1. Congratulations, you've been hired as a market analyst for the Federation of Quebec Maple Syrup Producers (QMSP) and you will be responsible for monitoring the market for maple syrup. The market can be described by the following calibrated demand and supply functions: (1) (2) Qd = 1180-20P +2P, Q, = 50P-200 where P is the price of a 16oz bottle of syrup, Pį is the price for a bottle of maple flavored corn syrup, and Qd and Q, are the quantity demanded and the quantity supplied of maple syrup. (a) How much maple syrup should the QMSP be prepared to give away if they decided to give maple syrup to everyone who wants it free of charge as a marketing ploy? (Hint: your answer will depend on Pt) Find the inverse demand and inverse supply equations. Determine the highest price at which suppliers would not be willing to sell any syrup. (b) Assuming that P, = 10, graph (inverse) supply and (inverse) demand for the market with a clearly labeled graph and calculate the equilibrium price (P*) and quantity (Q*) for the market. Be sure to find and graph the points where the curves intersect the axes. (c) Using calculus, find an expression for the impact of a small price change of maple flavored corn syrup on the quantity demand of maple syrup (note: we are asking only about a characterization of demand, not a change in the equilibrium). Provide a brief interpretation of your numerical result (no more than two sentences).
1. Congratulations, you've been hired as a market analyst for the Federation of Quebec Maple Syrup Producers (QMSP) and you will be responsible for monitoring the market for maple syrup. The market can be described by the following calibrated demand and supply functions: (1) (2) Qd = 1180-20P +2P, Q, = 50P-200 where P is the price of a 16oz bottle of syrup, Pį is the price for a bottle of maple flavored corn syrup, and Qd and Q, are the quantity demanded and the quantity supplied of maple syrup. (a) How much maple syrup should the QMSP be prepared to give away if they decided to give maple syrup to everyone who wants it free of charge as a marketing ploy? (Hint: your answer will depend on Pt) Find the inverse demand and inverse supply equations. Determine the highest price at which suppliers would not be willing to sell any syrup. (b) Assuming that P, = 10, graph (inverse) supply and (inverse) demand for the market with a clearly labeled graph and calculate the equilibrium price (P*) and quantity (Q*) for the market. Be sure to find and graph the points where the curves intersect the axes. (c) Using calculus, find an expression for the impact of a small price change of maple flavored corn syrup on the quantity demand of maple syrup (note: we are asking only about a characterization of demand, not a change in the equilibrium). Provide a brief interpretation of your numerical result (no more than two sentences).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Parts B and C
Transcribed Image Text:1. Congratulations, you've been hired as a market analyst for the Federation of Quebec Maple Syrup
Producers (QMSP) and you will be responsible for monitoring the market for maple syrup. The market can
be described by the following calibrated demand and supply functions:
Qd = 1180-20P +2P,
(1)
(2)
Qs = 50P-200
where P is the price of a 16oz bottle of syrup, Pį is the price for a bottle of maple flavored corn syrup, and Qd
and Q, are the quantity demanded and the quantity supplied of maple syrup.
(a) How much maple syrup should the QMSP be prepared to give away if they decided to give maple syrup to
everyone who wants it free of charge as a marketing ploy? (Hint: your answer will depend on Pt) Find the
inverse demand and inverse supply equations. Determine the highest price at which suppliers would not be
willing to sell any syrup.
(b) Assuming that P, = 10, graph (inverse) supply and (inverse) demand for the market with a clearly labeled graph
and calculate the equilibrium price (P*) and quantity (Q*) for the market. Be sure to find and graph the points
where the curves intersect the axes.
(c) Using calculus, find an expression for the impact of a small price change of maple flavored corn syrup on the
quantity demand of maple syrup (note: we are asking only about a characterization of demand, not a change
in the equilibrium). Provide a brief interpretation of your numerical result (no more than two sentences).
(d) Now suppose that corn syrup becomes more expensive due to a corn blight and makes the price of maple
flavored corn syrup rise (Pi = 45). Maple syrup producers are ecstatic, thinking this will allow them to
significantly raise the price of their own syrup. Calculate the new equilibrium price (P**) and quantity (Q**)
for maple syrup. Illustrate the changes on your graph from part (a). Are the maple syrup producers right?
%3D
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