Quarterly demand and supply for the Petram Company is given by Qd = 1000 + 0.5M + 0.25A – 100P and Qs = -750 + 100P, where Q is quantity per quarter, P is price, M is income, and A is advertising expenditure. Suppose that A = 1000 and M =20,000, and answer the following questions.
A. What is the equilibrium price and quantity?
B. What is the inverse demand?
Answer
Qd = 1000 + 0.5M + 0.25A – 100P
using the value of M and A
Qd = 1000 + 0.5*20000 + 0.25*1000 – 100P
Qd=11250-100P
Qs=-750+100P
A) the equilibrium is at Qd=Qs
equating both
11250-100P=-750+100P
200P=12000
P=60
Q=11250-100*60
=5250
the equilibrium price is $60 and quantity is 5250 units
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B) inverse demand is
Q=11250-100P
Q+100P=11250
100P=11250-Q
P=112.5-0.01Q ........... the inverse demand curve
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