Suppose that the demand schedule for new custom motorcycles in the island nation of Motora is given by ๐ท๐ซ= 120 โ 0.07Q and the supply schedule of these motorcycles is given by
๐ท๐บ= 6 + 0.06Q. ๐ท๐ซ and ๐ท๐บ represent the price of new custom motorcycles in thousands of dollars, and Q is the quantity demanded per year in thousands.

(a) Calculate the market equilibrium quantity of custom motorcycles. (Hint: Equate the demand and supply functions to calculate ๐๐.) (6 points)

(b) Use the above value of ๐ to calculate the market equilibrium price ๐ . (Hint: Substitute ๐๐your ๐ either into the supply function or the demand function and solve for ๐ .)
(c) Upcoming sections will ask you to sketch a graph of the demand and supply of custom motorcycles in Motora. Calculate the price (y-axis) intercept of the demand curve.
(d) Calculate the price (y-axis) intercept of the supply (private marginal cost) curve.

(e) Using the numerical values you have calculated in (a) through (d), sketch in the space below a graph of the demand and supply of new custom motorcycles. Make sure your graph clearly shows and labels (i) exactly where the demand and supply curves intersect the y-axis and (ii) the equilibrium market price and quantity of motorcycles (ignoring for now any externalities).

Sample Solution