The following table describes the limit order book for XYZ's opening call auction: [table]
Price | Buy Quantity | Sell Quantity $8.08 | 0 | 1600 $8.01 | 500 | 1700 $7.99 | 400 | 1300 $7.97 | 2000 | 0 $7.91 | 0 | 200 $7.87 | 1100 | 700 $7.84 | 1900 | 0 $7.82 | 800 | 0
[/table] What is the call price if there is no more orders entered?[Fill in the blank]

Question

BlackTom AI · Accepted Answer

The clearing rule selects the highest price at which cumulative buy quantity ≥ cumulative sell quantity, so we compute cumulative buys at or above each candidate price and cumulative sells at or below that price and find the highest price satisfying buy ≥ sell.

1) Relevant concepts
- In a call auction the clearing price is the price that maximizes matched volume. A commonly used tie-breaking rule (and the textbook rule used here) is to pick the highest price P for which cumulative buy quantity at prices ≥ P is at least the cumulative sell quantity at prices ≤ P. Mathematically: find highest P with Q_buy(≥P) ≥ Q_sell(≤P).

2) Reasoning and step-by-step calculation
Compute Q_buy(≥P) and Q_sell(≤P) at each price level (only levels with orders shown):

- P = $8.08:
  Q_buy(≥8.08) = 0
  Q_sell(≤8.08) = 1600+1700+1300+0+200+700 = 5500
  Matched = min(0,5500) = 0 (buy < sell)

- P = $8.01:
  Q_buy(≥8.01) = 500
  Q_sell(≤8.01) = 1700+1300+0+200+700 = 3900
  Matched = 500 (buy < sell)

- P = $7.99:
  Q_buy(≥7.99) = 500+400 = 900
  Q_sell(≤7.99) = 1300+0+200+700 = 2200
  Matched = 900 (buy < sell)

- P = $7.97:
  Q_buy(≥7.97) = 500+400+2000 = 2900
  Q_sell(≤7.97) = 0+200+700 = 900
  Matched = 900 (buy ≥ sell)

- P = $7.91:
  Q_buy(≥7.91) = 500+400+2000+0 = 2900
  Q_sell(≤7.91) = 200+700 = 900
  Matched = 900 (buy ≥ sell)

- P = $7.87:
  Q_buy(≥7.87) = previous 2900 + 1100 = 4000
  Q_sell(≤7.87) = 700
  Matched = 700

(Prices below yield zero sells so matched goes to 0 or remains smaller.)

3) Intermediate steps shown above
- Key intermediate sums: at $7.99 buys = 900, sells = 2200; at $7.97 buys = 2900, sells = 900.

4) Why the correct answer is correct
- We look for the highest price P with Q_buy(≥P) ≥ Q_sell(≤P). At $7.99 buy < sell, but at the next lower level $7.97 buy ≥ sell (2900 ≥ 900). Therefore $7.97 is the highest price where cumulative buy ≥ cumulative sell and is chosen as the clearing (call) price. This price also yields the maximum executable quantity (900) consistent with the auction rule.

5) Why other options are incorrect
- $8.01 and $8.08 produce fewer matches (500 and 0 respectively) because buy side is too small there.
- $7.99, $7.91 (and $7.97) each yield 900 matched, but $7.99 fails the buy ≥ sell test (900 < 2200), and $7.91 is lower than the highest price satisfying buy ≥ sell. $7.87 yields only 700 matched.
- “Cannot be determined” is incorrect because cumulative sums are sufficient to identify the clearing price via the stated rule.

6) Conclusion
Applying the highest-price-with-Q_buy≥Q_sell rule yields the call price $7.97, which matches the provided correct answer.

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