Handout 3

Handout 3 - Then we can substitute = 7.2 in either the...

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N N N O O O R R R T T T H H H C C C A A A R R R O O O L L L I I I N N N A A A S S S T T T A A A T T T E E E U U U N N N I I I V V V E E E R R R S S S I I I T T T Y Y Y College of Management – Department of Economics Instructor: Kosmas Marinakis Handout 3: Solving for the Equilibrium When the demand and supply are not given on a graph but they are given in equation form we should be able to solve this demand - supply system in order to derive the equilibrium price and quantity. Demand and supply equations (functions) are usually given solved for quantity. In other words, the LHS will contain only q . For example demand might be = 20 – 2 p and supply q = 2 + 0.5 . The solution of such sets of equations with 2 equations and 2 unknowns (2 by 2 linear systems) is very easy when we use the substitution method described below. Since the LHS is equal to in both equations, this means that the RHS in both equations must be equal too. That is, 20 – 2 = 2 + 0.5 . This is a very simple equation with only one unknown ( ). Solving this equation we easily derive that the equilibrium price is 7.2.
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Unformatted text preview: Then we can substitute = 7.2 in either the demand or the supply equation and derive the equilibrium quantity. In the demand: = 20 2 7.2 = 5.6 (or in the supply: = 2 + 0.5 7.2 = 5.6). So the equilibrium price ( p* ) is 7.2 and the equilibrium quantity ( q* ) is 5.6. Special Case Sometimes the supply curve might not be well behaved. An example is the vertical supply curve (totally inelastic). This curve has the form = some number. For example = 10 is a vertical supply curve and means that no matter what the price is the production will be always 10 units. In this case, the derivation of the equilibrium is even simpler. From the supply function = 10 we already know that the equilibrium value of will be 10. Then, we just plug = 10 in the demand equation and we derive the equilibrium ....
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