The Industry Analysts Have Long Recognized That There Is a High

The industry analysts have long recognized that there is a high degree of complementarity between automobile tires and gasoline.A recent study done by an automobile industry trade group estimated the following supply and demand functions:
Q_D^T = 5,250,000 - 12,500P^T - 750,000P^G
Q_S^T = -350,000 + 11,750P^T
Q_D^G = 80,500,000 - 30,000,000P^G - 2,500P^T
Q_S^G = 35,000,000 + 15,000,000P^G,
where O_D^T and Q_S^T refer to quantities of tires demand and supplied each month measured in sets of four,Q_D^G and Q_S^G refer to quantities of gasoline demanded and supplied each month measured in gallons,P^G is the price of gasoline per gallon,and P^T is the price per set of four tires.
a.Calculate the equilibrium price and quantity that will prevail in both the tire
and gasoline markets.(Hint: recall that Q_D must equal Q_S in each market.)
b.Assume that a recession causes the demand curve for gasoline to shift leftward as follows:
Q_D^G = 76,000,000 - 30,000,000P^G - 2,500P^T
Calculate the initial impact of this change in demand on the gasoline and tire markets.(You need calculate only one change in P and Q for each market.)
c.Discuss the changes that will occur after the initial round to move each market back to a stable equilibrium.Your answer to part (c)requires no calculations,but graphs would help convey your understanding of the process.