Microeconomics for Business 2019 Board Question Paper

Four Determinants of Demand

1. Price of the Commodity ($P_x$): Under the law of demand, an inverse relationship exists between the price of a good and the quantity demanded, ceteris paribus.
2. Income of the Consumer ($Y$): An increase in consumer disposable income increases the demand for normal goods but reduces the demand for inferior goods.
3. Prices of Related Goods ($P_r$): Demand changes based on substitutes (direct relationship, e.g., tea and coffee) and complementary goods (inverse relationship, e.g., cars and petrol).
4. Consumer Tastes, Preferences, and Fashion ($T$): Favorable shifts in consumer habits, cultural trends, or seasonal preferences increase demand regardless of price.

Meaning of Linear Demand Function

A linear demand function is a mathematical equation representing a straight-line demand curve where the relationship between price and quantity demanded changes at a constant rate (constant slope).

• Mathematical Form:
  $$Q_d = a - bP$$
  • Where:
    • $Q_d$ = Quantity demanded
    • $a$ = Autonomous demand (horizontal intercept when $P = 0$)
    • $b$ = Slope parameter ($Delta Q / Delta P$), indicating responsiveness of demand to price ($b > 0$)
    • $P$ = Price of the product

Solution: Factor Intensity and Returns to Scale

Given Cobb-Douglas production function:

$$Q = 100 L^{0.8} K^{0.4}$$

Here, output elasticity with respect to labor ($\alpha$) = $0.8$ and capital ($\beta$) = $0.4$.

1. Factor Intensity

• Comparing the output elasticities: $\alpha = 0.8 > \beta = 0.4$.
• Since the labor coefficient is twice the capital coefficient, the production technology is Labor-Intensive.

2. Degree of Returns to Scale ($r$)

$$r = \alpha + \beta = 0.8 + 0.4 = 1.2$$

• Since $r = 1.2 > 1$, the production function exhibits Increasing Returns to Scale (IRS). A $10\%$ simultaneous increase in all inputs leads to a $12\%$ increase in total output.

Definition of Marginal Rate of Substitution (MRS)

The Marginal Rate of Substitution of X for Y ($MRS_{xy}$) is the rate at which a consumer is willing to give up units of good $Y$ to obtain one additional unit of good $X$ while maintaining the same level of total satisfaction (remaining on the same indifference curve).

• Formula:
  $$MRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y}$$
• Diminishing MRS: Due to diminishing marginal utility, as consumption of $X$ increases, the consumer is willing to sacrifice progressively fewer units of $Y$, making the indifference curve convex to the origin.

Reasons Why Long-Run Average Cost (LAC) is U-Shaped

The Long-Run Average Cost (LAC) curve is U-shaped due to the operation of the Laws of Returns to Scale (or internal economies and diseconomies of scale):

1. Down-sloping Portion (Economies of Scale): As scale of plant expands, the firm experiences technical, managerial, financial, and marketing economies, decreasing per-unit costs.
2. Minimum Point: The firm reaches the Minimum Efficient Scale (MES) where per-unit cost is minimized.
3. Upward-sloping Portion (Diseconomies of Scale): Beyond the optimal scale, managerial coordination difficulties, communication bottlenecks, and bureaucratic delays cause per-unit cost to rise.

Essential Conditions for Price Discrimination

For a firm to successfully practice price discrimination (charging different prices to different buyers for the same product), three conditions must be satisfied:

1. Monopoly Power: The seller must have sufficient market power and control over total market supply (price maker).
2. Market Separation / No Resale Arbitrage: Sub-markets must be completely separated by geography, nature of use, or tariff walls so that buyers in the low-price market cannot resell to the high-price market.
3. Difference in Elasticity of Demand: Price elasticity of demand must differ across sub-markets. The seller charges higher prices in inelastic markets and lower prices in elastic markets.

Concept of Micro Dynamic Analysis

Micro dynamic analysis is the study of the behavior of individual economic units (consumers, firms, markets) over time, specifically analyzing the time path and sequential adjustment process through which a market moves from an initial disequilibrium to a new equilibrium.

