The cross price elasticity for widgets with respect to gadgets is -0.5. If the price of the gadgets rises from $0.95-1.10 (a 10% increase), what will the impact on the quantity demand for widgets at the current market price?
To understand the impact of the price increase of gadgets on the quantity demanded for widgets, we need to use the concept of cross price elasticity.
First, let's understand what cross price elasticity represents. Cross price elasticity measures the responsiveness of the quantity demanded of one product (in this case, widgets) to a change in the price of another product (gadgets). It tells us whether the two products are substitutes or complements.
In this case, the given cross price elasticity is -0.5. A negative cross price elasticity suggests that gadgets and widgets are substitutes, meaning that an increase in the price of gadgets would lead to an increase in the quantity demanded for widgets.
Now, let's calculate the percentage change in the quantity demanded of widgets due to a 10% increase in the price of gadgets.
The formula to calculate the percentage change in quantity demanded (ΔQ/Q) is:
ΔQ/Q = (Cross Price Elasticity) * (ΔP/P)
Where:
ΔQ/Q = Percentage change in quantity demanded
Cross Price Elasticity = -0.5
ΔP/P = Percentage change in price of gadgets = 10%
Substituting the given values into the formula, we have:
ΔQ/Q = (-0.5) * (10%) = -5%
This means that for each 10% increase in the price of gadgets, the quantity demanded of widgets will decrease by 5% (due to the negative sign).
Therefore, the impact on the quantity demanded for widgets at the current market price would be a decrease of 5%.