$($Answer on the lined area to the right; clearly label your responses; $30$ points$)$ Joyce owns a gas station and monopolizes gas sales along a remote stretch of road. In February, Joyce stayed open even though she earned negative economic profits.

a$.$ Draw a correctly labeled graph for Joyce's gas station during February and show each of the following.

i$.$ The profit$-$maximizing output and price, labeled $Q_J$ and $P_J$

ii$.$ The average total cost curve, labeled ATC

iii. Deadweight loss, completely shaded

b$.$ What must have been true for Joyce to continue operating during the month of February even though she earned negative economic profit?

c$.$ Assume that fixed costs for Joyce's gas station decrease. Would Joyce's profit$-$maximizing quantity increase, decrease, or stay the same in February? Explain.

d$.$ During the month of July, demand increases so that Joyce now earns a positive economic profit. However, she realizes her profits would have been higher if she had reduced the price of gasoline.

i$.$ At the quantity sold in July, was marginal revenue greater than, equal to$,$ or less than marginal cost?

ii$.$ Would the price decrease cause quantity demanded to increase, decrease, or stay the same?

iii. Would the price decrease cause the total revenue to increase, decrease, or stay the same? Explain.