This question requires you to solve a supply-and-demand model algebraically. Letting p be the price of the product, suppose the demand and supply functions for some product are given by
QD= 100 - 3p
QS =10 + 2p
a. Plot both the demand curve and the supply curve.
b. What is the condition for equilibrium in this market?
c. By imposing the condition for equilibrium, solve for the equilibrium price.
d. Substitute the equilibrium price into either the demand or the supply function to solve for the equilibrium quantity. Check to make sure you get the same answer whether you use the demand function or the supply function.
e. Now suppose there is an increase in demand so that the new demand function is given by
QD = 180-3p
Compute the new equilibrium price and quantity. Is your result consistent with the "law" of demand?
f. Now suppose that with the new demand curve in place, there is an increase in supply so that the ne supply function is given by Qs= 90 + 2p. Compute the new equilibrium price and quantity. Is your result consistent with the "law" of supply?