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AT&T. It is early in the days of cellular (or mobile) telephony, and you are the price manager for AT&T's cell phone plan. It has been determined that there are two market segments: low-value consumers and high-value consumers. For simplicity, assume that all consumers within a segment are identical. A consumer in the low-value segment has monthly demand (measured in number of minutes) of Q₁ (p) = 80 - p, and a consumer in the high-value segment has monthly demand of QH (P) = 100 -p, where p is in cents per minute. a. Assume AT&T charges a flat price per minute with no membership fee. Derive the expression for consumer surplus for a low-value consumer and for a high-value consumer as a function of the price, p. Low-value consumer surplus, CS, (p) = High-value consumer surplus, CS, (p) = Show Transcribed Text Assume AT&T's marginal cost is a constant 10 cents per minute. You have decided to use a two-part tariff and must choose the monthly fixed fee f and the per-minute charge p. There are 1,000,000 consumers of which a fraction a are low-value consumers. These assumptions also apply to parts (b)-(d). b. Suppose all 1,000,000 consumers are low-value consumers (so a = 1). Find the profit- maximizing two-part tariff; i.e., profit-maximizing values for p and f. Also calculate the associated monthly profit. Optimal per-minute charge, p = Optimal monthly fixed fee f = Profit per month= c. Suppose all 1,000,000 consumers are high-value consumers (so a = 0). Find the profit-

AT&T. It is early in the days of cellular (or mobile) telephony, and you are the price manager for AT&T's cell phone plan. It has been determined that there are two market segments: low-value consumers and high-value consumers. For simplicity, assume that all consumers within a segment are identical. A consumer in the low-value segment has monthly demand (measured in number of minutes) of Q₁ (p) = 80 - p, and a consumer in the high-value segment has monthly demand of QH (P) = 100 -p, where p is in cents per minute. a. Assume AT&T charges a flat price per minute with no membership fee. Derive the expression for consumer surplus for a low-value consumer and for a high-value consumer as a function of the price, p. Low-value consumer surplus, CS, (p) = High-value consumer surplus, CS, (p) = Show Transcribed Text Assume AT&T's marginal cost is a constant 10 cents per minute. You have decided to use a two-part tariff and must choose the monthly fixed fee f and the per-minute charge p. There are 1,000,000 consumers of which a fraction a are low-value consumers. These assumptions also apply to parts (b)-(d). b. Suppose all 1,000,000 consumers are low-value consumers (so a = 1). Find the profit- maximizing two-part tariff; i.e., profit-maximizing values for p and f. Also calculate the associated monthly profit. Optimal per-minute charge, p = Optimal monthly fixed fee f = Profit per month= c. Suppose all 1,000,000 consumers are high-value consumers (so a = 0). Find the profit-

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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AT&T. It is early in the days of cellular (or mobile) telephony, and you are the price manager for AT&T's cell phone plan. It has been determined that there are two market segments: low-value consumers and high-value consumers. For simplicity, assume that all consumers within a segment are identical. A consumer in the low-value segment has monthly demand (measured in number of minutes) of Q, (p) = 80 - p, and a consumer in the high-value segment has monthly demand of QH (P) = 100 -p, where p is in cents per minute. a. Assume AT&T charges a flat price per minute with no membership fee. Derive the expression for consumer surplus for a low-value consumer and for a high-value consumer as a function of the price, p. Low-value consumer surplus, CS, (p): = High-value consumer surplus, CS, (p) = Show Transcribed Text Assume AT&T's marginal cost is a constant 10 cents per minute. You have decided to use a two-part tariff and must choose the monthly fixed fee f and the per-minute charge p. There are 1,000,000 consumers of which a fraction a are low-value consumers. These assumptions also apply to parts (b)-(d). b. Suppose all 1,000,000 consumers are low-value consumers (so a = 1). Find the profit- maximizing two-part tariff; i.e., profit-maximizing values for p and f. Also calculate the associated monthly profit. Optimal per-minute charge, p = Optimal monthly fixed fee = Profit per month =_ c. Suppose all 1,000,000 consumers are high-value consumers (so a = 0). Find the profit- maximizing two-part tariff, and calculate the associated. Optimal per-minute charge, p = Optimal monthly fixed fee, f = Ċ Profit per month = Show Transcribed Text J Ĉ d. Suppose 500,000 consumers are low value and 500,000 consumers are high value (so a = 0.5). In no more than three or four sentences, explain what the optimal two-part tariff will look like relative to the answers in part b) and c) - and why.
Transcribed Image Text:AT&T. It is early in the days of cellular (or mobile) telephony, and you are the price manager for AT&T's cell phone plan. It has been determined that there are two market segments: low-value consumers and high-value consumers. For simplicity, assume that all consumers within a segment are identical. A consumer in the low-value segment has monthly demand (measured in number of minutes) of Q, (p) = 80 - p, and a consumer in the high-value segment has monthly demand of QH (P) = 100 -p, where p is in cents per minute. a. Assume AT&T charges a flat price per minute with no membership fee. Derive the expression for consumer surplus for a low-value consumer and for a high-value consumer as a function of the price, p. Low-value consumer surplus, CS, (p): = High-value consumer surplus, CS, (p) = Show Transcribed Text Assume AT&T's marginal cost is a constant 10 cents per minute. You have decided to use a two-part tariff and must choose the monthly fixed fee f and the per-minute charge p. There are 1,000,000 consumers of which a fraction a are low-value consumers. These assumptions also apply to parts (b)-(d). b. Suppose all 1,000,000 consumers are low-value consumers (so a = 1). Find the profit- maximizing two-part tariff; i.e., profit-maximizing values for p and f. Also calculate the associated monthly profit. Optimal per-minute charge, p = Optimal monthly fixed fee = Profit per month =_ c. Suppose all 1,000,000 consumers are high-value consumers (so a = 0). Find the profit- maximizing two-part tariff, and calculate the associated. Optimal per-minute charge, p = Optimal monthly fixed fee, f = Ċ Profit per month = Show Transcribed Text J Ĉ d. Suppose 500,000 consumers are low value and 500,000 consumers are high value (so a = 0.5). In no more than three or four sentences, explain what the optimal two-part tariff will look like relative to the answers in part b) and c) - and why.
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