• Key Feature: Unlike comparative statics which only compares initial and final equilibrium points without considering time, dynamic analysis incorporates time lags (e.g., Cobweb Model in agricultural supply where output in period $t$ depends on price in period $t-1$).

Four Core Properties of an Isoquant

1. Negatively Sloped (Downward Sloping): To keep output constant, an increase in one input (Labor) requires a reduction in another input (Capital).
2. Convex to the Origin: Due to the Diminishing Marginal Rate of Technical Substitution ($MRTS_{LK}$).
3. Never Intersect Each Other: If two isoquants intersect, it would imply that the same input combination yields two distinct output levels, which is technically impossible.
4. Higher Isoquant Represents Higher Output: An isoquant lying further to the right indicates larger input combinations producing greater total physical output.

Relationship Between Average Cost (AC) and Marginal Cost (MC)

1. When MC < AC: Average Cost is falling (MC pulls AC downward).
2. When MC = AC: Average Cost is at its minimum point. This is the optimal productive efficiency point.
3. When MC > AC: Average Cost is rising (MC pulls AC upward).
4. Intersection: The MC curve always cuts the AC curve from below at its lowest (minimum) point.

Laws of Returns to Scale

The laws of returns to scale explain the quantitative behavior of total physical output when all inputs are increased simultaneously in the same proportion in the long run:

1. Increasing Returns to Scale (IRS): Percentage increase in output is greater than the percentage increase in inputs ($\%\Delta Q > \%\Delta Inputs$).
2. Constant Returns to Scale (CRS): Percentage increase in output exactly equals the percentage increase in inputs ($\%\Delta Q = \%\Delta Inputs$).
3. Decreasing Returns to Scale (DRS): Percentage increase in output is less than the percentage increase in inputs ($\%\Delta Q < \%\Delta Inputs$).

Loanable Funds Theory of Interest

The Loanable Funds Theory (formulated by Knut Wicksell and developed by Bertil Ohlin, Gunnar Myrdal, and Dennis Robertson) states that the rate of interest is determined by the intersection of the total demand for and total supply of loanable funds in the credit market.

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1. Supply of Loanable Funds ($S_L$)

The supply of loanable funds consists of four key components:

$$S_L = S + DH + DI + BM$$

1. Savings ($S$): Savings by individuals, households, and corporate firms from disposable income. Higher interest rates induce individuals to save more (positive relation).
2. Dishoarding ($DH$): Bringing idle past cash hoards out into active circulation for lending. When interest rates rise, the opportunity cost of holding cash increases, encouraging dishoarding.
3. Disinvestment ($DI$): Allowing existing capital assets to depreciate without replacement or selling off equipment/inventories to provide loanable funds when interest returns are lucrative.
4. Bank Money ($BM$): Commercial banks expand credit and create deposits through lending operations. Banking institutions expand supply at higher lending rates.

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2. Demand for Loanable Funds ($D_L$)

The demand for loanable funds consists of three components:

$$D_L = I + H + DS$$

1. Investment Demand ($I$): Business firms borrow funds to purchase capital equipment, build plant capacity, and finance working capital. In accordance with the marginal efficiency of capital (MEC), investment demand is negatively related to the interest rate.
2. Hoarding Demand ($H$): Liquidity preference of individuals to hold money as a liquid asset for speculative and precautionary motives. It is inversely related to the interest rate.
3. Dissaving ($DS$): Consumer borrowing to finance urgent consumption expenditures exceeding current income (e.g., healthcare, education, consumer durables). Inversely related to interest rate.

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3. Market Equilibrium

• Equilibrium interest rate ($r^*$) is achieved where:
  $$S_L = D_L \implies S + DH + DI + BM = I + H + DS$$
• At any rate above $r^*$, excess supply forces the interest rate downward. At any rate below $r^*$, excess demand pulls the interest rate upward.

