Joel gets utility from board games (B) and earbuds (E). His utility function is U(B,E) = BE + B. The price of board games (B) is PB, and the price of...

Joel gets utility from board games (B) and earbuds (E).  His utility function is U(B,E) = BE + B.  The price of board games (B) is PB, and the price of earbuds (PE) is equal to $40. Joel’s income is $200.

(a)  Using the Lagrangian method derive Joel’s demand function for board games (B) as a function of PB. (b)  Suppose that Joel’s income doubles to $400.  Derive Joel’s new demand function for board games (B)as a function of PB. (c)  Are board games a normal or inferior good? why?