document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200876>Question 1200876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "QUESTION: Write a demand and a supply curve expressed in the form of an exponential and<BR>\n" );
document.write( "logarithmic functions respectively. <BR>\n" );
document.write( "Demonstrate graphically or otherwise, that the<BR>\n" );
document.write( "functions reflect all the characteristics of a demand and supply curve </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848046 by </B><A HREF=/tutors/aboutme.mpl?userid=asinus><B>asinus(45)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=asinus><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Demand Curve (Exponential)**\r<BR>\n" );
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document.write( "* **Function:** <BR>\n" );
document.write( "   * Qd = a * e^(-bP) <BR>\n" );
document.write( "      * Where:<BR>\n" );
document.write( "         * Qd is the quantity demanded<BR>\n" );
document.write( "         * P is the price<BR>\n" );
document.write( "         * a and b are positive constants\r<BR>\n" );
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document.write( "* **Characteristics:**<BR>\n" );
document.write( "    * **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.<BR>\n" );
document.write( "    * **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. <BR>\n" );
document.write( "    * **Smooth and Continuous:** The exponential function provides a smooth and continuous curve, which is generally observed in real-world demand relationships.\r<BR>\n" );
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document.write( "**2. Supply Curve (Logarithmic)**\r<BR>\n" );
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document.write( "* **Function:**<BR>\n" );
document.write( "   * Qs = c * ln(d + P)<BR>\n" );
document.write( "      * Where:<BR>\n" );
document.write( "         * Qs is the quantity supplied<BR>\n" );
document.write( "         * P is the price<BR>\n" );
document.write( "         * c and d are positive constants\r<BR>\n" );
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document.write( "* **Characteristics:**<BR>\n" );
document.write( "    * **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.<BR>\n" );
document.write( "    * **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).<BR>\n" );
document.write( "    * **Smooth and Continuous:** The logarithmic function provides a smooth and continuous curve, which is generally observed in real-world supply relationships.\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* These are simplified models. Real-world demand and supply curves can be more complex and influenced by various factors beyond just price.<BR>\n" );
document.write( "* The specific values of the constants (a, b, c, d) will determine the exact shape and position of the curves.\r<BR>\n" );
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document.write( "I hope this helps! Let me know if you'd like to explore any of these concepts in more detail.<BR>\n" );
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