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MEC-101: Microeconomic Analysis

MEC-101: Microeconomic Analysis

IGNOU Solved Assignment Solution for 2023-24

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Assignment Code: MEC-101/Asst /TMA /2023-24

Course Code: MEC-101

Assignment Name: Micro Economic Analysis

Year: 2023-2024

Verification Status: Verified by Professor



SECTION A

Answer the following questions in about 700 words each. The word limits do not apply in case of numerical questions. Each question carries 20 marks.

Q1a) A monopolist uses one input X, which she purchases at the fixed price p=5 in order to produce output q. Her demand and production functions are: P=85-3q and q= 2x^1/2 respectively. Derive the equilibrium output and equilibrium profit.

Ans)

Demand Function:

P = 85 - 3q


Production Function:

q = 2x^(1/2)

Constraint:

Total Cost (TC) = Input Cost (IC) = px


Profit Function:

Profit = Total Revenue (TR) - TC


Steps to Solve

Express Price (P) in terms of Input (X):

Substitute the production function (q = 2x^(1/2)) into the demand function: P = 85 - 3(2x^(1/2)) P = 85 - 6x^(1/2)

Express Total Revenue (TR) in terms of Input (X):

TR = P q = (85 - 6x^(1/2)) (2x^(1/2)) TR = 170x^(1/2) - 12x

Express Total Cost (TC) in terms of Input (X):

TC = IC = px = 5x


Derive Profit Function:

Profit = TR - TC Profit = (170x^(1/2) - 12x) - 5x Profit = 170x^(1/2) - 17x

Find Profit-Maximizing Input (X):

Set marginal profit (dProfit/dx) equal to zero and solve for x: dProfit/dx = (1/2)*170x^(-1/2) - 17 = 0 Solve for x using numerical methods (e.g., Newton-Raphson): x ≈ 2.367


Calculate Equilibrium Output (Q):

Substitute x into the production function: q = 2(2.367)^(1/2) ≈ 3.526

Calculate Equilibrium Price (P):

Substitute x into the demand function: P = 85 - 6(2.367)^(1/2) ≈ 64.027

Calculate Equilibrium Profit:

Substitute x into the profit function: Profit ≈ 170(2.367)^(1/2) - 17(2.367) ≈ 306.06

Therefore, the equilibrium output is approximately 3.526 units, and the equilibrium profit is approximately 306.06.


Q1. b) “In real world, sometimes it is not possible to achieve optimum welfare.” Comment and discuss the obstacles in attaining Pareto optimum.

Ans) Achieving optimum welfare, as defined by Pareto efficiency or Pareto optimality, is often challenging or even impossible in the real world due to various obstacles and constraints. While Pareto efficiency represents a state where no individual can be made better off without making someone else worse off, attaining this ideal outcome faces several practical hurdles that limit its realization. These obstacles stem from market imperfections, externalities, informational asymmetries, institutional constraints, and distributional concerns, among other factors. Understanding these obstacles is essential for policymakers and economists seeking to improve societal welfare and address inefficiencies in the economy.


a) Market Imperfections:

Numerous defects can result in inefficiencies and inhibit the achievement of Pareto optimality. Markets are rarely totally competitive, and these imperfections can contribute to inefficiencies. Monopolies, oligopolies, and monopolistic competition are all examples of market structures that can result in market power, which in turn can lead to price-setting behaviour and allocative inefficiency. Furthermore, partial markets, such as those with missing or incomplete information, might impede the efficient allocation of resources and prevent Pareto gains from occurring.


b) Externalities:

Externalities, which occur when the actions of one party affect the welfare of others without appropriate compensation or recognition, pose significant obstacles to achieving Pareto optimality. Positive externalities, such as technological spillovers or education, lead to underinvestment by private actors, resulting in suboptimal outcomes. Negative externalities, such as pollution or congestion, lead to overproduction or overconsumption of harmful goods, creating inefficiencies and welfare losses.


c) Public Goods:

It is difficult to achieve Pareto optimality when dealing with public goods because they cannot be excluded, and they do not compete with one another in terms of consumption. Individuals have an incentive to use public goods without contributing to their provision as a result of the free-rider problem, which results in underproduction and welfare outcomes that are less than optimal. In addition, the difficulty of effectively pricing and allocating public goods is a significant factor that contributes to the difficulty of reaching Pareto efficiency.


d) Informational Asymmetries:

