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Karen runs a small coffee shop in the train station in Sudbury, selling (self-made) croissants. She competes with Dream Snacks (DS), a small coffee shop also located in the train station, selling croissants. Karen and DS use slightly different recipes for their croissants. Customers therefore perceive their croissants as differentiated (i.e., heterogeneous) products. The demands for Karen's and DS' croissants are described by the following two (daily) demand functions: 9k = 100 - 20PK + 10PDS qDS = 100 - 20PDs + 10PK where the subscripts 'K' and 'DS' refer to Karen and DS respectively. The marginal cost of making croissants is $2 for Karen as well as for DS. However, neither Karen nor DS incurs a fixed cost when making croissants. Note: Please round your numbers to 2 decimal places. a) Suppose Karen and DS choose the prices for their croissants simultaneously. What are then the equilibrium prices and quantities? What are Karen's and DS' (daily) profits from selling croissants? (7 points) b) Now suppose that Karen and DS collude over the prices for their croissants (i.e., they form a cartel). Identify the cartel price for croissants at the train station, the quantity of croissants that Karen and DS will then produce and sell every day, and their (daily) profits. (6 points)