Question

Suppose that the demand for artichokes (Qa) is given as: Qa = 120 - 4P

a. What is the point price elasticity of demand if the price of artichokes is $10?

b. Suppose that the price of artichokes increases to $12. What will happen to the number of artichokes sold and the total expenditure by consumers on artichokes?

c. At what price if any is the demand for artichokes unit elastic?

Answer 1

a. point price elasticity of demand if the price of artichokes is $10 = -0.5

When price of artichokes = $10, quantity = 120 - 4P = 120 - 4*10 = 80

Formula for oint elasticity = (Q/ P) * (P/Q)

We need to calculate Q/ P first.

Q/ P = -4 / 1 = -4. (that is , with every increase  of $1, quantity decreases by 4. As given in demand function)

Point price elasticity =( Q/ P) * (P/Q) = -4(10/ 80) = -0.5

b. 72  

When price = $12, quantity = 120 - 4 * 12 = 72

c. $15

calculation:

when price = 15, quantity = 120 - 4*15 = 60

Ed = -4 (15/60) = -1 (unitary)

how to arrive at $15 = For unitary elastic demand , we need the point elasticity as -1 = -4 (1/4) --- Q/ P = -4 (in q (a) )

So, Q = 120 - 4P or 120 = Q + 4P  Q should be 4 times P

Thus, the value of Q = Value of 4P = 120 So, Q = 60; $P = 60 (So, P = 60/4 = 15)