Thursday, February 21, 2013

Supply & Demand | Find Market-Clearing Price & Quantity


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.





2 comments:

  1. Can a market clearing price be negative?

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