Question

Part 2 A firm specializes in the production of a certain product X. The demand for its new brand of product X is given by: Q = 1,000 - 4Px. Assume that you are the manager of the firm and you must determine the best price to charge for the good. The marginal cost of producing product X is zero. 1. Determine the inverse demand equation of product X. 2. Determine the marginal revenue as function of the quantity demanded of good X. 3. What price would you charge? Explain your answer! 4. Determine the arc price elasticity of demand when the price falls from P1=150 to P2=100. 5. Now, assume that the marginal cost of producing product X is 150. What price would charge per unit of product X?

Answer 1

1) Demand is Qx = 1000 - 4Px. Inverse demand is 4Px = 1000 - Qx or Px = 1000/4 - Qx/4. This gives Px = 250 - 0.25Qx

2) Find revenue function R = PxQx. Here we have R = 250Qx - 0.25Qx^2. Marginal revenue MR is the derivative of revenue function with respect to Qx. This implies MR = 250 - 0.5Qx

3) MR = MC would result in 250 - 0.5Qx = 0. This gives Qx = 250/0.5 = 500 units

4) When Px is 150, Qx = 1000 - 4*150 = 400 units. When Px is 100, Qx is 1000 - 4*100 = 600 units.

Use ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]

= (600 - 400)/((600 + 400)/2) divided by (100 - 150)/((150 + 100)/2)

= -1.00

5) Use MR = MC gives 250 - 0.5Qx = 150 or Qx = 100/0.5 = 200 units.

At this quantity the price is 250 - 200*0.25 = $200

Monopoly will charge $200 per unit