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, \(Q_{\mathrm{S}}\) 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 \(\mathrm{MEC}=0.0006 Q_{S}\) 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 difference in results is due to the fact that the competitive market equilibrium does not take into account the external cost of environmental damage. The competitive market overproduces paper causing excessive environmental damage, reflected in the lower price and higher quantity. When taking into account the environmental costs, production decreases and prices increase to reflect the social cost of producing paper.

Step-by-step solution

Find Equilibrium Price and Quantity

First, set the quantity demanded equal to the quantity supplied: \[160000 - 2000P = 40000 + 2000P\]. Then, simplify and solve for \(P\). This will give you the equilibrium price under competitive conditions. Substitute this price into either the supply or demand equation to find the corresponding quantity.

Calculate the Socially Efficient Price and Quantity

The socially efficient quantity is where the sum of the supply curve and the marginal external cost equals the demand curve: \[40000 + 2000P + 0.0006Q_S = 160000 - 2000P\]. This equation will require substitution and rearranging to solve for \(P\). The resulting value is the socially efficient price. Substitute this into the supply or demand equation to get the socially efficient quantity.

Explain Differing Results

The differences in the outcomes of steps 1 and 2 are due to the lack of incorporation of the external costs associated with the production of paper, in this case, environmental damage, into the market price. In the competitive market equilibrium, these external costs are not taken into account, leading to a higher quantity produced and a lower price. When these external costs are factored in, however, it results in a 'socially efficient' outcome where the quantity produced is lower and the price is higher.

Key concepts

Demand and Supply Curves

Understanding the demand and supply curves is essential for visualizing the behavior of buyers and sellers in the marketplace. These curves represent how much of a product consumers want to buy (demand) and how much producers are willing to sell (supply) at different price levels.

The demand curve typically slopes downwards, showing that as the price decreases, consumers are willing to buy more of the good. Mathematically, in the given exercise, the demand for paper is represented as \(Q_{D}=160,000-2000 P\), indicating that higher prices lead to a lower quantity demanded.

Conversely, the supply curve slopes upwards, illustrating that as the price increases, producers are more inclined to supply more goods. For the paper market exercise, the supply of paper is shown by the equation \(Q_{S}=40,000+2000 P\), demonstrating that at higher prices, more paper is supplied.

Finding where these two curves intersect gives us the market equilibrium - the price at which the quantity of paper demanded equals the quantity supplied, without considering any externalities.

Marginal External Cost

Marginal external cost (MEC) is a concept that refers to the cost of producing one additional unit of a good or service that is not reflected in the market price and is instead imposed on others. In the case of the paper market, the MEC is represented by the equation \(MEC=0.0006 Q_{S}\).

This cost, often coming from negative externalities like pollution, represents the additional cost to society that results from producing one more 100-pound lot of paper. When producers dump effluent into rivers, they don't bear the full cost of this action; the environment and society do. The MEC needs to be integrated into the supply curve to understand the true cost of production and move the market towards a socially optimal outcome.

Socially Efficient Price and Output

The socially efficient price and output are realized when the true cost of production, including external costs, is accounted for in the market. To determine these, we combine the supply curve with the MEC. This results in a new curve that represents the true cost to society of producing paper.

For our exercise, the socially efficient point is where the adjusted supply curve (including MEC) intersects the demand curve. This requires solving a revised equation that includes the MEC term. This new intersection point leads to an outcome where the paper's price reflects both private and external costs, and the output level is where the social benefit of consuming paper equals its true social cost.

This scenario often requires intervention, such as taxation or regulation, to make the producers internalize the MEC. When the MEC is included, it typically leads to a higher equilibrium price and a lower equilibrium quantity compared to the competitive market outcome.

Externalities in Economics

Externalities are costs or benefits of an economic activity that affect third parties not directly involved in the transaction. Negative externalities, like pollution from paper mills, impose additional costs on society which are not reflected in the market price of paper.

When negative externalities exist, the market often fails to allocate resources efficiently, leading to overproduction of the good and a lower market price than what would be considered ‘socially’ optimal. This is fundamentally why the competitive market equilibrium differs from the socially efficient outcome.

Regulating such activities or imposing taxes, commonly known as Pigovian taxes, can help to correct these market failures. By including these external costs in the production costs, producers are 'encouraged' to reduce their negative externalities, leading to a market outcome that better reflects the true cost of the goods to society as a whole.