Worldwide quarterly sales of a brand of cell phones was approximately

q = −p + 176 million phones when the wholesale price was $p.
(a) If the cellphone company was prepared to supply q = 9p − 344 million phones per quarter at a wholesale price of $p, what would be the equilibrium price? $52

(b) The actual wholesale price was $47 in the fourth quarter of 2004. Estimate the projected shortage or surplus at that price.
Shortage.
I can't find the exact amount of shortage, I don't know how.

Thank You

To determine the projected shortage or surplus at a given price, you need to compare the quantity demanded with the quantity supplied.

In this case, the demand equation for the brand of cell phones is q = -p + 176 million phones, and the supply equation is q = 9p - 344 million phones.

For part (b), we are given that the wholesale price is $47. We can substitute this value into the supply equation to find the quantity supplied:
q = 9(47) - 344
q = 423 - 344
q = 79 million phones

To find the projected shortage or surplus, we need to compare this quantity supplied with the quantity demanded. We can substitute the wholesale price of $47 into the demand equation:
q = -(47) + 176
q = 129 million phones

Comparing the quantity supplied (79 million phones) with the quantity demanded (129 million phones), we can see that there is a shortage of 50 million phones (129 - 79).

Therefore, the projected shortage at a wholesale price of $47 in the fourth quarter of 2004 would be 50 million phones.