# Consider an imperfectly competitive service provider, Muscat Automotive

Repair Services (MARS), whose total cost of production is 𝑪 = 𝟑𝟎𝑸 +

𝟎. 𝟏𝟔𝟓𝑸𝟐. Also, MARS faces two different market segments, A and B, whose demands can be linearly expressed as 𝑸𝑨 = 𝟐𝟒𝟎 − 𝑷𝑨 and 𝑸𝑩 = 𝟏𝟐𝟎 − 𝟎. 𝟓𝑷𝑩. (Hint: the marginal cost is the slope of the total cost function).

-Under a single-price strategy (no market segmentation), find MARS's profit-maximizing price and quantity.

-Under a single-price strategy (no market segmentation), find the consumer surplus.

-Draw the situation described in (1) and (2) above, clearly showing the profit-maximizing price and quantity and the area that represents the consumer surplus.

-If MARS decides to segment the market in accordance with the demands of groups A and B, find the profit-maximizing prices and quantities (𝑃 , 𝑄 ) and (𝑃 , 𝑄 ).

-What is the value of the consumer surplus for each group A and B, under this segmentation strategy?

-Draw the situation described in (4) and (5) above, clearly showing each group's profit- maximizing price and quantity, and the areas that correspond to their consumer surpluses.

-Verify the inverse elasticity rule under each of the scenarios described (1) and (4) above.

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