The Market Demand Function Based Assignment #2 Question #1:

The Market Demand Function Based Assignment #2 Question #1: (20 marks) The market-demand function, based on the value of marginal private benefit (MPB) for vaccination (Q), is PM = 100 – Q, where PM is the dollar-price per vaccination.

Assume that there are positive externalities from vaccination. The social demand function, which includes private benefits and externalities, is PS = 140 – Q, where PS is the social dollar value per vaccination. The market supply curve (based on marginal cost) is a horizontal line with MC = AC = $40. Find the following equilibrium solutions: Market equilibrium quantity (QM) = Total net benefit at the market equilibrium quantity = $ Socially optimal quantity (QS) = Total net benefit at the socially optimal quantity = $ Question #2: (60 marks) Each numerical solution is worth 2 marks.

Consider a single source of emissions in a given community. The community’s marginal damage cost function is MDC = 4E. The marginal abatement cost function is MAC = 20 – E. (a) Assume that no abatements are carried out. In other words, abatement (A) is zero and MAC is zero.

Find the following: Max E = A = Total abatement costs = $ Total damage costs = $ Aggregate costs = $ (b) Find socially optimal E (based on MDC = MAC rule) and associated values. E = A = Total abatement costs = $ Total damage costs = $ Aggregate costs = $ (c) Consider Coase Theorem and use MDC = MAC condition. Assume that the property rights belong to polluters. E = A = Price per unit of A =$ Total payments from victims to polluters = $ Net gain to polluters = $ Net gain to victims = $ (d) Consider Coase Theorem. Assume that the property rights belong to victims. E = A = Price per unit of E = $ Total payments from polluters to victims = $ Net gain to polluters = $ Net gain to victims = $ (e) Instead of Coase Theorem, consider socially optimal tax-rate per E. E = A = Tax-rate per E = $ Total tax-payments = $ Total abatement costs = $ (f) Instead of socially optimal tax-rate per E, consider socially optimal subsidy-rate per A. E = A = Total subsidy payments = $

Paper For Above instruction The assignment involves analyzing two interconnected economic scenarios: the first focuses on the demand and supply dynamics regarding vaccination benefiting from positive externalities, and the second

explores the economic implications of emissions control within a community, employing concepts such as marginal damage costs, abatement costs, Coase Theorem, and taxes/subsidies. This comprehensive discussion aims to demonstrate mastery of the core economic principles underlying market failures and policy interventions.

Analysis of Vaccination Market Equilibrium and Socially Optimal Outcomes The first part of the assignment delves into the equilibrium analysis of the vaccination market. The private marginal benefit (PM) from vaccination is given by the linear function PM = 100 – Q, indicating that as vaccination coverage (Q) increases, the private benefit per individual decreases linearly. Conversely, the social demand function PS = 140 – Q incorporates externalities, reflecting the total social valuation of vaccination by combining private benefits and marginal external benefits (positive externalities). The market supply curve, with a marginal (and average) cost of $40, remains constant, illustrating a perfectly elastic supply at this cost point.

To determine the market equilibrium quantity (QM), we set private marginal benefit equal to the marginal cost: 100 – Q = 40, solving for Q yields QM = 60. At this point, the private marginal benefit equals the marginal cost, with the total net benefit being the difference between the total benefits and total costs at QM. The total private benefits are calculated as the area under the demand curve up to QM, which equals the integral of (100 – Q) from 0 to 60, resulting in (1/2) * (100 + 40) * 60 = 4200. The total cost for this quantity is the marginal cost times quantity: 40 * 60 = 2400; thus, the net private benefit is 4200 – 2400 = 1800.

Similarly, for the socially optimal quantity (QS), we set social marginal benefit equal to the marginal cost: 140 – QS = 40, which yields QS = 100. The total social benefits can be calculated as the area under the social demand curve up to QS: (1/2) * (140 + 40) * 100 = 9500. The total social cost remains 40 * 100 = 4000. Therefore, the total net social benefit at QS is 9500 – 4000 = 5500. This indicates that increasing vaccination coverage to the socially optimal level yields higher overall benefits due to accounting for positive externalities.

Economic Analysis of Emissions Control and Policy Interventions The second component examines emissions in a community, focusing on the marginal damage cost (MDC = 4E) and the marginal abatement cost (MAC = 20 – E). Initially, with no abatement (A=0), the damages accrue unmitigated. The total damage costs are derived by integrating MDC over the emmission level E;

since MDC is linear, total damage cost = (1/2) * MDC at maximum emissions times the maximum emissions, leading to specific calculations depending on E. Under the no-abatement scenario, maximizing emissions means E is at its highest feasible level. If E is constrained to a scenario where no abatement occurs, E is at its maximum, and total damage costs are proportional to this E. Total abatement costs are zero as no abatement occurs, while the total damage costs are calculated as MDC * E. The overall aggregate costs, summing damage and abatement costs, reflect societal losses absent mitigation measures.

The socially optimal emission level (E*) is obtained by setting MDC equal to MAC: 4E = 20 – E, which results in E* = 4. Exploiting this condition, the associated costs are calculated. The total abatement costs (cost of reducing emissions to E*) are computed via the integral of MAC up to E*, and damage costs are the integral of MDC up to E*. The total societal costs, combining these elements, are minimized at this point, demonstrating efficient allocation.

The application of Coase Theorem considers property rights assumptions. When polluters hold the property rights, the equilibrium emission E and the corresponding price per unit of abatement or damage are determined through bargaining. Calculations involve equating MDC to MAC, then determining who pays whom, and assessing the net gains to both polluters and victims, along with overall payments transferred. Conversely, if victims hold property rights, the bargaining outcome shifts, altering the calculations of payments and net benefits accordingly.

Finally, policy interventions such as taxes and subsidies are analyzed. A tax per E at the socially optimal level E* is set equal to the marginal damage cost at E* (per Pigou’s approach), generating total tax revenue and abatement costs. Similarly, subsidies for abatement A are structured to encourage desired reductions, with total subsidies and associated costs calculated based on the optimal abatement level, ensuring societal welfare maximization.

Conclusion Overall, these analyses emphasize the importance of internalizing externalities through appropriate fiscal and legal mechanisms. The vaccination example underscores the need for government intervention to align private incentives with social benefits, especially in the presence of positive externalities. The emissions case demonstrates how marginal cost and damage functions inform optimal policy design, whether through market-based solutions like taxes and subsidies or bargaining frameworks like Coase Theorem. Effective

environmental and public health policies rely on understanding these fundamental economic principles to achieve socially efficient outcomes and sustainable resource management.

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