Use the graph provided below to answer parts $($a$)-($e$).$

BigMed, a profit$-$maximizing firm, has a patent on a medical device, making it the only producer of that device. The graph above shows BigMed's demand, marginal revenue, average total cost, average variable cost, and marginal cost curves.

$($a$)$ Calculate BigMed's total revenue if the firm produces the allocatively efficient quantity. Show your work.

$($b$)$ Starting at a price of $$100,$ if BigMed were to increase the price by $2\%,$ will the quantity demanded decrease by more than $2\%,$ by less than $2\%,$ or by exactly $2\%?$ Explain.

$($c$)$ At a quantity of $10$ units, is BigMed's marginal product increasing, decreasing, or constant? Explain.

$($d$)$ Identify the quantity that maximizes BigMed's profit. Explain.

$($e$)$ At the quantity identified in part $($d$),$ does BigMed earn a positive economic profit, a negative economic profit, or zero economic profit? Explain.

Assume that BigMed's patent expires. Tauem, a company with the capability to produce the same medical device as BigMed, intends to enter the market and charge a lower price than BigMed for the medical device. BigMed is considering whether to maintain its price or to lower its price to match Tauem's price. Tauem is considering whether to advertise its entry into the market.

The matrix below shows the payoffs for each combination of strategies, and both players $($BigMed and Tauern$)$ have complete information. The first entry in each cell represents BigMed's payoff and the second entry represents Tauem's payoff. Each player independently and simultaneously chooses its strategy. Use the matrix provided below to answer parts $(f-($h$).$