Answer to Question #301767 in Economics of Enterprise for Leonidos

Question

5. A retailer has noticed from the past several months, sales of product x has been close to 200 units per week. On two occasions, however, sales declined to 120 units per week. 2 The retailer notes that during these two periods, the store has reduced Y's price from Rs. 5 to Rs. 4. (a) What is the arc cross-price elasticity between x and y? (b) What level of sales for x would you predict if the price of y is increased to Rs. 6?

Answer 1

(a) What is the arc cross-price elasticity between x and y?

Here given Initial price (P_Y1)= Rs. 5 and new price (P_Y2)= Rs. 4

Initial demand (Q_X1)= 200 and new quantity (Q_X2)= 120 units Now Calculations of arc cross elasticity between X and Y is given by;

Ec = $\frac{∆Q}{∆P} = \frac{P_1 + P_2}{Q_1 + Q_2}=\frac{120-200}{4-5}\times\frac{5+4}{200+120} = 2.25$

Therefore, the coefficient of arc-cross elasticity between X and Y is 2.25

(b) What level of sales for x would you predict if the price of y is increased to Rs. 6?

If the price rises to Rs. 6, the resulting quantity is calculated as follows:

$\frac{Q_2 -200}{6 - 5}\times\frac{6 + 5}{200+Q_2} = 2.25$

$\frac{(Q_2 -200)11}{200+Q_2} = 2.25$

11Q₂ -2200 =  450 +2.25Q₂

 8.75Q₂ = 2650

Q2 = 303 units. 

As a result, when the price of item X increased to Rs 6 with the stated coefficient of cross elasticity, 303 units of sale are sold.