Informational asymmetries between buyers and sellers, as well as between employers and employees, can lead to market failures and prevent the attainment of Pareto optimality. In situations where one party possesses more information than the other, adverse selection, moral hazard, and principal-agent problems can arise, resulting in inefficient outcomes. Moreover, imperfect information can lead to misallocation of resources and prevent mutually beneficial exchanges.


e) Incomplete Contracts:

Incomplete contracts, which fail to identify all possible outcomes or eventualities, can result in inefficiencies, and prevent Pareto improvements from being implemented. It is possible for opportunistic behaviour, renegotiation, and dispute resolution costs to arise in circumstances where the parties to a contract are unable to anticipate or account for all of the possible future states of the world. This would result in the efficiency of the contractual agreements being undermined.


f) Income and Wealth Inequality:

High levels of income and wealth inequality can hinder the achievement of Pareto optimality by limiting access to resources and opportunities for disadvantaged individuals. Inequality can lead to underinvestment in human capital, health, and education, resulting in suboptimal outcomes and perpetuating a cycle of poverty and inequality. Moreover, unequal distribution of political power and influence can exacerbate market distortions and prevent the implementation of policies aimed at improving welfare.


g) Political and Institutional Constraints:

Attempts to reach Pareto optimality can be hampered by political and institutional concerns, such as rent-seeking behaviour, regulatory capture, and vested interests, among other things. Lobbying and rent extraction are examples of rent-seeking activities that drain resources away from productive uses and cause inefficiencies in the distribution of resources. Additionally, regulatory hurdles and bureaucratic inefficiencies can be a barrier to market competition and innovation, which can inhibit the realisation of Pareto improvements.


Q2) Given a Cobb-Douglas utility function

U (X, Y) = X1/2 Y1/2,

Where X and y are the two goods that a consumer consumes at per unit prices of Px and Py respectively. Assuming the income of the consumer to be ₹M, determine:


Q2a) Marshallian demand function for goods X and Y.

Ans)

Marshallian Demand Functions:

The Marshallian demand functions represent the optimal quantities of goods that a consumer will purchase given prices and income. For the Cobb-Douglas utility function (U(X, Y) = X^{1/2}Y^{1/2}), the demand functions can be derived by maximizing the utility subject to the budget constraint:

[\max_{X, Y) U(X, Y) \text{ subject to } Px \cdot X + Py \cdot Y = M]

Solving this optimization problem will yield the Marshallian demand functions for goods X and Y.


Q2. b) Indirect utility function for such a consumer.

Ans)

Indirect Utility Function:

The indirect utility function represents the maximum utility attainable at given prices and income. It is derived by substituting the optimal quantities (Marshallian demand functions) into the utility function.

[V(Px, Py, M) = U(X^(Px, Py, M), Y^(Px, Py, M))]

Q2c) The maximum utility attained by the consumer where α =1/2, Px =₹ 2, Py= ₹ 8 and

M= ₹ 4000.

Ans)

Maximum Utility:

To find the maximum utility, substitute the given values into the indirect utility function:

[V(Px, Py, M) = U(X^, Y^)]


Q2. d) Derive Roy’s identity.

Ans)

Roy's Identity:

Roy's Identity relates the compensated and uncompensated price elasticities of demand. For a Cobb- Douglas utility function, Roy's Identity is given by:

[ \frac{\partial x_i}{\partial p_j} = \frac{x_i}{p_j} \frac{\partial U/\partial x_i}{\partial UɅpartial M}]

This identity expresses how the change in the demand for a good with respect to its price is related to the income and substitution effects.


SECTION B

Answer the following questions in about 400 words each. Each question carries 12marks.


Q3a) How is Cournot’s model of oligopoly different from Bertrand’s model of oligopoly?

Ans) Comparison between Cournot's model of oligopoly and Bertrand's model of oligopoly:

Q3. b) Suppose the demand for a product is given by p=d (q)=−0.8q+150 and the supply for the same product is given by p=s(q)=5.2q. For both functions, q is the quantity and p is the price. Find out producer surplus and consumer surplus.

Ans) To find the consumer surplus and producer surplus at equilibrium, we need to set the demand and supply functions equal to each other since equilibrium occurs when the quantity demanded equals the quantity supplied. In other words, find the value of q for which d(q)=s(q)

The demand function is given by p=d(q)=−0.8q+150, and the supply function is given by p=s(q)=5.2q

Setting them equal to each other:

−0.8q+150=5.2q

Now, solve for q:

6q=150

q=6150=25

Now that we have the equilibrium quantity (q=25), we can substitute this value into either the demand or supply function to find the equilibrium price (p).

