Assignment One (DCQs – 500 words each, 20 marks)

Q.1 (a) Distinguish between law of demand and price elasticity of demand. Identify the factors on which price elasticity depends. How does elasticity of demand help the economic agents in decision making?

Answer:
The Law of Demand is a fundamental concept in microeconomics which states that, ceteris paribus (all other things being equal), the quantity demanded of a commodity falls when its price rises, and increases when its price falls. The relationship is inverse between price and quantity demanded. It is a qualitative statement which simply establishes the direction of change in demand when price changes. The law does not measure the magnitude of change, only the fact that such a change occurs.

On the other hand, Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in the price of a commodity. It is expressed as the percentage change in quantity demanded divided by the percentage change in price. It is a quantitative concept, unlike the law of demand. For example, if a 10% fall in price leads to a 20% rise in demand, the elasticity is 2, which shows demand is elastic.

Thus, while the law of demand explains the general direction of demand change, elasticity provides a numerical value to measure its degree.

Factors Affecting Price Elasticity of Demand:

1. Nature of the commodity: Necessities like food grains have inelastic demand, while luxuries and comfort goods have more elastic demand.

2. Availability of substitutes: More substitutes imply higher elasticity (e.g., Pepsi and Coke).

3. Proportion of income spent: Goods that take a larger share of income (like cars) are more elastic, while small daily items (like salt) are inelastic.

4. Time period: Demand is less elastic in the short run (habit formation, adjustment difficulties), and more elastic in the long run.

5. Definition of commodity: Broad categories like “food” are less elastic, but narrowly defined goods like “apples” are more elastic.

6. Addiction or habit: Goods like tobacco or alcohol show inelastic demand.

Role of Elasticity in Decision-Making:

• Producers: Firms use elasticity to set pricing strategies. If demand is elastic, lowering price can increase revenue. If demand is inelastic, firms may raise prices to maximize profits.

• Government: Elasticity helps in designing indirect taxes. Inelastic goods (like petrol) are taxed more because revenue increases without large fall in demand.

• Trade policy: Understanding elasticity helps in setting tariffs and evaluating international trade impacts.

• Factor pricing: Elasticity also influences the demand for factors of production, such as labor.

Conclusion:
While the law of demand gives the qualitative foundation, elasticity adds the quantitative precision. Together, they provide a powerful tool for economic agents—producers, consumers, and government—to make rational choices in resource allocation, pricing, and policy-making.

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Q.1 (b) Numerical: Given Qd = 10 – 2P + Ps ; where P = 10, Ps = 20. Find price elasticity of demand and cross elasticity of demand.

Solution:
The demand function:

$$Q_d=10-2P+P_s$$

Substitute values:

$$Q_d=10-2(10)+20=10-20+20=10$$

So, Q = 10 units.

(i) Price Elasticity of Demand (PED):
Formula:

$$E_p=\frac{\mathrm{\partial }Q}{\mathrm{\partial }P}\times \frac{P}{Q}$$

Here, $\frac{\mathrm{\partial }Q}{\mathrm{\partial }P}=-2$

$$E_p=(-2)\times \frac{10}{10}=-2$$

So, PED = –2 (elastic demand).

(ii) Cross Elasticity of Demand (CED):
Formula:

$$E_{ps}=\frac{\mathrm{\partial }Q}{\mathrm{\partial }{P}_s}\times \frac{P_s}{Q}$$

Here, $\frac{\mathrm{\partial }Q}{\mathrm{\partial }{P}_s}=+1$

$$E_{ps}=(1)\times \frac{20}{10}=2$$

So, CED = +2, showing strong substitutability between the two goods.

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Q.2 (a) What do you understand by the term ‘market failure’? Explain the various sources of market failure. Which policy instruments can be resorted to regulate the inefficient market situations?

Answer (Approx. 500 words):
A market failure occurs when the free market fails to allocate resources efficiently, leading to outcomes where social welfare is not maximized. In such cases, government intervention becomes necessary to correct inefficiencies and ensure equitable distribution.

Sources of Market Failure:

1. Externalities: When production or consumption imposes costs or benefits on third parties not involved in the market transaction.

   • Negative externalities: Pollution, traffic congestion.

   • Positive externalities: Vaccinations, education.

