Which of the following is true in the inelastic region of a monopolist’s demand curve as output increases?

Question

BlackTom AI · Accepted Answer

MR = dTR/dQ = P(1 + 1/ε), so the sign of marginal revenue is determined by the price elasticity of demand ε. 1) Relevant knowledge points and concepts - Total revenue (TR) = P(Q) × Q. Marginal revenue (MR) = dTR/dQ = P + Q(dP/dQ). - Price elasticity of demand ε = (dQ/dP) × (P/Q). For a normal downward-sloping demand curve ε < 0. The “inelastic” region means |ε| < 1 (so −1 < ε < 0). - Relationship MR and elasticity: rearrange MR = P + Q dP/dQ into MR = P[1 + (Q/P)dP/dQ]. Using ε, (Q/P)dP/dQ = 1/ε, so MR = P(1 + 1/ε). - MR is the slope of TR with respect to Q (dTR/dQ); if MR < 0, TR falls as Q increases. 2) Step-by-step reasoning - In the inelastic region ε is negative and satisfies −1 < ε < 0. - Compute 1/ε: because ε is between −1 and 0, 1/ε is negative and has magnitude greater than 1; thus 1/ε < −1. - Then 1 + 1/ε < 0, so MR = P(1 + 1/ε) < 0 (price P > 0). - Since MR = dTR/dQ and MR < 0, increasing output (raising Q) reduces total revenue (TR decreases). 3) Intermediate calculation example - Take a small numeric illustration: suppose a 1% decrease in price raises quantity by 0.5% (inelastic: |ε| = 0.5). Revenue change ≈ %ΔTR = %ΔP + %ΔQ = −1% + 0.5% = −0.5% → TR falls. MR corresponding to that small change is negative. 4) Why the correct answer is correct - The algebraic MR formula and the sign of ε in the inelastic region directly imply MR < 0. Because MR is the derivative of TR, a negative MR means TR decreases as Q increases. This exactly matches “Marginal revenue is negative and total revenue is decreasing.” 5) Why other options are incorrect (brief) - “Marginal revenue is increasing and total revenue is positive.” MR is not necessarily increasing; in inelastic region MR is negative, not “increasing.” TR may be positive but is decreasing as output rises. - “Marginal revenue is decreasing and total revenue is negative.” TR is not forced to be negative; TR = P×Q is typically positive. The key is TR decreases, not that its level is negative. - “Marginal revenue and total revenue are negative.” MR is negative, but TR (a level) need not be negative—TR falls but often remains positive. - “Marginal revenue is positive and total revenue is increasing.” That describes the elastic region (|ε| > 1), not the inelastic region, so it is incorrect here. 6) Conclusion Because in the inelastic region (−1 < ε < 0) MR = P(1 + 1/ε) < 0, marginal revenue is negative and total revenue decreases as output increases. This confirms the correct answer: “Marginal revenue is negative and total revenue is decreasing.”

Which of the following is true in the inelastic region of a monopolist’s demand curve as output increases?单项选择题

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