Question

Consider two firms (i.e., firms 1 & 2) with heterogeneous marginal abatement

cost functions:

MAC1=12 - 2E1

MAC2 =10 - E2
Assume the marginal external damages from emissions are:

M E D = 1/2 E A . where EA is the sum of the two firms’ emissions.

1. What quantity of emissions do firms produce in the absence of government intervention? What are the total external damages? What are the total abatement costs?

2. Derive the aggregate marginal abatement cost function (Hint: This will be a kinked function. From the MAC functions you should be able to determine the kink point. Then invert the MAC functions to solve for the emissions functions. Finally, sum up emissions conditional on different MAC levels).

3. What is the socially efficient level of emissions? How much does each firm emit at the socially efficient level? How much does each firm abate relative to the market equilibrium?

4. Assume the government uses a tradable permits program to achieve the social optimum. What quantity of emissions permits should the government allocate? If the government auctions permits off initially to the highest bidder, how many permits will each firm buy? How much will each firm pay in total for these permits?

5. Assume the government uses an emissions tax to achieve the social optimum. At what level should this tax be set? How much revenue will the tax generate?

6. Assume the government implements a command and control policy where each firm must cut its emissions in half relative to the situation where there is no government intervention. What would be the total abatement costs and total external damages from this policy? Would the policy be efficient? Why or why not?

Answer 1

Marginal damage cost of greenhouse gas emission estimates are widely used today to inform decision making on climate change mitigation and adaptation. The marginal damage cost of carbon is commonly referred to as the Social Cost of Carbon (SCC).Marginal damage figures are not the only measure used to quantify impacts from climate change, other studies have also presented total damage costs and more recently new measures like changes in the balanced growth equivalent (Stern 2006) have been used. Nevertheless, marginal damage estimates of carbon emissions seem to be most numerous in the literature, and today metastudies of marginal damage estimates give a comprehensive overview of these studies

The  20 fossil fuel companies whose relentless exploitation of the world’s oil, gas and coal reserves can be directly linked to more than one-third of all greenhouse gas emissions in the modern era.New data from world-renowned researchers reveals how this cohort of state-owned and multinational firms are driving the climate emergency that threatens the future of humanity, and details how they have continued to expand their operations despite being aware of the industry’s devastating impact on the planet. role in the escalating climate emergency, evaluates what the global corporations have extracted from the ground, and the subsequent emissions these fossil fuels are responsible for since 1965 – the point at which experts say the environmental impact of fossil fuels was known by both industry leaders and politicians.

The marginal abatement cost, in general, measures the cost of reducing one more unit of pollution. Although marginal abatement costs can be negative, such as when the low carbon option is cheaper than the business-as-usual option, marginal abatement costs often rise steeply as more pollution is reduced.Various economists, research organizations, and consultancies have produced marginal abatement cost curves. Bloomberg New Energy Finance.The US Environmental Protection Agency has done work on a marginal abatement cost curve for non-carbon dioxide emissions such as methane

A message authentication code (MAC) is a cryptographic checksum on data that uses a session key to detect both accidental and intentional modifications of the data. A MAC requires two inputs: a message and a secret key known only to the originator of the message and its intended recipient. MAC is based on a pseudorandom function (for convenience called F). It works similarly to encryption performed in the CBC mode,

An efficient level of emissions is one that maximises the net benefits from pollution, where net benefits are defined as pollution benefits minus pollution damages.The marginal benefit curve for emitting pollutants can also be read from right to left as the marginal cost of abating emissions. The marginal cost curve for increased emission levels can also be read from right to left as the demand curve for improved environmental quality.

Market equilibrium is a market state where the supply in the market is equal to the demand in the market. The equilibrium price is the price of a good or service when the supply of it is equal to the demand for it in the market.Equilibrium is achieved at the price at which quantities demanded and supplied are equal. We can represent a market in equilibrium in a graph by showing the combined price and quantity at which the supply and demand curves intersect.

A tradable permit system is a tool that allows the market to direct (typically) environmental efforts where a market does not naturally exist. The tradable permit system can be thought of as a three-step process to reduce pollution emissions. ... The government then issues 1,000,000 permits to emit 1 tonne of CO2.

For a given level of cost abatement, the cost effective implementation requires the marginalcost of abatement for the two firms to be equal. Given a total amount of 40 units of emissionabatement (e1+e2= 40), the cost effective solution, (e1, e2) must satisfy two equationsi.MC(e1) =MC(e2)ii.e1+e2

In the environmental policy of most countries, various forms of quotas and direct regulation are more important than environmental taxes. This paper addresses four arguments which are often given against the use of emission taxes. The three arguments related to information asymmetries and non-convexities are valid in the sense that they point to complications in the use of environmental taxes. The fourth argument is related to the employment effects of different types of environmental policies in economies with unemployment. Although this argument is frequently used by politicians, the analysis provides no justification for it. On the contrary: in the model used, employment is higher with environmental taxes than with non-revenue-raising environmental policies.

The goal here is to pursue the policy that minimizes expected abatement costs. Total abatement costs in each period are obtained by integrating the two marginal costs curves. (We assume no there is no fixed-cost term in the total abatement costs functions.) Expected total abatement costs are then equal to the certain costs in period 1, plus the costs incurred in period 2 which would be necessary to avoid environmental calamity

Here the first term is the certain total abatement costs in period 1. The second term represents the expected value of total abatement costs in period 2. The expression substitutes ( ) 1 1− a for 2 a ; this incorporates the idea that if the “bad” scenario arrives, then there will be a need for ( ) 1 1− a in abatement in period 2, so that cumulative abatement by the end of period 2 equals 1. To solve for the minimum, we differentiate the expected cost with respect to the choice variable 1 a , and setting this equal to zero