2. Public Goods: Goods that are non-excludable and non-rivalrous (like national defense, street lighting). Free markets underproduce them because of the free-rider problem.

3. Market Power (Monopoly/oligopoly): Firms with excessive power distort prices and output, leading to allocative inefficiency.

4. Imperfect Information: When consumers or producers lack full knowledge, decisions become inefficient (e.g., used car markets, health insurance).

5. Incomplete Markets: Sometimes markets fail to exist for essential goods like insurance for high-risk individuals.

6. Macroeconomic Instability: Markets may fail to ensure full employment and price stability.

Policy Instruments to Correct Market Failures:

• Taxes and Subsidies: Pigovian taxes on negative externalities (carbon tax) and subsidies for positive externalities (education grants).

• Regulations and Standards: Legal limits on pollution, quality standards for food and medicine.

• Provision of Public Goods: Government directly provides public goods like defense, law and order, basic infrastructure.

• Competition Policies: Anti-monopoly laws and promotion of fair competition.

• Correcting Information Failures: Mandatory product labeling, disclosure laws, awareness campaigns.

• Redistribution Policies: Progressive taxation and welfare transfers to reduce inequality caused by market imperfections.

Conclusion:
Market failures are inevitable in real economies. Appropriate government intervention—through fiscal, regulatory, and institutional measures—ensures efficient resource allocation and social welfare.

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Q.2 (b) What is production possibility frontier? How does the marginal rate of transformation relate to the production possibility frontier?

Answer (Approx. 500 words):
The Production Possibility Frontier (PPF) is a curve showing the maximum possible combinations of two goods or services that an economy can produce given its resources and technology, assuming full and efficient utilization. It illustrates the concept of scarcity, choice, and opportunity cost.

• Points on the PPF indicate efficient use of resources.

• Points inside the curve reflect underutilization or inefficiency.

• Points outside the curve are unattainable with existing resources.

Properties of PPF:

1. Downward sloping – trade-offs exist between goods.

2. Concave to origin – due to increasing opportunity cost (law of diminishing returns).

Marginal Rate of Transformation (MRT):
MRT is the slope of the PPF. It measures how much of one good must be sacrificed to produce one more unit of another good. Formally:

$$MR{T}_{xy}=\frac{\mathrm{\Delta }Y}{\mathrm{\Delta }X}$$

As we move along the PPF, MRT rises because resources are not equally efficient in producing all goods.

Relationship:

• MRT represents the opportunity cost of producing one good in terms of another.

• The curvature of the PPF reflects increasing MRT.

• When MRT is constant, PPF is a straight line (perfect substitutability).

• When MRT increases, PPF is concave, which is the usual case.

Conclusion:
The PPF framework highlights scarcity and efficient allocation of resources, while MRT quantitatively expresses trade-offs faced by the economy. Together, they provide a powerful tool to understand choices, efficiency, and growth possibilities.

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Assignment Two (Middle Category — ~250 words each, 10 marks each)

Q.3 (a)

Shapes of isoquants depending on degree of substitutability & properties of isoquants

An isoquant shows all combinations of two inputs (typically labour L and capital K) that produce the same level of output. The shape of an isoquant depends on how easily one input can be substituted for the other:

• Perfect substitutes: Isoquants are straight lines (negative slope). Inputs can be substituted one-for-one at a constant rate. MRTS (marginal rate of technical substitution) is constant.

• Perfect complements (fixed proportions): Isoquants are L-shaped (right angles). Inputs must be used in fixed proportions (e.g., one machine and one operator); no substitution beyond the fixed ratio.

• Diminishing MRTS (convex isoquants): The usual case—isoquants are convex to the origin. As you substitute capital for labour, MRTS diminishes because inputs are not perfect substitutes; resources are increasingly less suited to replacing each other.

Properties of isoquants:

1. Downward sloping: To keep output constant, a fall in one input must be compensated by a rise in the other.

2. Convex to the origin (usually): Reflects diminishing MRTS and diminishing marginal productivity of inputs.

3. Do not intersect: If two isoquants crossed, that would imply the same input bundle yields two different outputs—contradiction.

