The demand for fax machines has been estimated to be Q = 1,000 – P + 40 L, where P is the price of the machines and L is the average cost of a 10-minute midday call from Los Angeles to New York. At a fax machine price of $400 and a phone call cost of $10, the cross-price elasticity of demand for fax machines with respect to the price of phone service is:

Cross-price elasticity of demand for fax machine with respect to the price of phone service is 0.412

Explanation:

+ If the cost of a phone call is $10, according to the equation, fax machines demand would be: 1000 - 400 + 40 * 10 = 1,000

+ If the cost of the call is to be increase by 10% which is 10 x 1.1 = $11, fax machines demand would be : 1000 - 400 + 40 *1.1 = 1,040

+ Cross-price elasticity of demand for fax machine with respect to the price of the phone services is calculated as: % change in demand / % change in price; in which:

  % change in price = (change in price) / [( original price + price after change)/2] = 1 / [(10+11)/2] = 9.52%

  % change in quantity = (change in quantity) / [ (original quantity + quantity after change)/2] = 40 / [ (1000 +1040) /2 ] = 3.92%

So, cross price elasticity = 3.92% / 9.52% = 0.412.