A fried chicken franchise finds that the demand equation for its new roast chick
ID: 2895837 • Letter: A
Question
A fried chicken franchise finds that the demand equation for its new roast chicken product, "Roasted Rooster," is given by
q =36/p0.7
where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price. Find E(p)
E(p) =
Find the price elasticity of demand when the price is set at $4.40 per serving.
At a price of $4.40, a 1% increase in price leads to a (___________________) percent decrease in demand.
Interpret the result.
At a price of $4.40, the demand is (A). elastic (B). in elastic (C) of unity elastic _(___________________)
They should (A) lower (B) raise ( ______________) _the price per serving in order to increase revenue.
this above is q equal = ( fraction) 36 divide by p ^0.7Explanation / Answer
q = 36/ p0.7
Price elasticity of demand means how much the demand will be affected if price is changed,
This is given by dq/ dp
thus taking derivative with respect to price 'p' we get:
dq/dp = -0.7 * 36 * p1.7
dq/dp = -25.2 / p1.7 ;
At p = 4.4, dq/dp = -25.2/ (4.4)1.7 = -25.2/ 4.41.7 = -2.0301
This means that a one % change in price leads to a change of 2.0301 % in demand with the minus sign indicating that the change will be in opposite direction i.e. increase leading ot decrease and decrease leading ot increase;
Thus, at p=4.4$, a 1% increase in price leads to a 2.0301% decrease in demand;
As change in demand is greater than change in price in terms of magnitude, we can say that the demand is elastic;
As the demand is quite elastic, the should lower the price per serving in order to increase revenue as the decrease in revenue per unit will be more than compensated by the increase in quantity (number of units) of sale, since price is elastic;