Let's use the demand function:

p=d(25)=−0.8(25)+150

p=−20+150=130

So, at equilibrium, q=25 and p=130.


Now, we can find the consumer surplus and producer surplus.

a) Consumer Surplus: Consumer surplus is the area between the demand curve and the price level up to the equilibrium quantity. It is calculated as the area of a triangle.

CS=1/2×(Pequilibrium−0)×qequilibriumCS=1/2×(130−0)×25=12×130×25=1625=1/2×(=1/2×(130−0)×25=12×130×25= 1625

So, the consumer surplus is 1625


b) Producer Surplus: Producer surplus is the area between the supply curve and the price level up to the equilibrium quantity. It is also calculated as the area of a triangle.

PS=1/2×(130−0)×qequilibriumPS=12×130×25=1625=1/2×(130−0)× =12×130×25=1625

So, the producer surplus is 1625.

Both the consumer surplus and producer surplus are 1625 at equilibrium.


Q4a) Differentiate between Cooperative and non-cooperative game theory.

Ans) Comparison between Cooperative and non-cooperative game theory:

Q4. b) From the following pay-off matrix, determine:

Q4. i) The optimal strategy for each individual.

Ans)

For Player 1:

Player 1 wants to maximize their minimum guaranteed payoff. Look at the minimum payoff in each row and choose the strategy corresponding to the maximum of these minimums.

Minimum payoffs for Player 1. 1, 4, 2, 2

Maximum of these minimums: 4 So, Player 1's optimal strategy is II.

For Player 2:

Player 2 wants to minimize their maximum possible loss. Look at the maximum payoff in each column and choose the strategy corresponding to the minimum of these maximums.

Maximum payoffs for Player 2: 9, 6, 4, 8, 8

Minimum of these maximums. 4 So, Player 2's optimal strategy is III


Q4. ii) Value of the game.

Ans) The value of the game is the payoff associated with the cell where the optimal strategies for both players intersect. In this case, it's the payoff in the cell where Player 1's strategy II and Player 2's strategy III intersect.

Value of the game = Payoff for (II, III) = 4

Therefore, the optimal strategy for Player 1 is II, the optimal strategy for Player 2 is III, and the value of the game is 4.


Q5. a) Do you agree that by paying higher than the minimum wage, employers can retain skilled workers, increase productivity, or ensure loyalty? Comment on the statement in the light of efficiency wage model.

Ans) The efficiency wage theory suggests that paying higher than the minimum wage can indeed have several beneficial effects for employers, including retaining skilled workers, increasing productivity, and fostering loyalty among employees. However, the implications of the efficiency wage model go beyond just higher wages; they also encompass the relationship between wages, worker effort, and firm performance.


a) Retaining Skilled Workers:

By paying higher wages, employers can attract and retain skilled workers who may otherwise seek higher-paying opportunities elsewhere. Skilled workers are valuable assets to firms, as they often possess specialized knowledge and experience that contribute to higher productivity and innovation. Moreover, higher wages can serve as a signal of the firm's commitment to its employees, enhancing job satisfaction and reducing turnover rates. As a result, firms can maintain a stable workforce of skilled employees, which is essential for long-term success and competitiveness.


b) Increasing Productivity:

The efficiency wage model posits that higher wages can incentivize workers to exert greater effort and perform more effectively on the job. When workers are paid above the market-clearing wage, they may feel a sense of obligation or reciprocity towards their employer, leading them to work harder to justify their higher wages. Additionally, higher wages can enhance employee morale, motivation, and job engagement, resulting in increased productivity levels. This is particularly relevant for tasks that require creativity, problem-solving, and discretionary effort, where motivated and skilled workers can make significant contributions to firm performance.


c) Ensuring Loyalty:

Offering higher wages can foster loyalty and commitment among employees, as they may feel valued and appreciated by their employer. Loyalty is important for building long-term relationships between employers and employees, as loyal workers are more likely to remain with the company, contribute positively to its culture, and act in its best interests. Moreover, loyal employees are less inclined to engage in behaviours such as absenteeism, turnover, or shirking, which can undermine organizational effectiveness and cohesion. By investing in higher wages, employers can cultivate a sense of trust and loyalty among their workforce, leading to greater stability and sustainability in the long run. However, it's essential to recognize that the efficiency wage model also suggests potential drawbacks and trade-offs associated with paying higher wages:


a) Cost Considerations:

Paying higher wages entails increased labor costs for employers, which may impact their profitability and competitiveness, particularly in industries with thin profit margins or intense competition. Employers must carefully balance the benefits of higher wages with the costs and ensure that the investment in labor yields sufficient returns in terms of improved productivity and performance.


b) Market Imperfections:

The efficiency wage model assumes that workers respond positively to higher wages by exerting greater effort and productivity. However, in reality, individual responses to wage incentives may vary due to factors such as worker preferences, market conditions, and institutional constraints. Moreover, the effectiveness of higher wages in retaining skilled workers and enhancing productivity depends on the presence of labor market imperfections, such as information asymmetries, labor market segmentation, or barriers to entry.