4. Higher isoquants represent higher output: Isoquants farther from the origin denote higher production levels.

5. MRTS equals slope of isoquant: $MRT{S}_{LK}=\frac{\mathrm{\Delta }K}{\mathrm{\Delta }L}=\frac{M{P}_L}{M{P}_K}$
   

These shapes and properties help firms choose efficient input combinations depending on relative input prices and technological substitutability. For example, with highly substitutable inputs, firms will respond to price changes by large adjustments in input mix; with complements, adjustments are limited.

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Q.4

Suppose a competitive firm has total cost $TC(q)=450+15q+2q^2$and marginal cost $MC(q)=15+4q$. If market price $P=115$

(i) Level of output produced by the firm

For a price-taking (perfectly competitive) firm: choose $q$ where $P=MC(q)$ (provided $P$ covers AVC in short run).

Given $MC(q)=15+4q$, set:

$$\begin{gathered} 115=15+4q \\ 4q=100 \\ q=25\text{ units} \end{gathered}$$

(ii) Profit and Producer Surplus

Compute Total Revenue (TR), Total Cost (TC), Fixed Cost (FC), Variable Cost (VC).

• $TR=P\times q=115\times 25=2875$
  

• $TC(q)=450+15(25)+2(25{)}^2$
  

  • $15\times 25=375$
    

  • ${25}^2=625;2\times 625=1250$
    

  • So $TC=450+375+1250=2075$
    

• Profit $=TR-TC=2875-2075=800$
  

Producer surplus (PS) for the firm = $TR-VC$, where VC = $TC-FC$

• Fixed cost $FC=450$.

• Variable cost $VC=375+1250=1625$
  

• $PS=2875-1625=1250$
  

Interpretation: At $q=25$, the firm earns positive economic profit of Rs 800 (price covers average total cost), and producer surplus Rs 1250 measures the revenue above variable cost (contribution to fixed cost and profit).

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Q.5

Equilibrium in oligopoly vs. perfect competition and monopolistic competition; Cournot model

Distinctive features of equilibrium:

• Perfect competition (PC): Many firms, homogenous product, price takers. Equilibrium: $P=MC$ in long-run, zero economic profit, allocative and productive efficiency (if no externalities).

• Monopolistic competition (MCp): Many firms, differentiated products. Firms have some price-setting power. In long-run, entry erodes economic profits to zero; price > marginal cost (P > MC) and excess capacity typically exists (firms produce below minimum efficient scale).

• Oligopoly: Few interdependent firms; strategic interactions matter. Equilibrium depends on firms’ behavior (Cournot, Bertrand, Stackelberg, cartel). Price and quantity outcomes lie between monopoly and perfect competition; firms may earn positive long-run profits due to barriers to entry; market outcomes often inefficient.

Cournot model (quantity competition) — two-firm (duopoly) illustration:

Assume linear inverse demand: $P=a-bQ$, where $Q=q_1+q_2$. Constant marginal cost $c$.

Firm 1’s profit:

$${\pi }_1=(P-c)q_1=(a-b(q_1+q_2)-c)q_1\mathrm{.}$$

FOC for profit maximization (treat $q_2$ as given):

$$\frac{\mathrm{\partial }{\pi }_1}{\mathrm{\partial }{q}_1}=a-b(q_1+q_2)-c-b{q}_1=0$$
$$\Rightarrow a-c-2b{q}_1-b{q}_2=0$$

Reaction function:

$$q_1=\frac{a-c-b{q}_2}{2b}\mathrm{.}$$

Symmetrically for firm 2. Solve for symmetric equilibrium $q_1=q_2=q^{\ast }$

$$q^{\ast }=\frac{a-c}{3b}\mathrm{.}$$

Total output $Q^{\ast }=2q^{\ast }=\frac{2(a-c)}{3b}$.

Price:

$$P^{\ast }=a-b{Q}^{\ast }=a-\frac{2(a-c)}{3}=\frac{a+2c}{3}\mathrm{.}$$

Comparison: Cournot outcome yields price and output intermediate between monopoly (higher price, lower output) and perfect competition (P = c). Firms earn positive profits if $a>c$. Strategic interdependence (reaction functions) is central to oligopoly equilibrium; unlike PC or MCp, firms’ choices directly affect rivals’ profits and thus must be anticipated.

