Suppose the demand curve for a product is given by Q = 300 - 2P + 4I, where I is average income measured in thousands of dollars.
The supply curve is Q = 3P - 50.
a. If I = 25, find the market-clearing price and quantity for the
product.
b. If I = 50, find the market-clearing price and quantity for the
product.
c. Draw a
graph to illustrate your answers.
ANSWER
a. If I = 25, find the market-clearing price and quantity for the
product.
Given I = 25, the demand curve
becomes Q = 300 − 2P + 4(25), or Q = 400 − 2P. Set demand
equal to supply and solve for P and then Q:
400 - 2P = 3P - 50
P = 90
Q = 400 - 2(90) = 220
b. If I = 50, find the market-clearing price and quantity for the
product.
Given I = 50, the demand curve
becomes Q = 300 - 2P + 4(50), or Q = 500 - 2P. Setting demand equal to
supply, solve for P and then Q:
500 - 2P = 3P - 50
P = 110
Q = 500 - 2(110) = 280
c. Draw a
graph to illustrate your answers.
It is easier to draw the
demand and supply curves if you first solve for the inverse demand and supply
functions, i.e., solve the functions for P. Demand in part a is P = 200 -
0.5Q
and supply is P = 16.67 + 0.333Q. These are shown on the graph as Da and S. Equilibrium
price and quantity are found at the intersection of these demand and supply
curves. When the income level increases in part b, the demand curve shifts up
and to the right. Inverse demand is P = 250 - 0.5Q
and is labeled Db. The intersection of the new demand curve and original supply
curve is the new equilibrium point.
