Suponga que la demanda por X sea: Xd = 100 - 2Px. ¿Cuál será la ecuación de demanda consecuente con la afirmación: "La demanda por el bien X aumentó en 10%?"
Understand the Problem
La pregunta te pide determinar la nueva ecuación de demanda para el bien X después de un aumento del 10% en la demanda, dado que la ecuación de demanda original es Xd = 100 - 2Px. Ya has realizado el paso inicial para calcular la nueva ecuación de demanda, aplicandole el 10% de incremento.
Answer
$X_d^{new} = 110 - 2.2P_x$
Answer for screen readers
$X_d^{new} = 110 - 2.2P_x$
Steps to Solve
- Original demand equation
The original demand equation is $X_d = 100 - 2P_x$.
- Increase the entire equation by 10%
To reflect a 10% increase in demand, we need to multiply the entire original demand equation by 1.1 (which represents 100% + 10%). $$X_d^{new} = 1.1 \times (100 - 2P_x)$$
- Distribute the 1.1
Distribute the 1.1 across both terms inside the parenthesis. $$X_d^{new} = 1.1 \times 100 - 1.1 \times 2P_x$$
- Simplify
Simplify the equation by performing the multiplications. $$X_d^{new} = 110 - 2.2P_x$$
$X_d^{new} = 110 - 2.2P_x$
More Information
The new demand equation $X_d^{new} = 110 - 2.2P_x$ represents a 10% increase in the quantity demanded at every price level compared to the original demand equation. The demand curve has shifted to the right.
Tips
A common mistake is only applying the percentage increase to the constant term and not to the entire equation. For example, calculating $1.1 \times 100 - 2P_x$ is incorrect because only the intercept is modified, thus not resulting in a true 10% increase to demand at every price. We must multiply the ENTIRE demand equation by 1.1.
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