Schrecklich and LaMerde are two justifiably obscure nineteenth century impressionist painters. The world’s total stock of paintings by Schrecklich is 100, and the world’s stock of paintings by LaMerde is 150. The two painters are regarded by connoisseurs as being very similar in style. Therefore the demand for either painter’s work depends both on its own price and the price of the other painter’s work. The demand function for Schrecklichs is DS (P) = 200−4PS−2PL, and the demand function for LaMerdes is DL (P) = 200−3PL −PS, where PS and PL are respectively the price in dollars of a Schrecklich painting and a LaMerde painting.
(a) Write down two simultaneous equations that state the equilibrium condition that the demand for each painter’s work equals supply.
(b) Solving these two equations, one finds that the equilibrium price of Schrecklichs is ______ and the equilibrium price of LaMerdes is _______.
(c) On the diagram below, draw a line that represents all combinations of prices for Schrecklichs and LaMerdes such that the supply of Schrecklichs equals the demand for Schrecklichs. Draw a second line that represents those price combinations at which the demand for LaMerdes equals the supply of LaMerdes. Label the unique price combination at which bothmarkets clear with the letter E.
(d) A fire in a bowling alley in Hamtramck, Michigan, destroyed one of the world’s largest collections of works by Schrecklich. The fire destroyed a total of 10 Schrecklichs. After the fire, the equilibrium price of Schrecklichs was_________ and the equilibrium price of LaMerdes was _______.
(e) On the diagram you drew above, use red ink to draw a line that shows the locus of price combinations at which the demand for Schrecklichs equals the supply of Schrecklichs after the fire. On your diagram, label the new equilibrium combination of prices E.