Irene’s demand for pizza is given by Q = (0.3 ??)/?? where Q is weekly quantity of pizza bought (in slices), I is weekly income, and P is the price of pizza. Using this demand function, answer the following:
(a) Is this function homogenous in I and P?
(b) Please graph this function for the case I =200.
(c) One problem in using this function to study consumer surplus is that Q never reaches zero, no matter how high P is. Hence, suppose that the function holds only for P ? 10 and that Q = 0 for P > 10. How should you graph in part b be adjusted to fit this assumption?
(d) With this demand function and (I = 200), it can be shown that the area of consumer surplus is approximately CS = 198 ? 6P ? 60 ln(P), where “ln (P)” refers to the natural logarithm of P. Please show that if P = 10, CS = 0.
(e) Suppose P = 3. How much pizza is demanded, and how much consumer surplus does Irene receive? Give an economic interpretation to this magnitude.
(f) If P were to increase to 4, how much would Irene demand and what would her?