Price and Output Determination Under Monopolistic Competition in the Long Run

Monopolistic competition is characterized by a large number of sellers, product differentiation, free entry and exit, and independent decision making.

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1. Adjustment Process Toward Long-Run Equilibrium

• Short-Run Supernormal Profits: If existing firms earn economic profits in the short run, new firms are attracted to the industry due to freedom of entry.
• Impact of Entry: As new firms enter with close substitutes:
  1. The market share of existing firms decreases.
  2. The individual firm’s demand curve ($AR$) shifts to the left and becomes more price-elastic.
  3. This competitive process continues until abnormal profits are completely wiped out, leaving all firms with only normal profits.

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2. Long-Run Equilibrium Conditions

A monopolistically competitive firm reaches long-run equilibrium when two conditions are fulfilled simultaneously:

1. $MR = LMC$ (Marginal Revenue equals Long-Run Marginal Cost, with $LMC$ cutting $MR$ from below).
2. $AR = LAC$ (Price equals Long-Run Average Cost, meaning the firm earns zero economic profit / normal profit).

In the diagrammatic representation, the downward-sloping demand curve ($AR$) becomes tangent to the $LAC$ curve at the equilibrium output.

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3. Key Economic Implications

• Price Exceeds Marginal Cost ($P > MC$): Because the firm faces a downward-sloping demand curve ($P = AR > MR = MC$), price is higher than marginal cost, creating allocative inefficiency.
• Presence of Excess Capacity: The tangency between downward-sloping $AR$ and U-shaped $LAC$ occurs on the falling portion of $LAC$, to the left of the minimum point of $LAC$ ($MES$).
  $$\text{Excess Capacity} = Q_{opt} - Q_{actual}$$
  The firm does not produce at lowest possible cost, reflecting the economic trade-off consumers pay for variety and product differentiation.

Solution: Demand and Supply Analysis for Wheat

a) Price Elasticity of Demand at Equilibrium Price

• Equilibrium Condition: Market equilibrium occurs where Quantity Demanded equals Quantity Supplied ($Q_d = Q_s$).

  • Looking at the schedule: At Price = Rs 400 (Combination C), $Q_d = 75$ and $Q_s = 75$.
  • Therefore, Equilibrium Price ($P$) = Rs 400, and Equilibrium Quantity ($Q$) = 75 units.

• Slope of Demand: Between Combination C ($P=400, Q=75$) and D ($P=500, Q=50$):

  $$\frac{\Delta Q_d}{\Delta P} = \frac{50 - 75}{500 - 400} = \frac{-25}{100} = -0.25$$

• Price Elasticity of Demand ($E_p$):

  $$E_p = \left| \frac{\Delta Q_d}{\Delta P} \times \frac{P}{Q_d} \right| = \left| -0.25 \times \frac{400}{75} \right| = 0.25 \times 5.333 = 1.33$$
  (Or Arc Elasticity between B and D around C: $|\frac{50-100}{500-300} \times \frac{300+500}{100+50}| = |\frac{-50}{200} \times \frac{800}{150}| = 1.33$)

• Interpretation: $E_p = 1.33 > 1$ indicates that demand for wheat around equilibrium is price elastic.

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b) Price Elasticity of Supply ($E_s$) for Movement from B to D

• At Combination B: $P_1 = Rs\ 300$, $Q_{s1} = 50\text{ units}$
• At Combination D: $P_2 = Rs\ 500$, $Q_{s2} = 100\text{ units}$
• $\Delta P = 500 - 300 = Rs\ 200$; $\Delta Q_s = 100 - 50 = 50\text{ units}$

1. Using Point (Percentage) Method:
   $$E_s = \frac{\Delta Q_s}{\Delta P} \times \frac{P_1}{Q_{s1}} = \frac{50}{200} \times \frac{300}{50} = \frac{300}{200} = 1.50$$
2. Using Arc (Midpoint) Elasticity Method:
   $$E_s = \frac{\Delta Q_s}{\Delta P} \times \frac{P_1 + P_2}{Q_{s1} + Q_{s2}} = \frac{50}{200} \times \frac{300 + 500}{50 + 100} = \frac{1}{4} \times \frac{800}{150} = 1.33$$

• Interpretation: In both approaches, $E_s > 1$, indicating elastic supply over this price interval.

