D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. D(x) =e -x+3.5, S(x) = ex- 4.5 a) Find the equilibrium point. b) Find the consumer surplus at the equilibrium point. c) Find the producer surplus at the equilibrium point.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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D(x) is the​ price, in dollars per​ unit, that consumers are willing to pay for x units of an​ item, and​ S(x) is the​ price, in dollars per​ unit, that producers are willing to accept for x units.

D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units.

\[ D(x) = e^{-x + 3.5}, \quad S(x) = e^{-x - 4.5} \]

### Tasks
a) Find the equilibrium point.  
b) Find the consumer surplus at the equilibrium point.  
c) Find the producer surplus at the equilibrium point.

### Questions
a) What are the coordinates of the equilibrium point?  
- **Input:** [Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Do not include the $ symbol in your answer]

b) What is the consumer surplus at the equilibrium point?  
- **Input:** $ [Round to the nearest cent as needed.]

c) What is the producer surplus at the equilibrium point?  
- **Input:** $ [Round to the nearest cent as needed.]
Transcribed Image Text:D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. \[ D(x) = e^{-x + 3.5}, \quad S(x) = e^{-x - 4.5} \] ### Tasks a) Find the equilibrium point. b) Find the consumer surplus at the equilibrium point. c) Find the producer surplus at the equilibrium point. ### Questions a) What are the coordinates of the equilibrium point? - **Input:** [Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Do not include the $ symbol in your answer] b) What is the consumer surplus at the equilibrium point? - **Input:** $ [Round to the nearest cent as needed.] c) What is the producer surplus at the equilibrium point? - **Input:** $ [Round to the nearest cent as needed.]
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