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Assignment Three:-

Q.6

Given:
$Q_d=8000-1000P_x$ and $Q_s=-4000+2000P_x$
At equilibrium $Q_d=Q_s$

$$8000-1000P_x=-4000+2000P_x$$

Bring like terms together:

$$8000+4000=2000P_x+1000P_x$$
$$12000=3000P_x\Rightarrow P_x=\frac{12000}{3000}=4$$

Equilibrium price $P_x=Rs\mathrm{.}4$

Equilibrium quantity:

$$Q^{\ast }=8000-1000(4)=8000-4000=4000$$

So, equilibrium price = Rs. 4 and equilibrium quantity = 4000 units.

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Q.7

Decomposing the total price effect into substitution and income effects

Two standard approaches: Hicksian (compensated) and Slutsky (income-compensated).

1. Hicks (compensated) method: Keep the consumer on the same utility after the price change by compensating income. Graphically: draw initial budget line and indifference curve (IC1). When price falls, new budget line rotates outward to allow a higher utility (IC2). Construct a hypothetical budget line tangent to IC1 but with the new relative price — movement from original consumption to the compensated point is the substitution effect(movement along the same IC). The change from the compensated point to the new consumption point is the income effect (change in utility).

2. Slutsky method: Compensate the consumer so they can still buy the original bundle at new prices (i.e., adjust money income). Substitution effect: movement from original bundle to the bundle on the new price line tangent to a hypothetical budget that affords the original bundle. Income effect: movement from that compensated bundle to the final bundle.

Both can be shown with budget lines and indifference curves; Hicks isolates pure substitution (utility constant), Slutsky uses purchasing-power compensation (original bundle affordable).

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Q.8

Distortions that prevent achieving efficiency in a perfectly competitive market

1. Externalities: Unpriced social costs/benefits (pollution or knowledge spillovers) cause divergence between private and social optima.

2. Public goods: Non-rivalry and non-excludability (e.g., national defence) lead to under-provision due to free-riding.

3. Imperfect information: Asymmetric or incomplete information (e.g., adverse selection) causes suboptimal trades or market breakdowns.

4. Market power: Monopolies/oligopolies restrict output and raise price above marginal cost.

5. Transaction costs and incomplete markets: High transaction costs or missing markets (e.g., insurance for some risks) impede mutually beneficial exchanges.

6. Government distortions: Price controls, perverse subsidies, or taxes can prevent price from equalling marginal cost and quantity from reaching the efficient level.

These distortions cause divergence between private incentives and social welfare, necessitating corrective policy.

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Q.9

General equilibrium of production in a two-commodity (X, Y), two-factor (L, K) economy

General equilibrium of production is reached when firms choose input combinations and outputs such that (i) each firm maximizes profit given factor prices, (ii) factor markets clear (supply = demand for L and K), and (iii) production is feasible (given technology). In competitive factor markets, profit maximization implies factor prices equal marginal products: $w=M{P}_L$ and $r=M{P}_K$. For each commodity, cost-minimizing input choices equate MRTS to factor price ratio $(MRT{S}_{LK}=w\mathrm{/}r)$. Aggregate demands for L and K across firms must equal total endowments; when they do, factors are fully employed. Graphically, one can show firms’ isoquants and isocost lines; equilibrium occurs at tangency points whose aggregate outputs lie on the economy’s production possibility frontier. Thus general production equilibrium combines optimization and market-clearing conditions.

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Q.10

Distinguish between any two (i) and (ii):

(i) Marginal Physical Product (MPP) vs. Marginal Revenue Product (MRP)

• MPP is the extra physical output produced by employing one more unit of an input (holding other inputs fixed). It is a technical measure: $MP{P}_L=\mathrm{\Delta }Q\mathrm{/}\mathrm{\Delta }L$.

• MRP converts MPP into monetary terms: $MR{P}_L=P\times MP{P}_L$under perfect competition (or $MR\times MPP$ under imperfect competition). MRP indicates the additional revenue a firm obtains from an extra unit of input and determines the firm’s demand for that input.

(ii) Adverse Selection vs. Moral Hazard

• Adverse selection arises before a contract is signed due to hidden information about attributes (e.g., high-risk individuals buying insurance disproportionately). It leads to inefficient market composition.

• Moral hazard arises after contracting because one party’s actions are unobservable or uncontractible (e.g., insured individuals taking more risks). It causes inefficient behaviour because incentives are distorted.