Question

The market for paper in a particular region in the United States is characterized by the following demand and supply curves: \\[Q_{D}=160,000-2000 P \quad \text { and } \quad Q_{S}=40,000+2000 P\\] where \(Q_{D}\) is the quantity demanded in 100 -pound lots, \(Q_{S}\) is the quantity supplied in 100 -pound lots, and \(P\) is the price per 100 -pound lot. Currently there is no attempt to regulate the dumping of effluent into streams and rivers by the paper mills. As a result, dumping is widespread. The marginal external cost (MEC) associated with the production of paper is given by the curve \(\mathrm{MEC}=0.0006 \mathrm{Q}_{\mathrm{S}}.\) a. Calculate the output and price of paper if it is produced under competitive conditions and no attempt is made to monitor or regulate the dumping of effluent. b. Determine the socially efficient price and output of paper. c. Explain why the answers you calculated in parts (a) and (b) differ.

Short answer

The competitive market doesn't take into account the external cost of pollution, thus the price will be lower and quantity higher than in a socially efficient scenario, wherein these costs are taken into account.

Step-by-step solution

Calculate the Output and Price under Competitive Conditions

To find the equilibrium under competitive conditions (no regulation), equate the quantity demanded (\(Q_{D}\)) to the quantity supplied (\(Q_{S}\)). \n\nThus, \(160,000-2000P = 40,000+2000P\). Solving for P (price) and then substituting the price to either of the equations to get the equilibrium quantity.

Calculate the Socially Efficient Price and Output

To find the socially efficient price and output, consider the marginal external cost (MEC). The socially efficient level of output is found where the quantity demanded is equal to the quantity supplied, plus the marginal external cost (MEC).\n\n Therefore, set \(Q_D = Q_S + MEC\). \n\nSubstitute \(Q_S\) and \(MEC\) with their equivalent expressions in terms of \(Q\) and solve for \(Q\) and \(P\).

Comparison of Competitive vs Socially Efficient Outcomes

From step 1 and 2, we will have two sets of price and quantity values. Explain the difference in outcomes due to the existence of the external costs in production that were not taken into account in the competitive equilibrium situation.

Key concepts

Demand and Supply Curves

The demand and supply curves are fundamental tools used in economics to understand how market forces determine prices and quantities. In our scenario, the demand curve is given by the equation \(Q_{D} = 160,000 - 2000P\), where \(Q_{D}\) is the quantity demanded and \(P\) is the price per 100-pound lot of paper. As the price increases, the quantity demanded decreases, showing an inverse relationship.
Similarly, the supply curve is represented by \(Q_{S} = 40,000 + 2000P\), indicating a direct relationship between price and quantity supplied. As the price rises, suppliers are more willing to produce and sell more paper.

To find the equilibrium, where market supply equals demand, we set the demand and supply equations equal:
\[160,000 - 2000P = 40,000 + 2000P\] Solving this equation helps determine the equilibrium price \(P_e\) and equilibrium quantity \(Q_e\) that clear the market.

• When quantity demanded equals quantity supplied, the market is in equilibrium.
• Changes in external factors like costs or regulations can shift these curves, altering equilibrium.

Marginal External Cost

Marginal External Cost (MEC) is an essential concept when considering the impact of production on third parties who are not involved in a transaction. In the paper market context, the MEC is the additional cost imposed on the environment due to the effluent dumping by paper mills. The given MEC is expressed as \(MEC = 0.0006Q_{S}\).

This cost is not reflected in the supply curve under competitive conditions, leading to a market failure where the social costs exceed the private costs borne by producers.

To account for MEC in achieving social efficiency, we integrate it into the supply equation:

• The true social cost includes both private production costs and external environmental costs.
• Considering MEC helps in assessing true resource allocation and welfare implications.

Social Efficiency

Social efficiency occurs when the total welfare in the economy is maximized, and this includes both consumers' and producers' benefits while considering any externalities like MEC. Achieving social efficiency requires aligning the quantity supplied to factor in these external costs.

In our example, social efficiency is reached by adjusting the output level where \(Q_D = Q_S + MEC\). This includes the external marginal costs in the market supply, aptly balancing between production benefits and potential environmental harm.

The socially efficient price and quantity reflect the true cost of production, including the previously ignored external costs.

• Socially efficient outcomes typically result in lower quantities and higher prices than competitive equilibrium.
• Regulations or taxes might be necessary to internalize external costs and move markets toward social efficiency.

Until such externalities are addressed, market equilibrium does not coincide with social efficiency, spotlighting the importance of comprehensive policy interventions.