EconS 305 - Market Equilibrium Eric Dunaway Washington State University
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August 28, 2015
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Introduction
General announcement: My o¢ ce has changed to Hulbert Hall 323D. I have updated and reuploaded the syllabus. Yesterday, we described what factors in‡uence the amount of goods bought and sold in a market. Today, we’ll follow up by letting those factors form an equilibrium. First, something fun: https://wetheeconomy.com/…lms/supply-and-dance-man/
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Market Equilibrium
With supply and demand functions, we have everything we need to …nd an equilibrium. Remember that in equilibrium, supply must equal demand.
We can …nd the market equilibrium either graphically or mathematically. Graphically, we can simply put our two curves on the same graph and …nd the intersection point. Let’s look at our example from yesterday.
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Market Equilibrium
We can also solve for the equilibrium mathematically using the supply and demand functions. We’ll use the reduced ones for simplicity 20 4 + p 3 3 6 D (p, 20, 25) = 30 p 7
qS
= S (p, 2) =
qD
=
In equilibrium, we must have that the quantity supplied equals the quantity demanded, i.e., qS = qD . As a note, I didn’t vet these equations before I used them here. The algebra is a bit of a nightmare. An exam question would use something much nicer.
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Market Equilibrium Using the fact that supply must equal demand in equilibrium, qS = qD 6 20 4 + p = 30 p 3 3 7 46 110 p = 21 3 385 p = 16.7 23 and plugging this number back into the demand (or supply) function gives us the equilibrium quantity q = 30
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Market Equilibrium
Let’s look at another example. Consider a market with the following inverse demand and supply functions, 1 qD 2 p = 2 + qS
p = 8
Can we use the inverse demand and supply functions to …nd our equilibrium?
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Market Equilibrium Yes we can! They’re mathematically equivalent, so we will reach the same solution. Since both inverse functions are equal to the price, I can just set them equal to one another p = p 1 qD = 2 + qS 2
8
and since qS = qD in equilibrium, we can just call it q. 8
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1 q = 2+q 2 3 q = 6 2 q = 4
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Market Equilibrium
All that we need to do now is plug the equilibrium quantity back into either the inverse demand or supply functions to get our equilibrium price p = 2+q = 2+4 = 6 and we have our equilibrium price of 6 and quantity of 4.
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Market Equilibrium
How do markets get to equilibrium? Typically, when markets are out of equilibrium, over time, the market will naturally return to equilibrium. We call this the invisible hand, a term coined by Adam Smith
Practically, when the price is too high, suppliers are providing too much to the market and the demanders don’t want all of it. To get rid of their excess supply, the suppliers are forced to lower their price, pushing the market to equilibrium.
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Market Equilibrium
Using our …rst example, let the market price, p, be 25 which is higher than the equilibrium price of p = 16.7. We can plug this value into our supply and demand functions to get their respective quantities qS qD
20 4 + (25) = 26.7 3 3 6 = 30 (25) = 8.6 7
=
As we can see, there is much more supplied than demanded, and our excess supply is Excess Supply = qS
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qD = 26.7
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Market Equilibrium Similarly, if the price were too low, we would have excess demand. Consumers would want more than is being provided to the market, and would be willing to pay a higher price to persuade the producers to provide it. In this example, let p = 10. Plugging this into our supply and demand functions yields qS qD
20 4 + (10) = 6.7 3 3 6 = 30 (10) = 21.4 7
=
For this case, our excess demand is Excess Demand = qD Eric Dunaway (WSU)
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Market Shocks
Now that we have equilibrium all …gured out, let’s look at market shocks. A market shock is when some external force changes either the supply curve, the demand curve, or both.
Let’s look at two case studies. But …rst...
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Market Shocks
Recall the external factors that in‡uence supply and demand: Demand Price Income Tastes Information Prices of other goods and services Regulations
Supply Price Costs Regulations
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Carnival Cruise
In late 2013, a Carnival Cruise had a catastrophic failure with its sewage system, and travellers were stuck on the boat for over a week with raw sewage coming down the walls. Economically, how do you think this shocked the cruise market?
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Carnival Cruise
This was a type of information shock, where all of the bad publicity generated by the "poop cruise" caused a reduction in demand for cruises. People didn’t want to go anywhere near a cruise boat for a long time. "What else might be wrong?" "I need a shower!"
We would model this as a leftward shift in the demand curve. We could expect there to be less cruises at a lower price in equilibrium.
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California Drought
California is in the middle of the worst drought in recorded history. California also produces 80% of the world’s supply of almonds. Economically, what would happen to the market for almonds if the price of water rises in California?
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California Drought
This is a type of cost shock on the market for almonds. Part of the increased cost of water will be passed on to those consuming almonds. We model this as a leftward shift of the supply curve. We could expect there to be less almonds supplied and at a higher price in equilibrium.
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Market Shocks
While inspired by real world events, those are just two examples of shocks to the market. It is important to recognize how events correlate to all of the external factors that in‡uence supply and demand, and then determine which curve shifts and in what direction.
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Market Shocks In general, when supply or demand shift, we can expect the following results p q Supply " # Supply ! # " Demand # # " Demand ! " Notice that when demand shifts, both the equilibrium price and quantity move in the same direction. This is because the new equilibrium point is found by moving either up or down the supply curve, which is positively sloped. This also explains why shifts in the supply curve cause price and quantity to move in opposite directions since the new equilibrium is found by moving along the negatively sloped demand curve.
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Market Shocks
What if both supply and demand change at the same time? In this case, one of the changes in price or quantity will always be the same direction for both shifts. The other will depend on the magnitude of each shift, itself. Let’s look a couple of examples.
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Market Shocks
Notice that when supply and demand both shift to the left, the equilibrium quantity decreases both times. Thus, we know that when both curves shift left, the equilibrium quantity decreases. The opposite holds true for when both curves shift to the right. The equilibrium quantity will increase.
The equilibrium price, however, depends on the magnitudes of the shifts. It will either increase or decrease depending on which curve shifts more. "More" is a bit of a vague description. The relative slopes of the curves as well as how far they shift both in‡uence the equilibrium price heavily.
Let’s see what happens when the curves move in opposite directions.
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Market Shocks
This time, when supply shifts to the left and demand shifts to the right, both shifts cause an increase in the equilibrium price. This is due to the supply curve’s shift causing upward movement on the demand curve and vice-versa. Again, if the supply curve shifted to the right and the demand curve shifted to the left, the result would be the opposite.
The change in equilibrium quantity, however, is now ambiguous. The relative shifts and shapes of the supply and demand curve will determine its direction.
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Market Shocks
We can summarize all four possible dual curve shifts as follows:
Supply , Supply , Supply !, Supply !,
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Demand Demand ! Demand Demand !
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Summary
Supply and Demand come together to give an equilibrium quantity and price for a market. This equilibrium is naturally forming by the invisible hand, as it works to eliminate excess supply or demand. Shocks can a¤ect either the supply or demand curve, causing new equilibria to emerge.
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Preview for Monday
Economic Welfare We will see how well o¤ the Supply and Demand model makes consumers.
Perlo¤, Chapter 9, sections 2 and 3.
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Assignment 3
1. Consider the three bacon market situations below. In each, draw the initial supply and demand equilibrium in the bacon market, then show which curve(s) shifts and where the new equilibrium is located. Explain your reasoning. a. A reputable news agency reports that eating bacon leads to health bene…ts. b. A bacon producing …rm su¤ers a labor strike, forcing them to raise wages for their employees. c. The government starts an ad campaign for the bene…ts of consuming bacon. To …nance this ad campaign, the government imposes a per unit tax on bacon producers.
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