On October $29,2024,$ the Wall Street Journal published an article titled $$Logging Is a Way of Life in Appalachia. It$$s Hanging on by a Thread.$$Links to an external site. The article reported on the state of independent loggers$,$ who cut down hardwood trees and sell the logs to

domestic or foreign sawmills to be cut into lumber for construction. According to the article:

$$Appalachia$$s hardwood industry comprising loggers$,$ sawmills, truckers and manufacturers is struggling to survive.

The industry, a fixture of the regional economy, has been in decline for decades. A series of shocks since $2018$ has accelerated the decline: a trade war with China, a collapse in exports due to Covid, China$$s real$-$estate slump, and falling U$.$S$.$ home building.

Roughly two dozen sawmills in the region have gone out of business in the past year or so$,$ auctioning off their machinery, said Tom Inman, president of trade association Appalachian Hardwood Manufacturers.$$

$($You do not need to read the article in order to answer these questions. We will provide you with all relevant information in question directions$).$

Please do not make any additional assumptions other than what is already described in the question settings. Keep in mind that the suppliers are the independent loggers and the demanders are the sawmills.

Consider the market for logs in $2017,$ prior to the series of shocks described above. Assume the $2017$ market is in a long$-$run equilibrium $($LRE$).$ Furthermore, assume that the market is perfectly competitive and all the firms are identical.

Using our side$-$by$-$side graph methodology $($with market on the left and individual firm on the right$),$ graphically depict:

the market equilibrium price, P$0,$ and quantity, Q$0,$

the optimal output of an individual firm representative of the other firms in the industry at this LRE $($labeled as q$0),$ and

the individual firm$$s economic profit $0,$ if any $($Shade and clearly label the area representing positive or negative profits. If the profit is zero, it is not necessary to graphically depict it $$ instead, write $$$0=0$ on your graph$).$

Please include any curves necessary to identify these values. Be sure to label all relevant points, price and quantity axes, the supply and demand curves, the representative firm$$s marginal revenue, and the cost curves.$$Please use the subscript of $0($zero$)$ in labeling your curves and points $($for example, supply should be labeled as S$0).$ Note that you will reuse this graph as the basis of your graphical analysis in Questions $4$ and $6$ in this exam.