If consumers buy 1000 bottles of beer per week, and if the price of beer rises by $0.50 per bottle, then the consumers' surplus will decrease by $500. True, False, or Uncertain. Explain your answer.I am retiring this question. Using Jacob's numbers, let's assume that the initial price of beer is $2 per bottle and that the demand curve is linear. Furthermore, let's assume that for every $0.50 increase in price, the quantity demand falls by 200 units. These assumptions imply that the demand curve intercepts the price axis at $4.50. The graph below illustrates our situation.
If the price of beer rises from $2 to $2.50, the quantity demanded falls to 800. The resulting loss in consumer surplus is shown as the yellow area. A simple calculation shows that this area equals $450. That is, CS will fall by less than $500.
7 comments:
The correct answer to this question is "uncertain". There is not enough information provided to determine how much consumer surplus will decrease. Because we are not given the equilibrium price of the beer at the 1,000 bottle equilibrium quantity and because we are not given how much demand decreases per a certain amount of money, it is therefore impossible to determine how much the price decrease would influence the quantity demanded as well as the consumer surplus lost.
-Bethany McFarland
I would say true because no matter what the original price is, if there is a $.50 per bottle rise on price that would equal a decrease of $500 of consumer surplus per week on the 1000 bottles that are sold. The consumer surplus is decreasing by $.50 per bottle and there are 1000 bottles which would equal the $500 loss in consumer surplus.
Hint: Imagine a downward sloping demand curve for beer where 1000 units are being consumed. Map out the change in consumer surplus when the price rises by $0.50. Compare the CS before the price increase with that after the price increase.
It can be inferred, not only by process of elimination, that consumer surplus would not decrese by five hundred dollars. consumer surplus would decrease by fifty cents and X amount of consumed bottles. As a downward sloping demand curve would suggest, depending on how much beer cost in the begining- ex. $2 means $2.5 after the increase and a 200 beer decrease in consumption.
So the correct answer is false. CS would not decrease by $500.
Jacob, you're almost there, but still missing an important element of the analysis. You've said CS will not decrease by exactly $500. But, will CS decrease by more or less than $500? Explain.
ok,
To find the area of consumer surplus is the formula (Base*Height)/2. Assuming two things in this formula:
1. Demand curve is linear
2. Price of Beer at equilibrium is $2.00
So,
We know the base of the original consumer surplus (1000). To find the height, we need to find the intersection with the vertical axis. IF demand is linear and price is $2. We can find the slope of the Demand curve leads us to $2000 as our intersection point. meaning there would be one person out there who would pay $2000 for 1 beer Now we have a height, $1998 ($2000 minus the origenal $2 ). Our formula now reads:
CS= (1000*$1998)/2 = $999,000
IF the price of Beer goes up $.5, as I stated in my previous answer, only 800 beers will be bought. making our new base 800 and our new height 1997.5.
CS=(800*$1997.5)/2 = $799,000.
If the market price of Beer is raised $.5, then, consumer surplus would NOT fall $500. It would fall a substantial more than $500. Depending on the origenal price of beer. In this example, consumer surplus would drop by $200,000.
Jacob, your value for the price intercept is way off. If you are assuming a linear demand and an initial price of $2 and that quantity demanded will drop by 200 units for every $0.50 increase in price, then the price intercept must be $4.50.
I'm going to retire this question. See the main question for the correct answer.
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