Citadel Securities, a market maker, is actively making a market in APPL

Corporation$$s stock. Consider the following scenario:

Market Quotes:

Citadel Securities is currently quoting a bid price of $$50\mathrm{.}25$ and an ask

price of $$50\mathrm{.}75$ for APPL$$s stock.

Trading Volume:

Over the past hour, Citadel Securities executed buy orders for $1,000$ shares

at an average price of $$50\mathrm{.}30$ and sell orders for $800$ shares at an average

price of $$50\mathrm{.}70.$

Transaction Costs:

Citadel Securities charges a fixed transaction fee of $$0\mathrm{.}10$ per share for

executed trades.

Answer the following questions:

$($a$)$ Calculate Citadel Securities$$ net profit or loss from the trading ac$-$

tivity in APPL$$s stock over the past hour.

$($b$)$ Explain how the bid$-$ask spread contributes to Citadel Securities$$

revenue as a market maker.

$($c$)$ Discuss the impact of transaction costs on the profitability of market$-$

making activities and strategies dealers may employ to mitigate these

costs.

Ensure your responses are clear, concise, and demonstrate an understand$-$

ing of market$-$making activities and associated financial calculations.

$$ A$.$

Total revenue from buy orders $=1,000$ shares $\backslash$times $($$$50\mathrm{.}70$ $$50\mathrm{.}30)=$

$$400$