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Question 1200876: Good Afternoon, I have a question that requires two answers and I'm just wondering if someone could assist me, even if it's just helping with one.
QUESTION: Write a demand and a supply curve expressed in the form of an exponential and
logarithmic functions respectively.
Demonstrate graphically or otherwise, that the
functions reflect all the characteristics of a demand and supply curve
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! **1. Demand Curve (Exponential)**
* **Function:**
* Qd = a * e^(-bP)
* Where:
* Qd is the quantity demanded
* P is the price
* a and b are positive constants
* **Characteristics:**
* **Negative Slope:** As price (P) increases, the exponent (-bP) becomes more negative. This leads to a decrease in the value of e^(-bP) and consequently a decrease in quantity demanded (Qd). This reflects the law of demand.
* **Asymptotic to Price Axis:** As price approaches infinity, the exponent (-bP) approaches negative infinity. This causes e^(-bP) to approach zero, meaning the quantity demanded approaches zero but never reaches it.
* **Smooth and Continuous:** The exponential function provides a smooth and continuous curve, which is generally observed in real-world demand relationships.
**2. Supply Curve (Logarithmic)**
* **Function:**
* Qs = c * ln(d + P)
* Where:
* Qs is the quantity supplied
* P is the price
* c and d are positive constants
* **Characteristics:**
* **Positive Slope:** As price (P) increases, the argument of the natural logarithm (d + P) also increases. This leads to an increase in the value of ln(d + P) and consequently an increase in quantity supplied (Qs). This reflects the law of supply.
* **Asymptotic to Price Axis (potentially):** The exact behavior depends on the value of 'd'. If 'd' is zero, the supply curve will have a vertical asymptote at P = 0. If 'd' is positive, the curve will approach a vertical line as price approaches negative infinity (though this region might not be economically relevant).
* **Smooth and Continuous:** The logarithmic function provides a smooth and continuous curve, which is generally observed in real-world supply relationships.
**Note:**
* These are simplified models. Real-world demand and supply curves can be more complex and influenced by various factors beyond just price.
* The specific values of the constants (a, b, c, d) will determine the exact shape and position of the curves.
I hope this helps! Let me know if you'd like to explore any of these concepts in more detail.
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