Use the following figure, which illustrates the market for...

Use the following figure, which illustrates the market for cotton, to work. Suppose that the cotton growers use a chemical to control insects and waste flows into the town's river. The marginal social cost of producing the cotton is double the marginal private cost. If the town owns the river and taxes cotton growers so that the efficient quantity is grown, how much tax revenue does the town receive? Is the quantity of waste zero? Explain your answer.

Use the following figure, which illustrates the market for cotton, to work.
Suppose that the cotton growers use a chemical to control insects and waste flows into the town's river. The marginal social cost of producing the cotton is double the marginal private cost.
If the town owns the river and taxes cotton growers so that the efficient quantity is grown, how much tax revenue does the town receive? Is the quantity of waste zero? Explain your answer.

Key Concepts

Tax Revenue

Tax revenue is the total income generated by the collection of taxes on goods or services. In the context of a Pigovian tax, it is calculated by multiplying the per-unit tax by the efficient quantity produced. This revenue reflects the correction of the externality and does not imply that waste is completely eliminated; production still occurs, albeit at a reduced, socially optimal level.

Efficient Quantity

The efficient quantity is the level of output where the marginal social cost equals the marginal social benefit, rather than the marginal private cost equaling marginal benefit. Achieving this output requires addressing externalities, often through taxes, to ensure overall societal welfare is maximized.

Pigovian Tax

A Pigovian tax is imposed to correct market inefficiencies caused by negative externalities. It is designed to align the private cost of production with the social cost by taxing the producer an amount equivalent to the external cost per unit. This encourages firms to produce at the socially optimal level by internalizing the external cost.

Marginal Social Cost vs. Marginal Private Cost

Marginal private cost (MPC) is the cost incurred by a producer for producing an additional unit, while marginal social cost (MSC) includes both the private cost and the external costs imposed on society. In the problem, the MSC is stated as double the MPC, exemplifying how ignoring externalities results in a lower perceived cost of production than the actual cost to society.

Negative Externality

This concept refers to the situation where a firm’s production or consumption results in adverse effects on third parties that are not reflected in market prices. In such cases, the private costs do not cover the total social costs, leading to overproduction relative to the socially optimal level. Here, the waste flowing into the river is an external cost impacting the broader community.

Transcript

00:01 We are revisiting the cotton industry problem shown in the last problem.

00:06 And once again, we will have to draw our supply and demand curves one point at a time to effectively show the difference between marginal social cost and marginal private cost.

00:20 So to start with our demand curve, we have a point here.

00:25 We'll move a little bit more quickly this time.

00:27 We have a point here, a point here, a point here, a point.

00:31 Here, a point here and a point here, giving a demand curve that takes this shape.

00:42 And in our supply curve, we have a point here, here, here, and here.

00:51 So the supply curve takes this shape.

00:57 And once again, our marginal private cost is given by the supply curve.

01:03 But we are told that our marginal social is double the marginal private cost, which will double the price values at each of these points.

01:14 So here from 25 to 50, and then up to 75, from here 50, up to 100, and up to 125, giving a much steeper marginal social cost curve.

01:36 This is where the supply curve would be if we were operating at what society as a whole wants.

01:46 So let's say the government wants to impose a tax in order to bring the marginal private cost in line with the marginal social cost.

01:55 In other words, to make it so the producers actually make the socially optimal amount.

02:01 Well, the government would have to know that this 300 is the socially optimal amount...

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