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Assume that the demand of chocolate of a local producer is given by q = 9-√p in hundreds of kilograms, where p = [0, 81] is the price of a kilogram in USD. 1. Compute the elasticity of the demand as a function of p, and find where it is unit elastic, elastic, and inelastic. 2. Compute the revenue R(p) in USD as a function of p. Careful of units! 3. Compute R'(25). Interpret this quantity. Remember to write down units. 4. What is the sign of R'(25)? Considering what you obtained in Question 1, does this make sense? Why? 5. Now, compute the revenue R(q) in USD as a function of q. Careful of units! 6. Compute the marginal revenue Rm(q). 7. Compute Rm (4). Interpret this quantity. Remember to write down units. Since q= 4 corresponds to p= 25, why is the result different from Question 3?

Assume that the demand of chocolate of a local producer is given by q = 9-√p in hundreds of kilograms, where p = [0, 81] is the price of a kilogram in USD. 1. Compute the elasticity of the demand as a function of p, and find where it is unit elastic, elastic, and inelastic. 2. Compute the revenue R(p) in USD as a function of p. Careful of units! 3. Compute R'(25). Interpret this quantity. Remember to write down units. 4. What is the sign of R'(25)? Considering what you obtained in Question 1, does this make sense? Why? 5. Now, compute the revenue R(q) in USD as a function of q. Careful of units! 6. Compute the marginal revenue Rm(q). 7. Compute Rm (4). Interpret this quantity. Remember to write down units. Since q= 4 corresponds to p= 25, why is the result different from Question 3?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercise IV: Revenue functions Assume that the demand of chocolate of a local producer is given by q = 9 - √p in hundreds of kilograms, where p = [0, 81] is the price of a kilogram in USD. 1. Compute the elasticity of the demand as a function of p, and find where it is unit elastic, elastic, and inelastic. 2. Compute the revenue R(p) in USD as a function of p. Careful of units! 3. Compute R'(25). Interpret this quantity. Remember to write down units. 4. What is the sign of R'(25)? Considering what you obtained in Question 1, does this make sense? Why? 5. Now, compute the revenue R(q) in USD as a function of q. Careful of units! 6. Compute the marginal revenue Rm(q). 7. Compute Rm (4). Interpret this quantity. Remember to write down units. Since q= 4 corresponds to p= 25, why is the result different from Question 3?
Transcribed Image Text:Exercise IV: Revenue functions Assume that the demand of chocolate of a local producer is given by q = 9 - √p in hundreds of kilograms, where p = [0, 81] is the price of a kilogram in USD. 1. Compute the elasticity of the demand as a function of p, and find where it is unit elastic, elastic, and inelastic. 2. Compute the revenue R(p) in USD as a function of p. Careful of units! 3. Compute R'(25). Interpret this quantity. Remember to write down units. 4. What is the sign of R'(25)? Considering what you obtained in Question 1, does this make sense? Why? 5. Now, compute the revenue R(q) in USD as a function of q. Careful of units! 6. Compute the marginal revenue Rm(q). 7. Compute Rm (4). Interpret this quantity. Remember to write down units. Since q= 4 corresponds to p= 25, why is the result different from Question 3?
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