Which of the following is TRUE when there is the socially optimal amount of a private good with no externality?

Question

BlackTom AI · Accepted Answer

To evaluate which statement is true under the condition of a socially optimal quantity of a private good with no externality, we need to compare the relevant welfare conditions and what they imply about costs and benefits.
Option 1: 'Private benefits equal private costs.' This would be a condition for a specific market equilibrium if private marginal benefit (PMB) equaled private marginal cost (PMC). However, at the socially optimal quantity in the absence of externalities, the criterion is that social marginal benefit (SMB) equals social marginal cost (SMC), not merely private measures. Therefore, this statement is not the defining condition for social optimality when externalities are absent.
Option 2: 'Social marginal benefit equals private marginal cost.' This mixes concepts: the condition for social optimum is SMB = SMC. If there are no externalities, SMB equals private marginal benefit (PMB) and SMC equals PMC, but the precise requirement is SMB = SMC, which aligns with PMB = PMC only if SMB = PMB and SMC = PMC. In a no-externality setting, private and social marginal measures coincide, so SMB = SMC effectively corresponds to PMB = PMC. This option captures the core idea that welfare-maximizing quantity occurs where the benefit to society equals the cost to society, making it the true statement under the stated conditions.
Option 3: 'Consumer surplus equals producer surplus.' This equality is a property of certain market outcomes (often in a perfectly competitive equilibrium with identical margins on price), but it is not a defining condition for social optimality or for the presence of no externalities. It reflects distributional aspects rather than the efficiency condition SMB = SMC.
Option 4: 'Social marginal benefit exceeds social marginal cost.' When SMB > SMC, there would be additional welfare gains from increasing quantity, implying the current quantity is not socially optimal. Therefore, this statement contradicts the definition of the socially optimal point where SMB = SMC (assuming no externalities).
In summary, the key idea is that, without externalities, the social optimum is achieved where the society’s marginal benefit equals society’s marginal cost, and since private and social measures align in this case, the condition effectively reduces to the equality of SMB and SMC rather than a strict inequality.

AS.440.661.50.SP25 Module 5 Problem Set

Which of the following is TRUE when there is the socially optimal amount of a private good with no externality?

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