4 Cross-Price Elasticity

The marketing team of Burton Snowboard is analyzing her demand for two types of snowboard Professional and Standard models. At Thanksgiving sales, the Professional board is discounted from the original price  of $1,000. At this Thanksgiving sales, it is reported that the point cross-price elasticity of demand for the Standard board was 0.5 when there was a decrease in the quantity demanded of Standard boards by 10%. Also, you are told a total of 1,000 Professional boards have been sold at the sale, and the arc price elasticity of demand for Professional boards is equal to 1.

(a) From the cross-price elasticity of demand, what can be said about the substitutability and complementarity of the two models?

(b) What is the new price of the Professional snowboard after the discount?

(c) What is the original quantity demanded of the Professional snowboard before the decrease?

(d) What is the equation for the demand curve for Professional boards? Assume this demand curve is linear.

(e) What is the total revenue from selling Professional boards before the Thanksgiving sales and during the Thanksgiving sales?

(f) The name Black Friday" is there for a reason; it is the time of the year that shopkeepers can make prots (black) instead of (red) losses. Has Burton Snowboard succeeded in maximizing her revenue at the Thanksgiving sales? If not, suggest the price and quantity such that the company can maximize its revenue.