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### Solving_for_equilibrium

Course: ECON 201, Fall 2008
School: UVA
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Word Count: 281

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Hint Helpful Solving for Equilibrium Given a supply function and a demand function, how can you calculate the equilibrium price and quantity in that market? You could do it graphically by drawing the curves and reading P* and Q* off the graph, but you can get more accurate answers by using algebra. Consider the demand and supply functions QD = a - bP and QS = c + dP. To find P* and Q*, just remember the...

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Hint Helpful Solving for Equilibrium Given a supply function and a demand function, how can you calculate the equilibrium price and quantity in that market? You could do it graphically by drawing the curves and reading P* and Q* off the graph, but you can get more accurate answers by using algebra. Consider the demand and supply functions QD = a - bP and QS = c + dP. To find P* and Q*, just remember the equilibrium condition, namely quantity supplied equals quantity demanded. QS = QD c + dP = a - bP The value of P which solves this equation is P*, so simply solve for P. Once you know P*, you can calculate Q* by plugging the value of P* into either the supply function or the demand function. Here's a numerical example. Demand: QD = 1100 - 100P Supply: QS = 100 + 100P 1. Set the quantity demanded equal to the quantity supplied. 1100 - 100P = 100 + 100P 2. for Solve P. 100P + 100P = 1100 - 100 200P = 1000 P=5 1 3. Substitute P back into either the supply or the demand equation to obtain the equilibrium quantity. Demand QD = 1100 - 100P QD = 1100 - 500 QD = 600 Supply QS = 100 + 100P QS = 100 + 500 QS = 600 We can solve this problem in another way as well, using the fact that the price faced by demanders in equilibrium equals the price faced by suppliers. 1. Isolate P in both equations. Demand Q = 1100 - 100P 100P = 1100 - Q P = 11 - .01Q Supply Q = 100 + ...

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