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 +2Pl (1) Qs = 50P-200 (2) where is the price of a 16oz bottle of syrup, is the price for a bottle of maple flavored corn syrup, and Qd and Qs 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 ) 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 Pl = 10, graph (inverse) supply and (inverse) demand for the marketwith a clearly labeled graph andcalculatetheequilibrium price (P*) and quantity (Q*) forthemarket. 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 numericalresult (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 (Pl = 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?