For the last several years, production, demand and prices have been stable. Last
ID: 1167605 • Letter: F
Question
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 agriculturespeak 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
Explanation / Answer
We have quanity demanded of potatoes, Q = 450 million cwt
price of potatoes, P = $8MM per million cwt
and price elasticity , E = 0.8
(a) General form of linear demand function is as follows:
q = mp + b where q is quantity demanded, p is price, m is change in q with change in p and b gives the demand if the items were given away which is intercept of q.
thus, in the given case demand function would be as:
450 = m(8) + b
and m = -0.8 because elasticity show responsiveness of quantity demanded with change in price.
so, 450 = -0.8(8) + b
b = 456.4
thus intercept is 456.4
(b) We have demand function as q = -0.8P + 456.4
and supply function as q = 56P
equating the above two functions we get equilibrium as
-0.8P + 456.4 = 56P
P = $8.03.