Problem Set #2 - Supply & Demand 1. Assume Ellen's demand function for a good is given by the following expression: qa (P, Ps, Pc. V) = 6 -p+2 . Ps - 2 . Pc + 100 Additionally, assume ps = 1, pc = 4, and y = 1000 (where p, is the price of a substitute good, p. is the price of a complement, and y is Ellen's disposable income). a. If the price of the good was 8 (i.e. p = 8), how much would Ellen spend on the good - that is, what would be her total expenditure? b. Continuing to assume p = 8, would Ellen's total expenditure increase or decrease if the price were to rise by 1%? (Hint: rather than trying to solve for total expenditure if the price were 1% above 8 -i.e. p = 8.08 - can you answer this question using the elasticity of demand?) c. Continue to assume p = 8. However, now Ellen's disposable income has doubled, y = 2000. Would a 1% increase in the price (p) increase or decrease Ellen's total expenditure on the good? 2. Suppose Caden's demand function for Cheerios cereal depends on the price of a box of Cheerios (which is represented by p,), Caden's level of income (which is represented by y), and the price of a gallon of milk (which is represented by p2). Given those three variables, Caden's demand function for boxes of Cheerios is given by the following expression: 4a(P1. Pz. y) = 10 - 2 . P1 + y 100 Pz a. Suppose the price of a box of Cheerios is $2 (p, = 2), the price of a gallon of milk is $1 (p2 = 1), and Caden's income in $500 (y = 500). What is the cross-price elasticity of demand for Cheerios with respect to the price of milk (i.e. if the price of milk increased by 1%, how much would Caden's quantity demanded of Cheerios change)? b. Is milk a substitute or a complement to Cheerios for Caden? How do you know? C. Continue to assume the price of a box of Cheerios is $2 (p, = 2), the price of a gallon of milk is $1 (p2 = 1), and Caden's income in $500 (y = 500). Calculate the income elasticity of demand and interpret what it means in words. d. Does Caden currently view Cheerios as a normal or inferior good? How do you know