I assume that the price of a car is constant and that 30 cars are sold per month in a small town. On the other hand, the price of gasoline rises from 15 to 20 pesos per liter, there is no other factor that influences the purchase plans and the number of cars sold drops to 28 per month. a) What is the cross elasticity of demand for cars with respect to gasoline? b) According to the previous section, are cars considered a substitute or complementary good for gasoline?

Necesitamos encontrar la elasticidad cruzada de la demanda de los autos con respecto a la gasolina. La fórmula para la elasticidad cruzada es:

E_{A,G} = \frac{\Delta Q_A / Q_{A\text{original}}}{\Delta P_G / P_{G\text{original}}}

Donde:
- \Delta Q_A es el cambio en la cantidad demandada de autos.
- Q_{A\text{original}} es la cantidad original demandada de autos.
- \Delta P_G es el cambio en el precio de la gasolina.
- P_{G\text{original}} es el precio original de la gasolina.

Primero, calculamos los cambios:

\Delta Q_A = 28 - 30 = -2
Q_{A\text{original}} = 30
\Delta P_G = 20 - 15 = 5
P_{G\text{original}} = 15

Ahora, sustituimos en la fórmula de elasticidad cruzada:

E_{A,G} = \frac{(\frac{-2}{30})}{(\frac{5}{15})}

E_{A,G} = \frac{-\frac{2}{30}}{\frac{5}{15}}

E_{A,G} = \frac{-\frac{2}{30}}{\frac{1}{3}}

E_{A,G} = -\frac{2}{30} \times \frac{3}{1}

E_{A,G} = -\frac{6}{30}

E_{A,G} = -\frac{1}{5}

Los autos y la gasolina se consideran bienes complementarios porque la elasticidad cruzada es negativa.

El resultado final en formato simplificado es:
a) E_{A,G} = -\frac{1}{7}

b) Complementario