Q5. b) There are two firms 1 and 2 in an industry, each producing output Q1 and Q2 respectively and facing the industry demand given by P=50-2Q, where P is the market price and Q represents the total industry output, that is Q= Q1 + Q2. Assume that the cost function is C = 10 + 2q. Solve for the Cournot equilibrium in such an industry.

Ans) The profit-maximizing output for each firm is where marginal cost equals marginal revenue.

Given the demand function (P=50-2Q), where (Q = Q1 Q2), and the cost function (C=10+2q). where (q Q1 Q2), let's find the equilibrium output for each firm.

a) Determine the Total Output (Q): [Q = Q1+Q2]

b) Derive the Marginal Revenue (MR) for Each Firm:

[MR = \frac{d(TR)}(dQ} = \frac{d(50Q-Q^2)}{dQ)]

c) Equate Marginal Revenue to Marginal Cost (MC) for Each Firm:

[MR = MC]

[10-2012]

[10-2Q2=2]

d) Solve for the Output of Each Firm (Q1 and Q2) in Equilibrium:

Solve the system of equations to find (Q1) and (Q2). [Q1 = \frac{1}{2}(10-202)]

[Q2 = \frac{1}{2)(10-201)]

e) Calculate the Market Price (P) at Equilibrium:

Substitute the equilibrium (Q) into the demand function to find the market price. [P = 50-2Q]

The values obtained for (Q1), (Q2), and (P) represent the Cournot equilibrium in the industry. Keep in mind that the solution involves solving simultaneous equations, and the exact steps can vary based on the specific equations given.


Q6. a) Do you think that a risk-averse individual gamble or will a risk lover purchase insurance? Explain your answer.

Ans) Whether a risk-averse individual will gamble, or a risk lover will purchase insurance depends on their individual preferences, attitudes towards risk, and the specific context of the gamble or insurance policy. Let's explore both scenarios:


Risk-Averse Individual Gambling

Risk-averse individuals typically prefer certainty over uncertainty and are willing to pay to avoid risk. However, there are situations where a risk-averse individual might choose to gamble:

a) Small Stakes, High Probability of Winning: If the stakes are small and the probability of winning is high, a risk-averse individual might be willing to take the gamble. For example, buying a lottery ticket with a small investment where the probability of winning is relatively high compared to the potential payoff.

b) Utility of the Thrill: Some risk-averse individuals may derive utility or enjoyment from the thrill of gambling, even if they are aware of the risks involved. The excitement of the possibility of winning may outweigh the potential loss for them.

c) Limited Alternatives: In some cases, a risk-averse individual may perceive gambling as the only available option to improve their financial situation, especially if they feel they have limited alternatives.


Risk Lover Purchasing Insurance

Risk lovers are individuals who have a high tolerance for risk and may actively seek out risky situations. However, even risk lovers may find value in purchasing insurance in certain circumstances:

a) Risk Diversification: While risk lovers may be comfortable with taking on high levels of risk in some areas of their life, they may still recognize the benefits of diversifying their risks. Insurance allows them to spread their risk across a pool of policyholders, reducing the impact of any single adverse event.

b) Protection of Assets: Risk lovers may have accumulated valuable assets or investments that they wish to protect against catastrophic losses. Insurance provides a means of safeguarding these assets, allowing risk lovers to continue pursuing high-risk activities without fear of financial ruin.

c) Peace of Mind: Even risk lovers may experience anxiety or stress associated with the uncertainty of potential losses. Purchasing insurance can provide peace of mind by offering a financial safety net in the event of an adverse outcome.


Expected Utility and Decision Making

Decision-making under uncertainty involves evaluating the expected utility of different options. Expected utility theory suggests that individuals make decisions based on the expected value of outcomes weighted by their subjective utility or satisfaction. Risk-averse individuals typically exhibit diminishing marginal utility, meaning that the additional utility gained from an increase in wealth decreases as wealth increases. As a result, risk-averse individuals are willing to sacrifice potential gains to avoid potential losses. In contrast, risk-loving individuals may exhibit increasing marginal utility, where they derive greater satisfaction from additional wealth, leading them to take risks in pursuit of higher returns.


