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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. We can conclude that goods X and Y are Select one: a. complements, and have a cross-price elasticity of 0.60. b. substitutes, and have a cross-price elasticity of 1.67. c. substitutes, and have a cross-price elasticity of 0.60. d. complements, and have a cross-price elasticity of 1.67.

Respuesta :

Answer:

Option (b) is correct.

Explanation:

Initial price of good Y = Total revenue/units sold

                                    = $100/50

                                    = $2

New price of good Y = Total revenue/units sold

                                    = $120/40

                                    = $3

Percentage change in quantity demanded for good X:

[tex]=\frac{current\ quantity-Initial\ quantity}{average\ quantity}\times 100[/tex]

[tex]=\frac{40-20}{30}\times100[/tex]

      = 67%

Percentage change in price of good Y:

[tex]=\frac{current\ price-Initial\ price}{average\ price}\times 100[/tex]

[tex]=\frac{3-2}{2.5}\times100[/tex]

      = 40%

Therefore,

[tex]Cross\ price\ elasticity=\frac{percentage\ change\ in\ quantity\ demanded\ for\ good\ X}{percentage\ change\ in\ price\ of\ good\ Y}[/tex]

[tex]Cross\ price\ elasticity=\frac{0.67}{0.40}[/tex]

                                           = 1.67

Hence, good X and good Y are substitute goods because as the price of good Y increases as a result demand for good X increases and cross price elasticity is positive. The cross price elasticity is 1.67.

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