document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183246>Question 1183246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P = 0.09q + 50 be the supply equation for a manufacturer. The demand equation for his product is:\r<BR>\n" );
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document.write( "P = 0.07q + 65\r<BR>\n" );
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document.write( "	If a tax of N1.50/unit is to be imposed on the manufacturer, how will the original equilibrium price be effected if the demand remains the same?\r<BR>\n" );
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document.write( "	Determine the total revenue obtained by the manufacturer at the equilibrium point, both before and after the tax.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849898 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to analyze the impact of the tax on the equilibrium price and revenue:\r<BR>\n" );
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document.write( "**1. Find the original equilibrium:**\r<BR>\n" );
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document.write( "* Set the supply and demand equations equal to each other:<BR>\n" );
document.write( "   0.09q + 50 = 0.07q + 65\r<BR>\n" );
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document.write( "* Solve for q (equilibrium quantity):<BR>\n" );
document.write( "   0.02q = 15<BR>\n" );
document.write( "   q = 750\r<BR>\n" );
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document.write( "* Substitute the value of q back into either the supply or demand equation to find P (equilibrium price):<BR>\n" );
document.write( "   P = 0.09(750) + 50<BR>\n" );
document.write( "   P = 117.5\r<BR>\n" );
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document.write( "**2.  Incorporate the tax:**\r<BR>\n" );
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document.write( "A tax of N1.50/unit increases the supply equation by that amount. The new supply equation is:\r<BR>\n" );
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document.write( "P_taxed = 0.09q + 50 + 1.50<BR>\n" );
document.write( "P_taxed = 0.09q + 51.5\r<BR>\n" );
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document.write( "**3. Find the new equilibrium (after tax):**\r<BR>\n" );
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document.write( "* Set the new supply equation equal to the original demand equation:<BR>\n" );
document.write( "   0.09q + 51.5 = 0.07q + 65\r<BR>\n" );
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document.write( "* Solve for the new equilibrium quantity (q_taxed):<BR>\n" );
document.write( "   0.02q = 13.5<BR>\n" );
document.write( "   q_taxed = 675\r<BR>\n" );
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document.write( "* Substitute q_taxed back into the *original* demand equation to find the price the *consumer* pays (P_consumer):<BR>\n" );
document.write( "   P_consumer = 0.07(675) + 65<BR>\n" );
document.write( "   P_consumer = 112.25\r<BR>\n" );
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document.write( "* The manufacturer receives the consumer price *minus* the tax:<BR>\n" );
document.write( "   P_manufacturer = P_consumer - 1.50<BR>\n" );
document.write( "   P_manufacturer= 112.25 - 1.50 = 110.75\r<BR>\n" );
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document.write( "**4. Analyze the price effect:**\r<BR>\n" );
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document.write( "The equilibrium price *paid by the consumer* increased from N117.5 to N112.25. However, the price *received by the manufacturer* decreased from N117.50 to N110.75.\r<BR>\n" );
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document.write( "**5. Calculate total revenue:**\r<BR>\n" );
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document.write( "* **Before tax:**<BR>\n" );
document.write( "   Revenue_before = P * q = 117.5 * 750 = N88,125\r<BR>\n" );
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document.write( "* **After tax:**<BR>\n" );
document.write( "   Revenue_after = P_manufacturer * q_taxed = 110.75 * 675 = N74,756.25\r<BR>\n" );
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document.write( "**Summary:**\r<BR>\n" );
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document.write( "* The tax caused the equilibrium quantity to decrease from 750 to 675.<BR>\n" );
document.write( "* The price paid by the consumer decreased from N117.50 to N112.25.<BR>\n" );
document.write( "* The price received by the manufacturer decreased from N117.50 to N110.75.<BR>\n" );
document.write( "* The total revenue decreased from N88,125 to N74,756.25.<BR>\n" );
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