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 e. Is good X a normal good or an inferior good? How do you know? f. What is the demand function when M = $2,000, PY = $10 and PZ = $5? g. What is the supply function when PI = $10 and PT = $20? h. Solve for the equilibrium price (Po) and the equilibrium quantity (Qo).

Explanation / Answer

e. Good X is a normal good. This is because if tou see the sign before the Px, which is negative, so if we consider other things be constant, so a change in price of good X has a negative effect on quantity demanded.

That means if price of X increases then quantity demanded will fall and vice varsa.

f. Demand function will be

Qxd = 100 - 2Px + 0.01 * 2000 + 8 * 10 - 4 * 5

Qxd = 180 - 2Px

g. Supply function will be

Qxs = 50 + 3PX - 6 * 10 + 20

Qxs = 10 + 3Px

h. Now the equilibrium price and quantity will be calculated by equating demand function and supply function

Qxd = Qxs

180 - 2Px = 10 + 3Px

5Px = 170

Px = $32

and

Qx = 180 - 2 * 32 = 116.

So, equilibrium price (Po) = $32 and quantity(Qo) = 116 units.

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