Microeconomics for Business 2079 Board Question Paper

Four core characteristics of business economics:

1. Normative in Nature: Prescribes practical solutions (“what ought to be”) to achieve organizational goals.
2. Microeconomic Focus: Concentrates on internal operational decision-making of individual business units.
3. Pragmatic and Applied: Adopts practical quantitative tools (linear programming, regression, break-even analysis).
4. Macroeconomic Framework Awareness: Operates within the broader context of national fiscal, monetary, and regulatory policies.

In the linear supply function $Q_s = a + bP$:

1. Parameter ‘$a$’ (Intercept / Autonomous Supply): Represents the quantity supplied when market price is zero ($P = 0$). Typically negative or zero in production economics, indicating that producers will supply nothing if price does not cover minimum variable cost.
2. Parameter ‘$b$’ (Slope Coefficient): Represents the marginal responsiveness of quantity supplied to changes in price ($b = \frac{dQ_s}{dP} > 0$). It is positive, reflecting the Law of Supply (higher prices induce higher supply).

Four core assumptions of the Cardinal (Marshallian) Utility Approach:

1. Measurable Utility: Utility can be measured cardinally in quantifiable psychic units called utils.
2. Constant Marginal Utility of Money: The marginal utility of money ($MU_m$) remains constant as expenditures vary.
3. Diminishing Marginal Utility: As consumption of a good increases, each additional unit yields progressively less satisfaction.
4. Additive Utility: Total utility is the additive sum of individual utilities: $TU = U_1(X_1) + U_2(X_2) + \dots + U_n(X_n)$.

Reason: The Long-run Average Cost ($LAC$) curve is U-shaped due to the operation of the Laws of Returns to Scale:

1. Down-sloping Portion: Driven by Economies of Scale (labor specialization, bulk discounts, indivisible modern technology) which reduce unit costs as output expands.
2. Minimum Point: Optimal plant size where economies of scale are fully exhausted.
3. Upward-sloping Portion: Caused by Diseconomies of Scale (bureaucratic delays, coordination bottlenecks, and management inefficiencies in giant enterprises).

Four primary characteristics of an oligopoly market:

1. Few Dominant Sellers: A small group of large firms controls the vast majority of industry output.
2. Mutual Interdependence: The pricing and output actions of one firm directly trigger retaliatory moves by rival firms.
3. Kinked Demand Curve (Price Rigidity): Firms face an asymmetric demand curve that is elastic above the ruling price and inelastic below it.
4. Significant Barriers to Entry: High initial capital, proprietary patents, and brand loyalty restrict new entrants.

Four examples of contractual explicit costs:

1. Wages and salaries paid to employees.
2. Raw material invoices paid to vendors.
3. Office and factory rent paid to property owners.
4. Electricity and internet utility bills paid to service providers.

Definition: The Value of Marginal Product of Labor ($VMP_L$) is the monetary market value of the additional physical output produced by hiring one more unit of labor in a competitive product market.

Formula:

$$VMP_L = MP_L \times P$$

Where $MP_L$ is the physical marginal product of labor and $P$ is the market price of the finished output.

Key causes for Increasing Returns to Scale (IRS):

1. Division of Labor and Specialization: Workers focus on specific tasks, sharpening skill and eliminating idle machine time.
2. Technical Indivisibilities: Large, highly efficient machinery requires high operating scale to minimize unit cost.
3. Dimensional Economies: Doubling the dimensions of a storage tank or ship quadruples its surface area but octuples its internal volume.

Formula for Degree of Economies of Scope ($SC$):

$$SC = \frac{C(Q_1) + C(Q_2) - C(Q_1, Q_2)}{C(Q_1, Q_2)}$$

Where:

• $C(Q_1)$ = Standalone cost of producing output $Q_1$ alone
• $C(Q_2)$ = Standalone cost of producing output $Q_2$ alone
• $C(Q_1, Q_2)$ = Joint cost of producing both products together in a single enterprise

Nature of Microeconomics

1. Study of Individual Economic Units: Examines the behavioral choices of individual households, consumers, workers, and business enterprises rather than national aggregates.
2. Price Theory: Explains how relative market prices are determined through the decentralized interaction of market demand and market supply across product and factor markets.
3. Allocation of Resources: Analyzes how scarce economic inputs (land, labor, capital) are allocated between alternative uses to optimize economic output.
4. Use of the Ceteris Paribus Assumption: Employs partial equilibrium models holding “other things being equal” to isolate cause-and-effect relationships between specific variables.
5. Marginal Analysis as a Core Tool: Evaluates decision-making at the margin ($MB = MC, MR = MC, MP_L/w = MP_K/r$) to determine optimal points.

