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The market for superpremium ice creams is dominated by Ben&Jerry's and Haagen-Dazs, which compete with non-overlapping flavors and a "chunky" vs. "smooth" concept, depending on the presence of mix-ins (mix-ins are extra ingredients like chocolate, caramel, candy, and baked goods that have been added to the ice cream). Using a unit segment to represent smoothness of the ice cream, Haagen-Dazs (A) produces perfectly smooth flavors (i.e. is located at 0), while Ben&Jerry's (B) produces perfectly chunky flavors (i.e. is located at 1). Ice cream consumers differ in their preference for smoothness and are uniformly distributed along the segment. Each consumer has a disutility (in addition to the price) from departing from their favorite smoothness, equal to a unit transport cost of t = 2. Both firms have the same marginal cost c = 10 and no fixed costs. 1. Write the total cost of buying from A and B for a consumer located at z. 2. Find the marginal consumer and derive demand for the two firms. Show that demand for firm i, Di = 1/+ ¹² 3. Write the profit functions for each firm and derive their reaction functions. 4. Find the equilibrium prices, demand, and profits. Show that in equilibrium firms share equally the market, they set the same price pi= c +t, and gain profits 7¹ = 1.

The market for superpremium ice creams is dominated by Ben&Jerry's and Haagen-Dazs, which compete with non-overlapping flavors and a "chunky" vs. "smooth" concept, depending on the presence of mix-ins (mix-ins are extra ingredients like chocolate, caramel, candy, and baked goods that have been added to the ice cream). Using a unit segment to represent smoothness of the ice cream, Haagen-Dazs (A) produces perfectly smooth flavors (i.e. is located at 0), while Ben&Jerry's (B) produces perfectly chunky flavors (i.e. is located at 1). Ice cream consumers differ in their preference for smoothness and are uniformly distributed along the segment. Each consumer has a disutility (in addition to the price) from departing from their favorite smoothness, equal to a unit transport cost of t = 2. Both firms have the same marginal cost c = 10 and no fixed costs. 1. Write the total cost of buying from A and B for a consumer located at z. 2. Find the marginal consumer and derive demand for the two firms. Show that demand for firm i, Di = 1/+ ¹² 3. Write the profit functions for each firm and derive their reaction functions. 4. Find the equilibrium prices, demand, and profits. Show that in equilibrium firms share equally the market, they set the same price pi= c +t, and gain profits 7¹ = 1.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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The market for superpremium ice creams is dominated by Ben&Jerry's and Haagen-Dazs, which compete with non-overlapping flavors and a "chunky" vs. "smooth" concept, depending on the presence of mix-ins (mix-ins are extra ingredients like chocolate, caramel, candy, and baked goods that have been added to the ice cream). Using a unit segment to represent smoothness of the ice cream, Haagen-Dazs (A) produces perfectly smooth flavors (i.e. is located at 0), while Ben&Jerry's (B) produces perfectly chunky flavors (i.e. is located at 1). Ice cream consumers differ in their preference for smoothness and are uniformly distributed along the segment. Each consumer has a disutility (in addition to the price) from departing from their favorite smoothness, equal to a unit transport cost of t = 2. Both firms have the same marginal cost c = 10 and no fixed costs. 1. Write the total cost of buying from A and B for a consumer located at z. 2. Find the marginal consumer and derive demand for the two firms. Show that demand for firm i, Di = } + P. 2t 3. Write the profit functions for each firm and derive their reaction functions. 4. Find the equilibrium prices, demand, and profits. Show that in equilihrium firms share equally the market, they set the same price p' = c+ t, and gain profits t' = 1. 5. What would happen to prices and profits if consumers could not feel the difference between "smooth" and “chunky" texture? 6. In late 1992, Haagen-Dazs introduced Extraas, a line of chunky flavors. Few months later, Ben&Jerry's introduced smooth flavors, a strategy described by Ben Cohen, the cofounder and former CEO of Ben&Jerry's, as "When the smooth gets chunky, the chunky gets smooth". How would you represent this using the model? What do you think that the rationale was? What do you expect to happen to demand, prices and profits for the two firms? (no computations needed) 7. Knowing that price competition is very fierce in this market, is firms' choices of maximum differentiation optimal? Discuss.
Transcribed Image Text:The market for superpremium ice creams is dominated by Ben&Jerry's and Haagen-Dazs, which compete with non-overlapping flavors and a "chunky" vs. "smooth" concept, depending on the presence of mix-ins (mix-ins are extra ingredients like chocolate, caramel, candy, and baked goods that have been added to the ice cream). Using a unit segment to represent smoothness of the ice cream, Haagen-Dazs (A) produces perfectly smooth flavors (i.e. is located at 0), while Ben&Jerry's (B) produces perfectly chunky flavors (i.e. is located at 1). Ice cream consumers differ in their preference for smoothness and are uniformly distributed along the segment. Each consumer has a disutility (in addition to the price) from departing from their favorite smoothness, equal to a unit transport cost of t = 2. Both firms have the same marginal cost c = 10 and no fixed costs. 1. Write the total cost of buying from A and B for a consumer located at z. 2. Find the marginal consumer and derive demand for the two firms. Show that demand for firm i, Di = } + P. 2t 3. Write the profit functions for each firm and derive their reaction functions. 4. Find the equilibrium prices, demand, and profits. Show that in equilihrium firms share equally the market, they set the same price p' = c+ t, and gain profits t' = 1. 5. What would happen to prices and profits if consumers could not feel the difference between "smooth" and “chunky" texture? 6. In late 1992, Haagen-Dazs introduced Extraas, a line of chunky flavors. Few months later, Ben&Jerry's introduced smooth flavors, a strategy described by Ben Cohen, the cofounder and former CEO of Ben&Jerry's, as "When the smooth gets chunky, the chunky gets smooth". How would you represent this using the model? What do you think that the rationale was? What do you expect to happen to demand, prices and profits for the two firms? (no computations needed) 7. Knowing that price competition is very fierce in this market, is firms' choices of maximum differentiation optimal? Discuss.
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