c2e - 2.e The Algebra of Supply Demand P S 15 3 D Q Using...

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2.e. The Algebra of Supply & Demand Using the equation for a straight line, y = mx + b, we can determine the equations for the supply and demand curve to be the following: Demand: P = 15 – Q Supply: P = 3 + Q To solve for the equilibrium price and equilibrium quantity, set the demand equation equal to the supply equation. 15 – Q = 3 + Q Q* = 6 Plug Q back into either the demand or supply equation to solve for P P* = 15 – 6 = 9 D S 15 3 P Q D S Q* P* 15 3
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To calculate the amount of shortage resulting from a price ceiling at $6, set the supply and demand curve both equal to $6 Demand: 6 = 15 – Q Q = 9 Supply: 6 = 3 + Q Q = 3 THE AMOUNT OF SHORTAGE IS 9 – 3 = 6 UNITS To calculate the new equilibrium after imposing a $5 tax, set the new demand curve equal to the supply curve. (Remember to solve for the equation of the new demand curve first.) Equation of new demand curve: P = 10 – Q 10 – Q = 3 + Q Q = 3.5 Plug Q into either the demand or supply curve equation to solve for Ps (price sellers will pay) P = 10 – 3.5 = 6.5
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