The generalized demand and supply functions for good X are Qxd = 100 – 2PX + 0.0

Question

The generalized demand and supply functions for good X are Qxd = 100 – 2PX + 0.01M + 8 PY - 4Pz Qxs = 50 + 3PX – 6PI + PT Where Qxd = quantity demanded of good X Px = price of good X M = consumer income PY = price of good Y Pz= price of good Z Qxs = quantity supplied of good X Px = price of good X PI = price of input I PT = price of technology T a. h. Solve for the equilibrium price (Po) and the equilibrium quantity (Qo). b. l. Suppose that incomes increase to $2,500. Solve for the new equilibrium price (P1) and the new equilibrium quantity (Q1).

Explanation / Answer

At equilibrium,

Qxd=Qxs

Or,100 – 2PX + 0.01M + 8 PY - 4Pz = 50 + 3PX – 6PI + PT

Or,5PX=50+.01M+14PY-4PZ-PT

Or,PX=10+.002M+1.6PY-.8PZ+1.2PI-.2PT=P0

Now putting value of P0 into demand function we can get Q0

Q0=100-2(10+.002M+1.6PY-.8PZ+1.2PI-.2PT)+.01M+8PY-4Pz

=100-20-.004M-3.2PY+1.6PZ-2.4PI+.4PT+.01M+8PY-4PZ

Or,Qo=80+.006M+4.8PY-2.4PZ-2.4PI+.4PT

Putting value of M=2500 we get,Q1=80+(.006*2500)+4.8PY-2.4PZ-2.4PI+.4PT=95+4.8PY-2.4PZ-2.4PI+.4PT

P1= 10+.002M+1.6PY-.8PZ+1.2PI-.2PT

=15+1.6PY-.8PZ+1.2PI-.2PT

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