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16. Equilibrium - Solutions

16. Equilibrium - Solutions - Chapter 16 NAME Equilibrium...

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Chapter 16 NAME Equilibrium Introduction. Supply and demand problems are bread and butter for economists. In the problems below, you will typically want to solve for equilibrium prices and quantities by writing an equation that sets supply equal to demand. Where the price received by suppliers is the same as the price paid by demanders, one writes supply and demand as functions of the same price variable, p , and solves for the price that equalizes supply and demand. But if, as happens with taxes and subsidies, suppliers face different prices from demanders, it is a good idea to denote these two prices by separate variables, p s and p d . Then one can solve for equilibrium by solving a system of two equations in the two unknowns p s and p d . The two equations are the equation that sets supply equal to demand and the equation that relates the price paid by demanders to the net price received by suppliers. Example: The demand function for commodity x is q = 1 , 000 10 p d , where p d is the price paid by consumers. The supply function for x is q = 100 + 20 p s , where p s is the price received by suppliers. For each unit sold, the government collects a tax equal to half of the price paid by con- sumers. Let us find the equilibrium prices and quantities. In equilibrium, supply must equal demand, so that 1 , 000 10 p d = 100 + 20 p s . Since the government collects a tax equal to half of the price paid by consumers, it must be that the sellers only get half of the price paid by consumers, so it must be that p s = p d / 2. Now we have two equations in the two unknowns, p s and p d . Substitute the expression p d / 2 for p s in the first equation, and you have 1 , 000 10 p d = 100 + 10 p d . Solve this equation to find p d = 45. Then p s = 22 . 5 and q = 550. 16.1 (0) The demand for yak butter is given by 120 4 p d and the supply is 2 p s 30, where p d is the price paid by demanders and p s is the price received by suppliers, measured in dollars per hundred pounds. Quantities demanded and supplied are measured in hundred-pound units. (a) On the axes below, draw the demand curve (with blue ink) and the supply curve (with red ink) for yak butter.

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202 EQUILIBRIUM (Ch. 16) 0 40 60 80 100 Yak butter 20 40 60 80 Price 20 120 Blue line Red line p1 q1 q2 p2 (b) Write down the equation that you would solve to find the equilibrium price. Solve 120 4 p = 2 p 30 . (c) What is the equilibrium price of yak butter? \$25. What is the equilibrium quantity? 20. Locate the equilibrium price and quantity on the graph, and label them p 1 and q 1 . (d) A terrible drought strikes the central Ohio steppes, traditional home- land of the yaks. The supply schedule shifts to 2 p s 60. The demand schedule remains as before. Draw the new supply schedule. Write down the equation that you would solve to find the new equilibrium price of yak butter.
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