Alex consumes pizza and burgers. His utility function isu(P,B) =PBwhere P is the number of pizzas and B is the number of burgers. Alex has $90 to spend, and he plans to spend it all on pizza and burgers. The price of one pizza is $30 and the price of one burger is $9.

1. (a)Find and label Alex's initial optimal bundle on a graph where pizza is on the x-axis and burgers are on the y-axis. Label this point A.
2. (b)Suppose that the local burger restaurant is running a promotion selling burgers at $2 a burger. Solve for Alex's new optimal bundle. Label this bundle B on your graph from part (a).
3. (c)Find the substitution effect, income effect ,and the total effect for both goods following the decrease in the price of burgers from $9 to $8. Label the intermediate bundle used to find the substitution and income effects point C on your graph from part (a).
4. (d)Are pizza and burgers normal or inferior goods? Explain your answer.