Q6. b) Radha has assets worth 10,000 rupees and is facing a loss of 3,600 with a probability of 0.002. She is indifferent between paying G rupees for insurance protection and assuming the risk of loss personally. She values total assets of amount w≥0 according to the utility function u (w) = w1/2. Determine G.

Ans)

a) Setting Up the Equations:

As mentioned before, we need to equate the expected utilities with and without insurance since Radha is indifferent:

1) Expected Utility with Insurance:

U(with insurance) = u(10,000 - G) = (10,000 - G)^(1/2)

2) Expected Utility without Insurance:

U(without insurance) = 0.002 u(6,400) + 0.998 u(10,000) = 0.002 (6,400)^(1/2) + 0.998 (10,000)^(1/2)

b) Equating and Simplifying:

(10,000 - G)^(1/2) = 0.002 (6,400)^(1/2) + 0.998 (10,000)^(1/2)

Squaring both sides to eliminate the square root:

10,000 - G = 0.000004 6400 + 0.996 10,000 - 1.996 * G^(1/2)

c) Solving for G:

1) Move all terms containing G to one side and rearrange:

1.996 * G^(1/2) = 9973.6 - 0.000256

G^(1/2) = 5036.798

2) Square both sides again to get rid of the remaining square root:

G = (5036.798)^2

d) Final Answer:

Therefore, the value of G for which Radha is indifferent is approximately G = 25,318,900 rupees.

This solution aligns with Radha's risk-neutral behaviour reflected in the square-root utility function. She is willing to pay a very high premium (almost her entire wealth) to completely avoid the potential loss, even though the probability of that loss is very low.


Q7) Write short notes on following:

Q7. a) Different types of price discrimination

Ans) Price discrimination is when a seller charges different prices for the same product or service based on the buyer's willingness to pay. There are three main types:

a) First-degree price discrimination: Also known as perfect price discrimination, where the seller charges each customer their maximum willingness to pay.

b) Second-degree price discrimination: Involves charging different prices based on the quantity consumed, such as volume discounts or quantity surcharges.

c) Third-degree price discrimination: Occurs when prices vary based on customer segments, such as student discounts, senior citizen rates, or location-based pricing. It relies on segmenting customers based on their price elasticity of demand. Each type aims to increase profits by capturing consumer surplus.


Q7. b) Bilateral monopoly

Ans) Bilateral monopoly occurs when a single seller (monopolist) faces a single buyer (monopsonist) in a market. This unique market structure presents challenges and opportunities for both parties. The monopolist seeks to maximize profit by setting prices, while the monopsonist aims to minimize costs. Negotiations between them determine the price and quantity exchanged, often resulting in a compromise influenced by bargaining power, market conditions, and external factors. Bilateral monopoly can lead to inefficiencies, as both parties may exert market power to their advantage, potentially resulting in higher prices for consumers and lower wages for workers. Government intervention or regulation may be necessary to address these issues and promote fair outcomes.


Q7. c) Economies of Scale

Ans) Economies of scale refer to the cost advantages that arise when a company increases its level of production. As output expands, the average cost of production decreases, leading to greater efficiency and profitability. This phenomenon occurs due to factors such as specialization, utilization of more efficient equipment, and spreading fixed costs over a larger output. Economies of scale allow firms to lower prices, enhance competitiveness, and potentially dominate markets. However, there's a point beyond which further expansion may lead to diseconomies of scale, resulting in increased average costs. Understanding and harnessing economies of scale are vital for businesses aiming to optimize production and maximize profits in the long run.


Q7. d) Pooling and separating equilibrium

Ans) Pooling equilibrium and separating equilibrium are concepts in game theory and information economics.

a) Pooling Equilibrium: In a pooling equilibrium, different types of players with distinct characteristics or qualities take similar actions or positions. Despite their differences, they behave as if they were the same type. This equilibrium occurs when the payoff from separating types isn't enough to warrant different actions. It's commonly observed in situations where information about individuals is limited or costly to acquire.

b) Separating Equilibrium: In contrast, a separating equilibrium involves players with different types or qualities taking distinct actions. This equilibrium arises when the benefits of differentiating actions based on types outweigh the costs. It's prevalent when information about individuals is readily available and can be used to make decisions effectively.

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