Help with Supply and Demand Function equilibrium, restrictions

• Jun 12th 2010, 09:49 AM
ihatemath09
Help with Supply and Demand Function equilibrium, restrictions

Consider the following market demand and supply functions:

D(p)= {30-2p p> or = 10
{50-ap p< 10

S(p)= -10+3p

a)If a = 2, find the excess demand function z(p). Find equilibrium price and quantity for this market. Or, explain why you cannot find them. What would one observe in this market?

b) What restriction must we impose on parameter a to ensure that a positive equilibrium price exists? Find the equilibrium price and quantity.

c) Suppose the intercept for supply curve S(p) could vary, so that supply curve becomes S(p) = b + 3p, and the demand curve remains at what was found in part (b). What restriction must we impose on b to ensure that equilibrium with a positive price and a positive quantity exists?
• Jun 12th 2010, 09:58 AM
SpringFan25
Since you have not asked a specific question ill assume you are stuck at step 1.

Step 1:
The excess demand function is D(p) - S(p).
The Equilibrium price is the value p for which excess demand is zero.

So, to find an equilibrium see if:

30-2p = -10 + 3p has a solution \$\displaystyle p \geq 10\$

and see if
50 - ap = -10 +3p has a solution \$\displaystyle p < 10\$