Factors Causing Shifts in the Demand Curve

A shift in the demand curve (change in demand) occurs when any determinant of demand other than the good’s own price changes:

1. Consumer Income ($Y$):

   • Normal Goods: Increase in income shifts demand curve to the right ($D_1 \to D_2$).
   • Inferior Goods: Increase in income shifts demand curve to the left ($D_1 \to D_3$).

2. Prices of Related Commodities:

   • Substitutes ($P_s$): A rise in the price of Coke increases demand for Pepsi (rightward shift).
   • Complements ($P_c$): A rise in petrol prices reduces the demand for automobiles (leftward shift).

3. Consumer Tastes and Preferences: Favorable changes in fashion, dietary trends, or technological adoption expand market demand.

4. Demographic Factors and Market Size: Growth in population or immigration broadens the aggregate consumer base.

5. Future Price Expectations: Antcipation of higher future prices accelerates current buying (shifting demand rightward today).

Joint Profit Maximization Cartel

Concept: When firms in an oligopoly form a centralized cartel, they agree to act as a single multi-plant monopoly to maximize the combined aggregate profit of the industry.

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Step-by-Step Mechanism:

1. Industry Demand and Marginal Revenue: The central cartel management calculates the total market demand curve ($AR$) and derives the corresponding market Marginal Revenue ($MR_m$).
2. Industry Marginal Cost Curve ($\sum MC$): The cartel derives the aggregate marginal cost curve by horizontally summing the individual marginal cost curves of all member firms:
   $$\sum MC = MC_1 + MC_2 + \dots + MC_n$$
3. Cartel Equilibrium Condition: Total industry output ($Q^*$) and market price ($P^*$) are determined where:
   $$MR_m = \sum MC$$
4. Quota Allocation: Output is distributed across individual firms such that the marginal cost of every member firm is identical and equal to cartel marginal revenue:
   $$MC_1(q_1) = MC_2(q_2) = \dots = MC_n(q_n) = MR_m$$
   This ensures that industry output is produced at the lowest possible aggregate cost.

Concept of Economic Rent

In modern economic analysis, Economic Rent is defined as the payment made to a factor of production over and above its transfer earnings (the minimum earnings required to keep it in its current employment / opportunity cost).

$$\text{Economic Rent} = \text{Actual Earnings} - \text{Transfer Earnings}$$

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Determination of Economic Rent

Economic rent is determined by the interaction of the demand for and supply of the productive factor:

1. Perfectly Inelastic Supply ($e_s = 0$):
   • The factor has no alternative use; transfer earnings are zero.
   • All actual earnings constitute pure economic rent (e.g., original land, unique talent of a star athlete).
2. Perfectly Elastic Supply ($e_s = \infty$):
   • The factor can easily migrate to alternative uses at the prevailing rate.
   • Economic rent is zero; all earnings are transfer earnings.
3. Less than Perfectly Elastic Supply ($0 < e_s < \infty$):
   • Part of the earnings represents transfer earnings and the remaining triangular area above the supply curve represents economic rent.

Step 1: Formulate Total Profit Function ($\Pi$)

$$\Pi = TR - TC$$

$$\Pi = (100Q - Q^2) - (50 + 20Q) = 80Q - Q^2 - 50$$

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Part (a): Output for Maximum Profit ($Q^*$)

First-Order Condition ($MR = MC$ or $\frac{d\Pi}{dQ} = 0$):

$$\frac{d\Pi}{dQ} = 80 - 2Q = 0 \implies 2Q = 80 \implies Q^* = \mathbf{40 \text{ units}}$$

Second-Order Condition Check:

$$\frac{d^2\Pi}{dQ^2} = -2 < 0 \quad (\text{Confirmed Maximum})$$

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Part (b): Maximum Profit ($\Pi_{max}$)

Substitute $Q^* = 40$ into the profit function:

$$\Pi_{max} = 80(40) - (40)^2 - 50 = 3,200 - 1,600 - 50 = \mathbf{\text{Rs. } 1,550}$$

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Part (c): Price at Maximum Profit ($P^*$)

Average Revenue / Price function:

$$P = \frac{TR}{Q} = \frac{100Q - Q^2}{Q} = 100 - Q$$

Substitute $Q^* = 40$:

$$P^* = 100 - 40 = \mathbf{\text{Rs. } 60}$$

Conclusion:

• Profit-maximizing output is 40 units.
• Maximum profit is Rs. 1,550.
• Product price is Rs. 60.

