From the information given, the demand for the widget is elastic because the price elasticity computed is above 1. The actual answer is 2.
What is the calculation that supports the above assertion?
Pe = (Percentage ΔQ)/Q/(Percentage ΔP)/P
Pe = (4/12) %/(1/8) %
Pe = 2.667
Because the the answer above is greater than 1, therefore, we can conclude that the demand for Widgets are price elastic.
What is the price of widgets that maximize the hardware stores revenue?
The price at which the the supplier will maximize revenue is derived by computing the revenue for all the price points. This is because we are not given a function of the revenue.
Price 1 - 10 * 2 = $20
Price 2 - 9 * 6 = $54
Price 3 - 8 *12 = $ 96
Price 4 - 7 * 16 = $ 112
Price 5 - 6 * 18 = $ 108
Price 6 - 5 * 20 = $100
From the above, it is clear that the price at which revenue is maximized is $7 as this yields a total revenue of $112.
The price of widgets is $9. If the hardware store wants to increase its revenue, how should it change the price?
Because the price is elastic and the price point form the above calculation at which price is maximized is $7, the firm should thus consider a reduction in it's price to $7.
Using the midpoint formula, calculate the price elasticity of demand for widgets when price increases from $7 - $8
Recall the formula given above.
Thus:
Price elasticity of demand (Pe) = ((96-112)/(112+96)/2)) ÷((8-7)/(8+7)/2))
Pe = -2.14
From the above, we can conclude that the price is elastic because the result albeit negative is greater than 1. The negativity of the result is an indicator that show the product is at this time perceived as an inferior good.
Using the midpoint formula, calculate the price elasticity of demand for widgets when price decreases from $6 - $5
Note that when
price=$6,
Quantity=18; and
When Price=$5,
Quantity= 20
Hence,
Price elasticity of demand (Pe) = ((20-18)/(20+18)/2)) ÷((5-6)/(5+6)/2))
Pe = - 0.58
Because the results here are less than one, it shows that the demand is now inelastic at those price points.
Based on the scenario in part E how does the decrease in price affect the hardware stores revenue?
Yes the decrease in price affects revenue. This is because the goods is now being perceived as inferior good and the consumers are quick to act according to the Substitution Effect, where they opt for a substitute goods at the former price or a price that is slightly higher.
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