Answer to Question #59245 in Microeconomics for Bob

Question

4. Given the following demand and supply functions:
QDX = 1600 - 3PX + 0.4PY - 0.3PZ + 0.003I
QSX = 500 + 15PX - 2W - 0.3R
Where: PY = $160; PZ = $55; I = $4850; W = $11; R=$145

a) What is the equilibrium price?
b) What is the equilibrium quantity?
c) Calculate the point price elasticity of demand, at the equilibrium values (using the equilibrium price and equilibrium quantity in part (a). Show your calculation.
d) Find the point income elasticity of demand. Interpret your result.

Answer 1

4. QDX = 1600 - 3PX + 0.4PY - 0.3PZ + 0.003I,
QSX = 500 + 15PX - 2W - 0.3R,
Where: PY = $160; PZ = $55; I = $4850; W = $11; R=$145
a) In equilibrium QDX = QSX, so:
1600 - 3PX + 0.4PY - 0.3PZ + 0.003I = 500 + 15PX - 2W - 0.3R,
1600 - 3PX + 0.4*160 - 0.3*55 + 0.003*4850 = 500 + 15PX - 2*11 - 0.3*145,
18PX = 1600 + 64 - 16.5 + 0.003*4850 - 500 + 22 + 43.5
PXe = 1227.55/18 = $68.2 - equilibrium price.
b) The equilibrium quantity is QXe = 500 + 15*68.2 - 2*11 - 0.3*145 = 1457.5.
c) The point price elasticity of demand, at the equilibrium values is Ed = Qd'*PXe/QXe = -3*68.2/1457.5 = -0.14, so the demand is inelastic.
d) The point income elasticity of demand, at the equilibrium values is Ed = Qd'*I/QXe = 0.003*4850/1457.5 = 0.01, so it is a necessity good.