For the last several years, production, demand and prices have been stable. Last year the quantity of potatoes transacted in the United States was 450 million cwt (cwt is agriculture speak for 100 pounds), and prices were $8MM per million cwt. Econometric estimates have determined that, at this level, the own-price point elasticity of demand is 0.8.
a. Assume that demand is linear. Derive the slope and intercept of QD(P), a linear demand function.
b. A marketing campaign touting the health benefits of rice has produced a recent forecast that the demand for potatoes will fall over the next year by 20 percent. If this report is accurate, what would the new equilibrium price for potatoes be? Use the linear demand function derived above, and assume that the supply curve is given by QS(P) = 56P