * Marginal Rate of Substitution (MRS): Rate at which a consumer substitutes one good for another while maintaining constant utility. $MRS = |\frac{\Delta x_2}{\Delta x_1}|$.

• Budget Constraint: The income limit on consumer choice.     * Equation: $p_1x_1 + p_2x_2 \leq M$.     * Budget Line: $x_2 = \frac{M}{p_2} - \frac{p_1}{p_2}x_1$. Slope is $-\frac{p_1}{p_2}$.

• Optimal Choice: The consumer maximizes satisfaction by choosing the bundle where the budget line is tangent to the highest possible IC. At this point, $MRS = \frac{p_1}{p_2}$.

Elasticity Concepts

• Price Elasticity of Demand ($e_D$): $\frac{\% \Delta Q}{\% \Delta P} = ( \frac{\Delta Q}{\Delta P} ) \times ( \frac{P}{Q} )$.     * Inelastic: |e_D| < 1.     * Elastic: |e_D| > 1.     * Unitary Elastic: $|e_D| = 1$.     * Perfectly Inelastic: $|e_D| = 0$ (Vertical Demand Curve).     * Perfectly Elastic: $|e_D| = \infty$ (Horizontal Demand Curve).

• Elasticity of Supply ($e_S$): $\frac{\% \Delta Q_S}{\% \Delta P} = ( \frac{\Delta Q_S}{\Delta P} ) \times ( \frac{P}{Q_S} )$. Measured geometrically from the origin/axis intercepts.

Questions & Discussion

• Question: Why is the TR curve a straight line starting from the origin?     * Response: Because in perfect competition, the price is constant ($TR = p \times q$). The constant slope is the market price. It starts at the origin because if quantity is zero, revenue is zero.

• Question: What happens to demand for a normal good when income increases?     * Response: The demand curve shifts to the right, because at each price, the consumer is now willing and able to purchase more of the good.

• Question: Explain the relationship between SMC and AVC curve.     * Response: Both start from the same point. When SMC < AVC, AVC falls. When SMC > AVC, AVC rises. Therefore, SMC intersects AVC at its minimum point.