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c) Supply Increases by 10 Units at Each Price

• New Supply schedule:
  • Price 200: $Q_s' = 35$
  • Price 300: $Q_s' = 60$
  • Price 400: $Q_s' = 85$
  • Price 500: $Q_s' = 110$
  • Price 600: $Q_s' = 135$
• Impact on Elasticity of Supply:
  • $\Delta Q_s' / \Delta P$ remains constant ($50 / 200 = 0.25$).
  • Movement from B to D on new schedule:
    $$E_s' = \frac{50}{200} \times \frac{300}{60} = 0.25 \times 5 = 1.25$$
  • Price elasticity of supply decreases (from 1.50 to 1.25).
• Reasons:
  1. Because the base quantity denominator ($Q_s$) increased at each price while $\Delta Q / \Delta P$ remained identical, the percentage change in quantity supplied relative to the percentage change in price becomes smaller.
  2. Economically, this shift represents an expansion in production capacity or reduction in input costs, shifting the entire supply curve rightward.

Solution: Consumer Budget Constraint and Price Consumption Curve (PCC)

Given:

• Total Budget ($M$) = $\text{Rs } 40,000$
• Initial Price of Good X ($P_{x1}$) = $\text{Rs } 800/\text{unit}$
• Initial Price of Good Y ($P_y$) = $\text{Rs } 1600/\text{unit}$

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a) Initial Budget Constraint and Equal Split Bundle

• Budget Line Equation:
  $$P_x \cdot X + P_y \cdot Y = M \implies 800X + 1600Y = 40,000$$
• Intercepts:
  • Horizontal Intercept ($X_{max}$ when $Y = 0$): $\frac{40,000}{800} = 50\text{ units}$
  • Vertical Intercept ($Y_{max}$ when $X = 0$): $\frac{40,000}{1600} = 25\text{ units}$
• Equal Split Consumption:
  • Expenditure on $X$ = $\text{Rs } 20,000 \implies X_1 = \frac{20,000}{800} = 25\text{ units}$
  • Expenditure on $Y$ = $\text{Rs } 20,000 \implies Y_1 = \frac{20,000}{1600} = 12.5\text{ units}$
• Initial Position ($E_1$): Coordinate $(X_1, Y_1) = (25, 12.5)$ lying directly on initial budget line $AB$.

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b) New Budget Constraint after Price of X Falls to Rs 400

• New price of X ($P_{x2}$) = $\text{Rs } 400$; $P_y = \text{Rs } 1600$; $M = \text{Rs } 40,000$.
• New Intercepts:
  • Horizontal Intercept ($X'_{max}$): $\frac{40,000}{400} = 100\text{ units}$
  • Vertical Intercept ($Y_{max}$): unchanged at $25\text{ units}$ (budget line pivots outward to $AB'$).
• New Expenditure Allocation:
  • Expenditure on $X$ = $\text{Rs } 24,000 \implies X_2 = \frac{24,000}{400} = 60\text{ units}$
  • Expenditure on $Y$ = $\text{Rs } 16,000 \implies Y_2 = \frac{16,000}{1600} = 10\text{ units}$
  • Total expenditure = $24,000 + 16,000 = \text{Rs } 40,000$.
• New Position ($E_2$): Coordinate $(X_2, Y_2) = (60, 10)$ lying directly on new budget line $AB'$.

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c) Derivation of PCC and Nature of Goods

1. Price Consumption Curve (PCC):
   • The PCC is obtained by joining consumer equilibrium points $E_1(25, 12.5)$ and $E_2(60, 10)$ as the price of Good X falls from Rs 800 to Rs 400.
   • As $P_x$ decreases, consumption of $X$ increases from $25$ to $60$ units while consumption of $Y$ decreases from $12.5$ to $10$ units.
   • Hence, the PCC slopes downward to the right.
2. Nature of Good X:
   • Since quantity demanded of $X$ rises when its price falls, Good X obeys the Law of Demand and is a Normal Good (specifically, price elastic, since total outlay on X rose from Rs 20,000 to Rs 24,000).
3. Nature of Good Y:
   • Good X and Good Y are Substitutes, because a decrease in the price of X caused the consumer to buy less of good Y.

