Akerlof Market for Lemons Adverse-Selection Cutoff Formula

Pinpoint the exact quality share q* below which high-quality sellers withdraw

In George Akerlof’s (1970) Market for Lemons, share q_plum of goods are high-quality "plums" (worth B_H to buyers and S_H to sellers, B_H > S_H) and share (1 - q_plum) are low-quality "lemons" (worth B_L to buyers and S_L to sellers, B_L > S_L), with asymmetric information preventing buyers from telling them apart before purchase and S_H > B_L. Uninformed buyers offer at most pooling expected value B_bar = q_plum * B_H + (1 - q_plum) * B_L. Whenever q_plum < q* = (S_H - B_L) / (B_H - B_L), B_bar falls below S_H, driving EVERY plum seller out of the market and collapsing the equilibrium price to B_L!

Test on a used-equipment market with B_H = 20,000 (B2), S_H = 15,000 (B3), B_L = 8,000 (B4), S_L = 6,000 (B5), and plum share q_plum = 0.50 (B6): first-best full-information trade surplus would be 0.50 * (20,000 - 15,000) + 0.50 * (8,000 - 6,000) = 3,500.00 per unit. Yet critical share is q* = (15,000 - 8,000) / (20,000 - 8,000) = 0.5833 (58.33%)! At q_plum = 0.50, pooling WTP is only 14,000 < 15,000, so plums withdraw, equilibrium price collapses to 8,000, and realized surplus per listed unit plunges to 0.50 * (8,000 - 6,000) = 1,000.00 (destroying 2,500.00 of efficient gains from trade!). Raise q_plum to 0.65 (via certified inspection warranties) and pooling price jumps to 15,800 >= 15,000, restoring full trade!

Critical Plum Share Threshold q* = (S_H - B_L) / (B_H - B_L) Formula

Validate gains from trade for each quality tier (B_H > S_H, B_L > S_L) and adverse-selection ordering (S_H > B_L).

=LET(b_hi, B2, s_hi, B3, b_lo, B4, s_lo, B5, IF(OR(s_lo < 0, b_lo <= s_lo, s_hi <= b_lo, b_hi <= s_hi), "Invalid Lemons Ordering", ROUND((s_hi - b_lo) / (b_hi - b_lo), 4)))

Adverse-Selection Equilibrium Market Price Formula

Branch on B_bar >= S_H: only when pooling expected value clears plum sellers’ reservation price S_H does the pooling price survive; otherwise plums exit and buyers rationally pay B_L.

=LET(b_hi, B2, s_hi, B3, b_lo, B4, s_lo, B5, q_pl, B6, IF(OR(s_lo < 0, b_lo <= s_lo, s_hi <= b_lo, b_hi <= s_hi, q_pl <= 0, q_pl >= 1), "Invalid Lemons Ordering", LET(b_bar, q_pl * b_hi + (1 - q_pl) * b_lo, ROUND(IF(b_bar >= s_hi, b_bar, b_lo), 2))))

Further reading

• Arte Sheets Lesson — Vickrey Second-Price and Myerson Optimal Reserve Price Formula
• Microsoft Support — IF function