Widgets are made only in America. They are provided by a constant$-$cost industry, which is in long$-$run equilibrium. The following charts show the American demand curve for widgets, the foreign demand curve for widgets, and the marginal cost curve of a typical American widget firm:

$\backslash$table$[[$American Demand,Foreign Demand,Firm's Marginal Cost Curve$],[$Price $($$$),$Quantity,Price $($$$),$Quantity,Quantity,Marginal Cost $($$$)],[3,200,3,150,1,2],[5,160,5,140,2,5],[7,75,7,120,3,7],[9,60,9,100,4,9],[11,45,$of $11,90,5,11],[13,30,13,80,6,13],[15,15,15,70,7,15],[17,10,17,60,8,17]]$

Initially, American firms are not allowed to sell to foreigners. $($Thus$,$ the foreign demand curve is irrelevant.$)$ In the United States, the industry is in long$-$run equilibrium and widgets sell for $$7$ apiece. Now the government decides to issue $10$ export licenses; a firm with an export license can sell as many widgets to foreigners as it wants to$.$ The export licenses are sold at auction to the highest bidders.

a$.$ What is the price of an American widget sold on the foreign market?

b$.$ What is the price of an export license?

c$.$ In the short run, what is the new price of a widget sold in America? Be sure to justify your answer.

d$.$ In the long run, what is the new price of a widget sold in America?

$($Hint: A firm that can sell as much as it wants to foreigners at a high price will not choose to sell anything at all to Americans at a low price.$)$