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A monopolist discriminates the price of its product among two groups as follows: Q1 = 100...

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.

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