Solution: Profit Maximization Under TR-TC and MR-MC Approaches

Given:

• Demand function: $P = 50 - 0.5Q$
• Cost function: $TC = 350 + 10Q$

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a) TR-TC Approach

1. Total Revenue Function ($TR$):
   $$TR = P \times Q = (50 - 0.5Q)Q = 50Q - 0.5Q^2$$
2. Profit Function ($\pi$):
   $$\pi = TR - TC = (50Q - 0.5Q^2) - (350 + 10Q) = -0.5Q^2 + 40Q - 350$$
3. First-Order Condition (FOC):
   $$\frac{d\pi}{dQ} = 0 \implies -Q + 40 = 0 \implies Q^* = 40\text{ units}$$
4. Second-Order Condition (SOC):
   $$\frac{d^2\pi}{dQ^2} = -1 < 0 \quad (\text{Condition for maximum profit satisfied})$$
5. Optimal Values:
   • Price ($P$): $P = 50 - 0.5(40) = 50 - 20 = \text{Rs } 30$
   • Total Revenue ($TR$): $TR = 50(40) - 0.5(40)^2 = 2000 - 800 = \text{Rs } 1,200$
   • Total Cost ($TC$): $TC = 350 + 10(40) = 350 + 400 = \text{Rs } 750$
   • Maximum Profit ($\pi$): $\pi = TR - TC = 1200 - 750 = \text{Rs } 450$

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b) MR-MC Approach

1. Marginal Revenue ($MR$):
   $$MR = \frac{d(TR)}{dQ} = 50 - Q$$
2. Marginal Cost ($MC$):
   $$MC = \frac{d(TC)}{dQ} = 10$$
3. First-Order Condition:
   $$MR = MC \implies 50 - Q = 10 \implies Q^* = 40\text{ units}$$
4. Second-Order Condition:
   $$\text{Slope of } MR = \frac{d(MR)}{dQ} = -1; \quad \text{Slope of } MC = \frac{d(MC)}{dQ} = 0$$
   • Since Slope of $MC (0) >$ Slope of $MR (-1)$, $MC$ cuts $MR$ from below (SOC satisfied).
5. Values:
   • Price ($P$): $50 - 0.5(40) = \text{Rs } 30$
   • $TR$: $40 \times 30 = \text{Rs } 1,200$
   • Maximum Profit: $TR - TC = 1,200 - (350 + 400) = \text{Rs } 450$

Solution: Business Profit vs. Economic Profit

1. Annual Revenue:

• Monthly revenue = $\text{Rs } 130,000$
• Total Annual Revenue ($TR$) = $130,000 \times 12 = \text{Rs } 1,560,000$

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2. Explicit (Accounting) Costs:

• Monthly operating expenses:
  • Advertisement = $\text{Rs } 9,000$
  • Employee Salary = $\text{Rs } 50,000$
  • Supply of materials = $\text{Rs } 15,000$
  • Utilities = $\text{Rs } 2,000$
  • Total Monthly Explicit Costs = $9,000 + 50,000 + 15,000 + 2,000 = \text{Rs } 76,000$
• Total Annual Explicit Costs ($TC_{explicit}$) = $76,000 \times 12 = \text{Rs } 912,000$

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3. Implicit (Opportunity) Costs:

• Foregone salary from sacrificed job = $\text{Rs } 360,000/\text{year}$
• Foregone interest on savings ($5\%$ of $\text{Rs } 480,000$) = $0.05 \times 480,000 = \text{Rs } 24,000/\text{year}$
• Foregone rental income on own house ($1,500 \times 12$) = $\text{Rs } 18,000/\text{year}$
• Total Annual Implicit Costs ($TC_{implicit}$) = $360,000 + 24,000 + 18,000 = \text{Rs } 402,000$

