The demand curve for Widgets is given by
QD = 5800 - 200p + 30pG
where QD is the quantity of widgets demanded, y is the per capita income and pG is the price of Gizmos. The supply of Widgets is given by:
QS = 250p - 1250
a. Solve for the equilibrium price and quantity of widgets in terms of the price of Gizmos.
b. Compute the comparative static derivatives for the changes in the equilibrium price and quantity of Widgets with respect to a change in the price of Gizmos.
a. Set quantity demand equal to quantity supply to find price:
5800 - 200p + 30pG = 250p - 1250
Solving, p* = (6050 + 30pG)/450
Substitute into demand or supply to find quantity:
Q*= 250(6050 + 30pG)/450 - 1250
b. dQ*/dpG = 15/9 and dp*/dpG = 1/15
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