Suppose that demand is linear, Q^d = 100 - 12P. At P = 5 and Q = 40, the price elasticity of demand is: A) -2/3 B) -2 C) -12 D) -3/2

Question

Quizplus · Accepted Answer

To calculate the price elasticity of demand (PED), we use the formula:

PED = (% Change in Quantity Demanded)/ (% Change in Price)

From the information given, we know that:

Q1 = 40 
P1 = 5

If we increase the price by 1 unit, it will decrease the quantity demanded by:

Q2 = 40 - 1 = 39

To calculate the percentage change in quantity demanded, we use the formula:

% Change in Quantity Demanded = (Q2 - Q1)/ Q1 x 100%

% Change in Quantity Demanded = (39 - 40)/ 40 x 100%

% Change in Quantity Demanded = -2.5%

Similarly, the percentage change in price is:

% Change in Price = (P2 - P1)/ P1 x 100%

% Change in Price = (6 - 5)/ 5 x 100%

% Change in Price = 20%

Now we can calculate the price elasticity of demand as:

PED = (% Change in Quantity Demanded)/ (% Change in Price)

PED = (-2.5%)/ (20%)

PED = -0.125

Since the PED is less than 1, we know that demand is inelastic, and the absolute value of the PED gives us the elasticity. Therefore, the price elasticity of demand at a price of 5 and a quantity of 40 is:

PED = 0.125

But the question asks for the negative value of the elasticity, so we get:

PED = -0.125 = -3/24 = -1/8 = -1.25

Thus, the answer is D (-3/2).

Suppose That Demand Is Linear, Qd = 100 - 12P

Suppose That Demand Is Linear, Q^d = 100 - 12P