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Answers:

a) Business (Accounting) Profit:

$$\text{Business Profit} = \text{Total Revenue} - \text{Explicit Costs}$$

$$\text{Business Profit} = 1,560,000 - 912,000 = \mathbf{Rs\ 648,000}$$

b) Economic Profit:

$$\text{Economic Profit} = \text{Total Revenue} - (\text{Explicit Costs} + \text{Implicit Costs})$$

$$\text{Economic Profit} = 1,560,000 - (912,000 + 402,000) = 1,560,000 - 1,314,000 = \mathbf{Rs\ 246,000}$$

c) Managerial Recommendation:

• Yes, starting the new business is beneficial for him.
• Reasons:
  1. The business earns a positive economic profit of Rs 246,000, which means it generates earnings well above the combined opportunity costs of his labor (salary), financial capital (bank interest), and real estate (house rent).
  2. He is earning $\text{Rs } 246,000$ more than what he would have earned across all his best alternative endeavors combined.

Case Analysis: Market Dynamics of the Nepalese Tea Industry

The Nepalese tea industry displays characteristics of a competitive market structure with large numbers of smallholder tea farmers (producers) and widespread domestic and export consumer demand.

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a) Effect of Government Subsidy on Tea Farming

1. Nature of Policy: A per-unit or lumpsum production subsidy provided to tea farmers reduces the marginal and average cost of tea cultivation.
2. Shift in Curves:
   • The market supply curve for tea shifts to the right (or vertically downward) by the amount of the subsidy, moving from $S_1$ to $S_2$.
   • The market demand curve ($D$) remains unchanged initially.
3. Equilibrium Impact:
   • Equilibrium Price: Decreases from $P_1$ to $P_2$. The cost savings are shared between producers and consumers depending on relative price elasticities.
   • Equilibrium Quantity: Increases from $Q_1$ to $Q_2$, as lower market prices encourage higher consumption and expand export volume.

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b) Effect of Increase in Import Tax on Coffee

1. Economic Relationship: Tea and coffee are close substitute goods in consumption ($E_{xy} > 0$).
2. Mechanism:
   • An increase in import tariffs/taxes on coffee raises the domestic retail price of coffee.
   • In response to costlier coffee, consumers substitute away from coffee toward tea.
3. Shift in Curves:
   • The demand curve for tea shifts to the right (upward) from $D_1$ to $D_2$.
   • The supply curve of tea ($S$) remains unchanged.
4. Equilibrium Impact:
   • Equilibrium Price: Increases from $P_1$ to $P_2$ due to heightened demand pressure.
   • Equilibrium Quantity: Increases from $Q_1$ to $Q_2$ as farmers supply more at higher prevailing market prices.

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c) Simultaneous Effect of Subsidy to Tea Farming and Import Tax on Coffee

When both policies occur concurrently:

• Supply Effect (Subsidy): Shifts tea supply curve rightward ($S_1 \to S_2$).
• Demand Effect (Coffee Tax): Shifts tea demand curve rightward ($D_1 \to D_2$).

Combined Market Outcome:

1. Equilibrium Quantity:
   • Unambiguously Increases. Both the rightward shift in supply and the rightward shift in demand work in the same direction to expand market transactions ($Q_2 > Q_1$).
2. Equilibrium Price:
   • The net effect on price is indeterminate (ambiguous) and depends on the relative magnitude of the shifts:
     • If Supply Shift > Demand Shift: The downward price pressure from subsidies exceeds the upward demand pressure; equilibrium price falls.
     • If Demand Shift > Supply Shift: The upward price pressure from coffee substitution exceeds the subsidy expansion; equilibrium price rises.
     • If Supply Shift = Demand Shift: The downward and upward price pressures exactly offset each other; equilibrium price remains unchanged at a substantially higher equilibrium volume.