Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

تمرين 28

Irene's demand for pizza is given by:
where Q is the 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 homogeneous in I and P?
b. 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 your 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. 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 consumer surplus be? Give an economic interpretation to why the value of CS has fallen.