document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199609>Question 1199609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the demand function for a monopoly's product is P=400-2Q and the average cost function is 𝐴𝐶=400/Q+4+0.2𝑄, where Q is the number of units and p is the price per unit. i) Write the Total Cost (TC) and Total Revenue (TR) functions. ii) Calculate the profit maximizing price and quantity. Determine the maximum profit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848446 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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=848446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **i) Find Total Cost (TC) and Total Revenue (TR) functions**\r<BR>\n" );
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document.write( "* **Total Cost (TC):**<BR>\n" );
document.write( "   * TC = (Average Cost) * Q <BR>\n" );
document.write( "   * TC = (400/Q + 4 + 0.2Q) * Q<BR>\n" );
document.write( "   * TC = 400 + 4Q + 0.2Q²\r<BR>\n" );
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document.write( "* **Total Revenue (TR):**<BR>\n" );
document.write( "   * TR = Price (P) * Quantity (Q)<BR>\n" );
document.write( "   * TR = (400 - 2Q) * Q<BR>\n" );
document.write( "   * TR = 400Q - 2Q²\r<BR>\n" );
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document.write( "**ii) Calculate Profit-Maximizing Price and Quantity**\r<BR>\n" );
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document.write( "1. **Find Marginal Cost (MC):**<BR>\n" );
document.write( "   * MC = d(TC)/dQ = 4 + 0.4Q\r<BR>\n" );
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document.write( "2. **Find Marginal Revenue (MR):**<BR>\n" );
document.write( "   * MR = d(TR)/dQ = 400 - 4Q\r<BR>\n" );
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document.write( "3. **Set MR = MC to find profit-maximizing quantity:**<BR>\n" );
document.write( "   * 400 - 4Q = 4 + 0.4Q<BR>\n" );
document.write( "   * 396 = 4.4Q<BR>\n" );
document.write( "   * Q = 90 units\r<BR>\n" );
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document.write( "4. **Find profit-maximizing price:**<BR>\n" );
document.write( "   * P = 400 - 2Q <BR>\n" );
document.write( "   * P = 400 - 2 * 90 <BR>\n" );
document.write( "   * P = 220\r<BR>\n" );
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document.write( "5. **Calculate Maximum Profit:**<BR>\n" );
document.write( "   * Profit (π) = TR - TC<BR>\n" );
document.write( "   * π = (220 * 90) - (400 + 4 * 90 + 0.2 * 90²) <BR>\n" );
document.write( "   * π = 19800 - (400 + 360 + 1620) <BR>\n" );
document.write( "   * π = 19800 - 2480 <BR>\n" );
document.write( "   * π = 17320\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **Profit-maximizing quantity (Q): 90 units**<BR>\n" );
document.write( "* **Profit-maximizing price (P): $220**<BR>\n" );
document.write( "* **Maximum Profit: $17,320**<BR>\n" );
document.write( " </SPAN>\n" );
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