Answer to Question #242428 in Microeconomics for Mendie

Question

Consider the following, showing price and quantity data for goods T and Z at four different points (A, B, C, &D)

GOOD T
Point Price(N). Quantity( kilos)
A: 5 200
B: 8 180
C: 9 150
D. 11 100

GOOD Z
Point: Price(N). Quantity(kilos)
A: 8 300
B: 10 200
C: 13 150
D: 15 120

Calculate
a. Estimate the arc cross-price elasticity of demand for commodity T with respect to changes in the price of commodity between:
I. Points A to B
II. Points C to D

b. Discuss your results in (I) and (II) of question (a) with respect to the relationship between each pair of goods

c. Calculate (the arc) own price elasticity of demand for commodity Z between points C and D

Answer 1

a. The arc cross-price elasticity of demand for commodity T with respect to changes in the price of commodity Z between:

I. Points A to B is:

$Ecp = \frac{180-200} {10-8} ×\frac{10+8} {180+200} = -0.474.$

II. Points C to D

$Ecp = \frac{100-150} {15-13} ×\frac{15+13} {100+150} = -2.8.$

b. So, the goods are complements.

c. The arc own price elasticity of demand for commodity Z between points C and D is:

$Ecp = \frac{120-150} {15-13} ×\frac{15+13} {120+150} = -1.56.$

So, the demand is elastic.