Question $2)(6$ points$)$ Consider the High West question from the notes. Recall the price of each bottle was p$($y$)=45$ y$/10000$ and the cost of producing y bottles of whiskey is C$($y$)=2000+($y$/100)2.$

Now suppose that the government taxes High West at $$4$ per bottle of whiskey. Re$-$write High West$$s profit function, tax$($y$),$ to account for the taxes they pay.

If the tax is accounted for as a cost, what is High West$$s new marginal cost?

What is High West$$s new profit maximizing quantity of whiskey? Is it higher or lower than the pre$-$tax

quantity, why might this be the case?