cross-price elasticity

Question

 Last month, sellers of good Y took in $100 in total revenue on sales of 50 units of good Y. This month sellers of good Y raised their price and took in $120 in total revenue on sales of 40 units of good Y. At the same time, the price of good X stayed the same, but sales of good X increased from 20 units to 40 units.  Are goods X and Y substitutes or complements? What is the cross-price elasticity?

Answer 1

 Original price of Y = $100/50 = $2

   New price of Y = $120/40 = $3

  Using the midpoint method,

    average price of Y = (3+2)/2= $2.5

  % change of price Y = 1/2.5= 40%  (increase in the price of Y)

 Average demand of X = (20+40)/2 = 30   

  % change of demand for X = 20/30 = 67%  (demand for X increased from 20 to 40)

  Cross elasticity = 67%/40% = 1.67 > 0    

X and Y are substitutes