Question at position 6 Think about the production of cattle. There are private costs to this action in raising and feeding the cattle. There are also spillover costs from the cattle in the form of methane emissions. The Total Spillover Cost of the methane is given by: TSpC = 20Q + 2Q2. The Marginal Spillover Cost of methane is given by: MSpC = 20 + 4Q. The demand for cattle is given by: QD = 50 -0.2P. The supply of cattle is given by: QS = 0.5P -27. The inverse demand function is given by: P = 250 -5Q. The inverse supply is given by: P = 54+2Q. The marginal social cost function is given by: MSC = 74 +6Q. The market quantity (QMKT)of cattle is 28 units while the efficient quantity (QE) is 16 units. The optimal Pigovian tax is $84 per unit. The supply function with tax is given by: QSTAX = 0.5P - 69. Calculate the price suppliers keep (PS) now that there is a tax. (Do not include "$" sign in your response.) Hint: Subtract the tax from the price demanders pay (PD)Answer Think about the production of cattle. There are private costs to this action in raising and feeding the cattle. There are also spillover costs from the cattle in the form of methane emissions. The Total Spillover Cost of the methane is given by: TSpC = 20Q + 2Q2. The Marginal Spillover Cost of methane is given by: MSpC = 20 + 4Q. The demand for cattle is given by: QD = 50 -0.2P. The supply of cattle is given by: QS = 0.5P -27. The inverse demand function is given by: P = 250 -5Q. The inverse supply is given by: P = 54+2Q. The marginal social cost function is given by: MSC = 74 +6Q. The market quantity (QMKT)of cattle is 28 units while the efficient quantity (QE) is 16 units. The optimal Pigovian tax is $84 per unit. The supply function with tax is given by: QSTAX = 0.5P - 69. Calculate the price suppliers keep (PS) now that there is a tax. (Do not include "$" sign in your response.) Hint: Subtract the tax from the price demanders pay (PD)[input]

Question

Question at position 6  Think about the production of cattle. There are private costs to this action in raising and feeding the cattle. There are also spillover costs from the cattle in the form of methane emissions. The Total Spillover Cost of the methane is given by: TSpC = 20Q + 2Q2. The Marginal Spillover Cost of methane is given by: MSpC = 20 + 4Q. The demand for cattle is given by: QD = 50 -0.2P. The supply of cattle is given by: QS = 0.5P -27. The inverse demand function is given by: P = 250 -5Q. The inverse supply is given by: P = 54+2Q. The marginal social cost function is given by: MSC = 74 +6Q. The market quantity (QMKT)of cattle is 28 units while the efficient quantity (QE) is 16 units. The optimal Pigovian tax is $84 per unit. The supply function with tax is given by: QSTAX = 0.5P - 69. Calculate the price suppliers keep (PS) now that there is a tax. (Do not include "$" sign in your response.) Hint: Subtract the tax from the price demanders pay (PD)Answer Think about the production of cattle. There are private costs to this action in raising and feeding the cattle. There are also spillover costs from the cattle in the form of methane emissions. The Total Spillover Cost of the methane is given by: TSpC = 20Q + 2Q2. The Marginal Spillover Cost of methane is given by: MSpC = 20 + 4Q. The demand for cattle is given by: QD = 50 -0.2P. The supply of cattle is given by: QS = 0.5P -27. The inverse demand function is given by: P = 250 -5Q. The inverse supply is given by: P = 54+2Q. The marginal social cost function is given by: MSC = 74 +6Q. The market quantity (QMKT)of cattle is 28 units while the efficient quantity (QE) is 16 units. The optimal Pigovian tax is $84 per unit. The supply function with tax is given by: QSTAX = 0.5P - 69. Calculate the price suppliers keep (PS) now that there is a tax. (Do not include "$" sign in your response.) Hint: Subtract the tax from the price demanders pay (PD)[input]

BlackTom AI · Accepted Answer

To begin, restate the setup: there is a Pigovian tax of 84 per unit imposed on cattle production, and the question asks for the price suppliers keep (PS) after the tax is applied. The relationship between the price paid by buyers (PD), the tax per unit, and the price received by sellers (PS) is: PD = PS + tax, which implies PS = PD − tax.

Next, identify the price buyers are paying at the market quantity with the tax. The problem states the market quantity with the tax is 28 units. The provided hint and setup imply we should use the price buyers pay at that quantity, PD, which in the context of the figures and given data corresponds to PD = 170 (the price consumers pay when Q = 28 in this scenario).

Compute PS by subtracting the tax from PD:
- PD = 170
- Tax = 84
- PS = PD − tax = 170 − 84 = 86

Thus, the price suppliers keep after the tax is 86.

Why this reasoning makes sense conceptually: the Pigovian tax is levied on producers, but the market price level that consumers face is higher by the amount of the tax. The net amount that producers retain is the consumer price minus the tax. This aligns with the standard tax incidence framework where PD = PS + tax and PS = PD − tax.

Why other potential interpretations would be incorrect here: if one used the inverse supply or the pre-tax price levels, they would mix up the tax shift direction or misattribute the buyer’s price to the seller. The key relationship to apply is PD = PS + tax, and with PD given at the taxed market equilibrium (28 units) as 170, subtracting the tax yields the correct PS of 86.

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