Step 1: Cost Definitions and Formulas

• $TFC = TC(0) = \mathbf{50}$ (Fixed cost is Rs. 50 at all outputs).
• $TVC = TC - TFC$
• $AFC = TFC / Q$
• $AVC = TVC / Q$
• $ATC = TC / Q$
• $MC = \Delta TC$

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Step 2: Complete Cost Table

Decomposition of Price Effect for Normal Substitutes (Hicksian Method)

Concept: When the price of Good $X$ (which has normal substitutes) falls, the consumer alters their consumption basket due to two concurrent economic forces:

1. The Substitution Effect ($SE$): Good $X$ becomes relatively cheaper compared to Good $Y$.
2. The Income Effect ($IE$): Real purchasing power increases, expanding affordable consumption.

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Graphical Decomposition Procedure:

1. Initial Point ($E_1$): Budget line $AB$ touches initial indifference curve $IC_1$ at point $E_1$, consuming $OX_1$.
2. Fall in $P_x$ ($E_2$): Budget line pivots outward to $AB_1$, reaching tangency with higher curve $IC_2$ at point $E_2$, consuming $OX_2$.
   $$\text{Total Price Effect } (PE) = X_1 X_2$$
3. Compensating Variation: Draw fictitious budget line $CD$ parallel to $AB_1$ and tangent to the original curve $IC_1$ at point $E_3$:
   • Substitution Effect ($E_1 \to E_3$): Consumer increases purchases of Good $X$ by $X_1 X_3$ purely because it is relatively cheaper, with real utility held constant.
   • Income Effect ($E_3 \to E_2$): Restoring the compensated income moves the consumer from $IC_1$ to $IC_2$, increasing consumption of $X$ by $X_3 X_2$.
4. Result:
   $$\text{Total Price Effect} = \text{Substitution Effect } (X_1 X_3) + \text{Income Effect } (X_3 X_2) = X_1 X_2$$

Managerial Significance of Production Function

1. Least-Cost Combination of Inputs: Guides management in finding the optimal combination of inputs where the Marginal Rate of Technical Substitution equals input price ratio:
   $$MRTS_{LK} = \frac{w}{r} \iff \frac{MP_L}{w} = \frac{MP_K}{r}$$
2. Optimal Factor Employment: Establishes the profit-maximizing hiring rule where the factor price equals Value of Marginal Product ($w = VMP_L$).
3. Long-Run Capacity Expansion: Identifies whether the firm is operating under increasing, constant, or decreasing returns to scale, guiding plant capacity choices.
4. Technical Progress Evaluation: Allows firms to distinguish between labor-saving, capital-saving, or neutral technological progress.
5. Cost Function Derivation: Serves as the mathematical dual and engineering foundation for all short-run and long-run cost curves.

Part (a): Arc Elasticity of Supply Calculations

Formula:

$$E_s = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}$$

1. Movement from B to D:

   • Point B: $P_1 = 10, Q_1 = 200$; Point D: $P_2 = 20, Q_2 = 400$$E_s = \frac{400 - 200}{20 - 10} \times \frac{10 + 20}{200 + 400} = \frac{200}{10} \times \frac{30}{600} = 20 \times \frac{1}{20} = \mathbf{1.00}$$

2. Movement from D to B:

   • Point D: $P_1 = 20, Q_1 = 400$; Point B: $P_2 = 10, Q_2 = 200$$E_s = \frac{200 - 400}{10 - 20} \times \frac{20 + 10}{400 + 200} = \frac{-200}{-10} \times \frac{30}{600} = 20 \times \frac{1}{20} = \mathbf{1.00}$$

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Part (b): Nature of Elasticity of Supply

Notice that the supply function is strictly proportional:

$$Q_s = 20P$$

When a straight-line supply curve passes directly through the origin $(0, 0)$, its price elasticity of supply is strictly unitary ($E_s = 1$) at every point along the curve.