p is in dollars and q is the number of units.Find the elasticity of the demand function at the price
A) -4.04
B) 1.00
C) 4.04
D) -0.78
E) 0.78

Question

​p is in dollars and q is the number of units.Find the elasticity of the demand function  at the price  ​
A) ​-4.04 
B) ​1.00 
C) ​4.04 
D) ​-0.78 
E) ​0.78

Quizplus · Accepted Answer

To find the elasticity of the demand function, we use the formula:

E = (% change in quantity demanded) / (% change in price)

We are given that p is in dollars and q is the number of units. Therefore, we can write the demand function as:

q = 11ea8970_69cc_995f_861b_9d4b0c1c5b0f_TB1301_11/p

We differentiate this with respect to p to get the following expression for elasticity:

E = (p/q) * (-dq/dp)

We are given that the price is 11ea8970_69cc_9960_861b_dfdc83b6a79f_TB1301_11. Plugging this into the demand function, we get:

q = 11ea8970_69cc_995f_861b_9d4b0c1c5b0f_TB1301_11/11ea8970_69cc_9960_861b_dfdc83b6a79f_TB1301_11
q = 1

This tells us that at the price of 11ea8970_69cc_9960_861b_dfdc83b6a79f_TB1301_11, the number of units demanded is 1. Now we need to find the derivative of the demand function with respect to p. We have:

q = 11ea8970_69cc_995f_861b_9d4b0c1c5b0f_TB1301_11/p
dq/dp = -11ea8970_69cc_995f_861b_9d4b0c1c5b0f_TB1301_11/p^2

Plugging in the price of 11ea8970_69cc_9960_861b_dfdc83b6a79f_TB1301_11, we get:

dq/dp = -11ea8970_69cc_995f_861b_9d4b0c1c5b0f_TB1301_11/(11ea8970_69cc_9960_861b_dfdc83b6a79f_TB1301_11)^2
dq/dp = -11ea8970_69cc_995f_861b_9d4b0c1c5b0f_TB1301_11/121

Finally, plugging in the values we have calculated into the expression for elasticity, we get:

E = (11ea8970_69cc_9960_861b_dfdc83b6a79f_TB1301_11/1) * (-11ea8970_69cc_995f_861b_9d4b0c1c5b0f_TB1301_11/121)
E = -4.04

Therefore, the elasticity of the demand function at the price of 11ea8970_69cc_9960_861b_dfdc83b6a79f_TB1301_11 is -4.04, which means that demand is highly elastic. A 1% increase in price would lead to a 4.04% decrease in quantity demanded.

​P Is in Dollars and Q Is the Number of Units.Find

P Is in Dollars and Q Is the Number of Units.Find