Question

PROBLEM #5 Based on an extensive marketing study, a cereal manufacturer determines the demand and supply of cereal to be as follows: Qd=86 - 3P + 10PF – 25PM + 2Y Qs=15P - 5PW In these equations, P represents the price of a box of cereal; PF is the price of a pound of fruit; PM is the price of a gallon of milk; Y is the average hourly wage of consumers in this market; and PW is the price of wheat required per box of cereal. Briefly explain how the demand equation demonstrates that cereal and fruit are substitutes in this market. Suppose the price of fruit is $2 per pound; the price of a gallon of milk is $3; the average hourly wage is $17; and the price of wheat per box is $2. Find the equilibrium quantity and price of cereal boxes. Now consider the more general relationship between the price of cereal and the price of milk. Suppose the average hourly wage is still $17, the price of a pound of fruit is still $2, and the price of wheat is still $2 per box of cereal, but that the price of a gallon of milk (PM) is variable. Find an expression for the equilibrium price of a box of cereal as a function of the price of a gallon of milk. Confirm that your general equation is correct by verifying the price you found for a box of cereal when the price of a gallon of milk was $3. (You may find small differences in your comparison due to rounding.)

Answer 1