A monopolist discriminates the price of its product among two groups as follows: Q 1 = 100 - p 1 (demand of customers in group 1) Q 2 = XXXXXXXXXX5p 2 (demand of customers in group 2) TC = XXXXXXXXXXQ...

A monopolist discriminates the price of its product among two groups as follows:

 Q₁ = 100 - p₁ (demand of customers in group 1)

 Q₂ = 120 - 0.5p₂ (demand of customers in group 2)

 TC = 2000 + ( Q₁ + Q₂)² (total cost of production)

a) Find the optimal sales to the first, Q₁ * , and to the second, Q₂ * , group.

b) Find prices to be charged to the first, p₁ * , and to the second, p₂ * , group.

c) Find the profit of this firm.

d) Show that the group with more elastic demand gets lower price.