Question

1. There are 2 user groups for your product. Group 1 are students with a demand given by 2000-50 P1 = Q1 and Group 2 are other customers with a demand given by 5500- 100 P2 = Q2.        Total Cost = Fixed Cost + Variable Cost = $20,000 + $15Q Marginal Cost = ∂TC/∂Q = $15 for each. Note: Q= Q1 + Q2. Solve for P1 Q1 P2 Q2.

2. 
   

1. Please solve for the equilibrium prices and quantities for both user groups P1 P2 Q1 Q2

2. Solve for the price elasticity of demand for both groups at equilibrium quantities.

Answer 1

Group 1, Q1 = 2,000 - 50P1

=> P1 = 40 - 0.02Q1

TR1 = 40Q1 - 0.02Q1^2

Differentiate TR wrt Q1 we get

MR1 = 40 - 0.04Q1

Equate it to MC, we get

40 - 0.04Q1 = 15

=> 0.04Q1 = 25

=> Q1 = 625

P1 = 40 - 0.02 × 625 = $ 27.5

Now, for group 2

Q2 = 5500 - 100P2

=> P2 = 55 - 0.01Q2

TR2 = 55Q2 - 0.01Q2^2

MR2 = 55 - 0.02Q2

Equate it to MC

55 - 0.02Q2 = 15

=> 0.02Q2 = 40

=> Q2 = 2,000

P2 = 55 - 0.01 × 2,000 = $ 35 per unit

B. The price elasticity of demand can be measured as follows

Group 1,

Differentiate Q1 wrt P1, we get

Calculating the elasticity

Group 2,

Plug in the calculated values, we get