Question

[Income and Cross Price Elasticity of Demand]

(a) Given Q = 700?2P+0.02Y, where P = 25, and Y = 5000. Find (a) the price elasticity of demand and (b) the income elasticity of demand. (b) Given Q1 = 100?P1 +0.75P2 ?0.25P3 +0.0075Y. At P1 = 10, P2 = 20,P3 = 40 and Y = 10000, Q1 = 170. The cross price elasticity of demand for good 1 when price of good 2 is changing is given by

?12 = ?Q1 ?P2 × P2 Q1 .

The cross price elasticity of demand for good 1 when price of good 3 ?13 is defined in similar manner. Find th cross price elasticities of demand for good 1. (c) Given Q1 = 50?4P1 ?3P2 +2P3 +0.001Y. At P1 = 5, P2 = 7,P3 = 3 and Y = 11000, Q1 = 26. (i) Find cross price elasticities of demand for good 1, (ii) the income elasticity of demand, (iii) Are good 1 and good 2 substitutes or complements? (iv) Are good 1 and good 3 substitutes or complements? (v) Determine the effect on Q1 of a 10 percent price increase for each of the other goods individually

Answer 1

(a) Q = 700 - 2P + (0.02Y) = 700 - (2 x 25) + (0.02 x 5,000) = 700 - 50 + 100 = 750

(i) Price elasticity of demand = (Q/P) x (P/Q) = - 2 x (25/750) = - 0.067

(ii) Income elasticity = (Q/Y) x (Y/Q) = - 2 x (25/750) = 0.02 x (5,000/750) = 0.13

(b) Q1 = 100 - 10 + (0.75 x 20) - (0.25 x 40) + (0.0075 x 10,000) = 170 (given)

Cross price elasticity with good 2 = (Q1/P2) x (P2/Q1) = 0.75 x (20/170) = 0.088

Cross price elasticity with good 3 = (Q1/P3) x (P3/Q1) = - 0.25 x (40/170) = - 0.059

(c) Q1 = 26 (given)

(i)

Cross price elasticity with good 2 = (Q1/P2) x (P2/Q1) = - 3 x (5/26) = - 0.58

Cross price elasticity with good 3 = (Q1/P3) x (P3/Q1) = 2 x (3/26) = 0.23

(ii) Income elasticity = (Q1/Y) x (Y/Q1) = 0.001 x (11,000/26) = 0.42

(iii) Since cross price elasticity with good 2 is negative, good 1 and good 2 are complements.

(iv) Since cross price elasticity with good 2 is positive, good 1 and good 2 are substitutes.

(v) Cross price elasticity = % Change in demand for good 1 / % Change in price of related good

For good 2,

- 0.58 = % Change in demand for good 1 / 10%

% Change in demand for good 1 = -0.58 x 10% = - 5.8% (decrease)

For good 3,

0.23 = % Change in demand for good 1 / 10%

% Change in demand for good 1 = 0.23 x 10% = 2.3% (increase)