Consider two users, ASAM and BELON, who utilize Al chatbots with distinct preferences to two available chatbots: Chatbot 1: Fast, intelligent, creative, but there is a 5% chance of incorrect answers. Chatbot 2: Slower, less intelligent, but always correct. ASAM uses both chatbots but prefers Chatbot 1 more strongly, while BELON also uses bot bots but tends to value Chatbot 2 more.

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Chapter1: Making Economics Decisions
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Consider two users, ASAM and BELON, who utilize Al chatbots with distinct preferences for
two available chatbots:
Chatbot 1: Fast, intelligent, creative, but there is a 5% chance of incorrect answers.
Chatbot 2: Slower, less intelligent, but always correct.
ASAM uses both chatbots but prefers Chatbot 1 more strongly, while BELON also uses both
bots but tends to value Chatbot 2 more.
These utility functions represent their preferences:
ASAM's Utility Function:
UA (x1, x2) = 2x1.5 + x2.5
BELON's Utility Function:
UB (x1, x₂)
Where X₁ and x2 denote the hours of use of Chatbot 1 and Chatbot 2, respectively.
= = x0.5 +2x9.5
1. Indifference Curves: Sketch ASAM's and BELON's indifference curves. Discuss notable
features and differences between the curves for each consumer.
2. ASAM's Optimal Usage (individual demand): Derive ASAM's optimal consumption of
each chatbot. x ₁ and x 2 for ASAM, as a function of his budget of $m, and the price per
hour of the chatbots p₁ and p2, respectively. Hint: you can use tangency conditions
directly.
3. BELON's Optimal Usage (individual demand): Similarly, derive BELON's optimal
consumption of each chatbot. x ₁ and x 2 for BELON, as a function of his budget of $mg
and the price per hour of the chatbots p₁ and p2, respectively. Hint: you can use
tangency conditions directly.
4. Market demand: Suppose the market has a total of 15 consumers. Ten consumers are
identical to ASAM, and ten are identical to BELON. Find the market demand curve for
Chatbot 1 as a function of mA, MB, and
and p2.
P1
5. Now assume mA = mB = $1000, and p₁-0.2 and p2=0.1. What is the total number of
minutes that consumers demand for Chatbot 1?
Transcribed Image Text:Consider two users, ASAM and BELON, who utilize Al chatbots with distinct preferences for two available chatbots: Chatbot 1: Fast, intelligent, creative, but there is a 5% chance of incorrect answers. Chatbot 2: Slower, less intelligent, but always correct. ASAM uses both chatbots but prefers Chatbot 1 more strongly, while BELON also uses both bots but tends to value Chatbot 2 more. These utility functions represent their preferences: ASAM's Utility Function: UA (x1, x2) = 2x1.5 + x2.5 BELON's Utility Function: UB (x1, x₂) Where X₁ and x2 denote the hours of use of Chatbot 1 and Chatbot 2, respectively. = = x0.5 +2x9.5 1. Indifference Curves: Sketch ASAM's and BELON's indifference curves. Discuss notable features and differences between the curves for each consumer. 2. ASAM's Optimal Usage (individual demand): Derive ASAM's optimal consumption of each chatbot. x ₁ and x 2 for ASAM, as a function of his budget of $m, and the price per hour of the chatbots p₁ and p2, respectively. Hint: you can use tangency conditions directly. 3. BELON's Optimal Usage (individual demand): Similarly, derive BELON's optimal consumption of each chatbot. x ₁ and x 2 for BELON, as a function of his budget of $mg and the price per hour of the chatbots p₁ and p2, respectively. Hint: you can use tangency conditions directly. 4. Market demand: Suppose the market has a total of 15 consumers. Ten consumers are identical to ASAM, and ten are identical to BELON. Find the market demand curve for Chatbot 1 as a function of mA, MB, and and p2. P1 5. Now assume mA = mB = $1000, and p₁-0.2 and p2=0.1. What is the total number of minutes that consumers demand for Chatbot 1?
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