Economics 473 Spring 2020 Problem Set Three Submit Your Answ

1economics 473 Spring 2020 Problem Set Threesubmit Your Answe

This document presents solutions to two primary questions related to market economics: a wholesale electricity market scenario and a greenhouse gas (GhG) emissions case involving social cost, benefits, and policy measures. The first problem examines competitive supply curves and equilibrium prices under varying demand conditions and explores the impact of renewable energy entry. The second problem analyzes optimal emission levels, the effects of taxation, and cap-and-trade systems in the context of greenhouse gas emissions and their associated social costs and benefits.

Paper For Above instruction

Problem 1: Wholesale Electricity Market Analysis

In this scenario, the electricity market comprises two types of suppliers: coal and natural gas. The coal suppliers have a marginal operating cost of $24/MWh with a capacity of 3,000 MW, while natural gas suppliers have a marginal cost of $40/MWh with a capacity of 2,000 MW. The task involves constructing the competitive supply curve, analyzing equilibrium prices under different demand levels, and understanding the implications of renewable energy entry.

a. Equilibrium price at 2,400 MW demand

When demand is perfectly inelastic at 2,400 MW, the equilibrium price is determined by the marginal cost of the supply that meets this demand. The supply curve is horizontal at the marginal costs of suppliers, arranged from lowest to highest cost. Since demand of 2,400 MW is less than the total capacity (5,000 MW), we need to identify which suppliers will provide the supply at equilibrium.

The coal suppliers provide 3,000 MW at $24/MWh, and the natural gas suppliers can supply an additional 2,000 MW at $40/MWh. Because demand is 2,400 MW, the entire demand is met by the lowest-cost coal suppliers, with the marginal supplier (the last unit needed) costing $24/MWh. Therefore, the equilibrium price is $24/MWh.

In this setting, both types of suppliers do not earn profits since price equals marginal cost, and no excess profit is generated.

b. Equilibrium price at 4,400 MW demand

With demand at 4,400 MW, the supply must combine coal and natural gas. The coal suppliers can provide all their 3,000 MW at $24/MWh. The remaining 1,400 MW must come from natural gas suppliers, who charge $40/MWh. The marginal unit needed to meet this demand is the last unit supplied by the natural gas suppliers, costing $40/MWh. Thus, the equilibrium price in this case is $40/MWh.

At this price, both coal and natural gas suppliers earn zero profit since the price equals their marginal costs. No supplier earns profits beyond covering their costs.

c. Impact of renewable energy (solar) entry with zero marginal cost

If 1,500 MW of solar capacity with zero marginal cost enters the market, the supply curve shifts substantially at the zero-cost segment. This solar capacity effectively acts as a perfect substitute at zero marginal cost and will supply up to 1,500 MW.

In the case of 2,400 MW demand (part a), now the solar capacity can meet a significant portion of demand at zero cost, lowering the market price to $0/MWh. Since total demand is 2,400 MW, with 1,500 MW supplied by solar at zero cost, the remaining 900 MW could theoretically be supplied by the coal market at zero marginal cost, which is not possible unless additional supply is available at zero cost. Therefore, the market price drops to $0, and suppliers (coal and natural gas) do not earn profits.

In the 4,400 MW demand (part b), the solar capacity supplies 1,500 MW at zero marginal cost. The remaining 2,900 MW are supplied by the cheapest providers remaining at their respective costs, with the highest marginal cost considered for the last units. The equilibrium price is now determined by the marginal cost of the last units needed beyond solar capacity: the coal suppliers provide 3,000 MW at $24/MWh, but since only 900 MW are needed after solar supply, the price remains at $24/MWh, assuming the demand is satisfied at that level. Overall, the entry of zero-cost solar lowers the equilibrium prices at both demand levels, with potential for prices to fall to zero if solar capacity exceeds demand.

Problem 2: Greenhouse Gas Emissions and Policy Analysis

In this scenario, the social cost of carbon (SCC)—the marginal cost of emissions—is fixed at $20 per ton. The marginal benefit (MB) from emissions diminishes linearly from $100 per ton at zero emissions to zero at 1,000 tons per day. The analysis addresses the determination of optimal emissions levels, effects of taxation, and cap-and-trade schemes.

a. Expected emissions without regulation

The socially optimal emissions are found where the MB curve equals the SCC. Since MB declines linearly from $100 to $0 as emissions increase from 0 to 1,000 tons, setting MB equal to $20 allows calculation of the unregulated (private) emissions level.

Slope of MB: (0 - 100) / (1000 - 0) = -0.1 per ton

MB at quantity Q: MB = 100 - 0.1Q

Set MB = $20: 20 = 100 - 0.1Q

0.1Q = 80 → Q = 800 tons per day.

Therefore, in the absence of regulation, emissions would be approximately 800 tons per day, which exceeds the socially optimal level considering the social cost.

b. Finding socially optimal emissions and abatement

The socially optimal level occurs where the MB curve intersects the SCC of $20. This was calculated previously at Q = 800 tons. Emissions abatement involves reducing emissions from the unregulated 800 tons to the optimal 600 tons (if this was the previous level); but for clarity, at the point where MB equals the SCC, the emissions are at 800 tons, which can be seen as the social optimum. The total abatement is the difference between the unregulated level (approximately 1,000 tons, if the MB curve is at MB = $0 at 1,000 tons) and the optimal 800 tons, which is 200 tons per day.

c. Effects of a $10 per ton emissions tax

Imposing a $10 tax per ton shifts the optimal emissions downward because it increases the marginal cost of emissions from $20 to $30 for the firms (assuming the tax applies equally to all emissions). The new optimal emissions level occurs where MB equals the sum of the SCC and the tax: MB = SCC + tax = 20 + 10 = $30. Solving for Q:

Set MB = $30: 30 = 100 - 0.1Q → 0.1Q = 70 → Q = 700 tons per day.

Compared with the previous unregulated level of 800 tons, this results in a decrease of 100 tons due to the $10 tax, representing additional abatement. This level ($700) is slightly below the socially optimal point, indicating a partial correction toward optimal emissions.

d. Tax revenue generated

The total tax revenue is the tax per ton multiplied by the quantity of emissions after taxation, which is 700 tons:

Tax revenue = $10 x 700 = $7,000 per day.

e. Extra Credit: Cap-and-Trade System Analysis

If the government establishes a cap-and-trade program with a cap set at the socially optimal level of 800 tons, the trading price for emissions permits would theoretically equal the marginal benefit of emissions at that level, which is $20 per ton (the social cost). This is because permits would be trading at a price that internalizes the social cost of emissions, aligning private incentives with social welfare.

Whether permits are auctioned or allocated freely (grandfathered), the trading price should theoretically remain the same at $20 per ton if the cap is binding and market is efficient. However, the method of allocation can influence market dynamics and the distribution of revenues: auctions generate revenue for the government, which can be used to fund clean energy initiatives or offset other taxes; free allocation may avoid initial price shocks but could lead to windfall profits for firms. Nevertheless, the equilibrium permit price should equal the marginal social cost, independent of initial permit distribution, assuming perfect markets and no market failures.

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