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During $2023,$ Chester $($a married taxpayer filing a joint return$)$ had the following transactions involving capital assets:

Gain on the sale of an arrowhead collection $($acquired as an investment at different times but all pieces have been held for more than $1$ year$)$

$$6,000$

Loss on the sale of IBM Corporation stock $($purchased $11$ months ago as an investment$)$

$(3,500)$

Gain on the sale of a city lot $($acquired $5$ years ago as an investment$)$

$2,000$

a$.$ Indicate the tax treatment for each item.

Gain on the sale of an arrowhead collection

Loss on the sale of IBM Corporation stock

Gain on the sale of a city lot

Long$-$term capital gain $$

Overall, Chester has a long$-$term capital gain $$ of $$,$ of this gain is from collectibles, which are taxed at a maximum rate of

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b$.$ If Chester has taxable income $($including the property transactions$)$ of $$378,400,$ what is the income tax regarding these transactions?

He has a marginal tax rate of $32\%.$

If Chester has taxable income $($including the property transactions$)$ of $$74,125,$ what is the income tax regarding these transactions? He has a marginal tax rate of $12\%.$