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Magazine Chapter 9: Q5. (page 344)
About 100 million pounds of jelly beans are consumed in the United States each year, and the price has been about 50 cents per pound. However, jelly bean producers feel that their incomes are too low and have convinced the government that price supports are in order. The government will therefore buy up as many jelly beans as necessary to keep the price at \(1 per pound. However, government economists are worried about the impact of this program because they have no estimates of the elasticities of jelly bean demand or supply.
a. Could this program cost the government more than \)50 million per year? Under what conditions?Could it cost less than \(50 million per year? Under what conditions? Illustrate with a diagram.
b. Could this program cost consumers (in terms of lost consumer surplus) more than \)50 million per year? Under what conditions? Could it cost consumers less than $50 million per year? Under what conditions? Again, use a diagram to illustrate.
Short Answer
a. If the price elasticity of supply is greater than 1, then the program will cost the government more than $50 million per year. If the price elasticity of supply is less than 1, then the program will cost the government less than $50 million per year.
b. If the price elasticity of demand is greater than 1, then the program will cost the consumers more than $50 million per year. If the price elasticity of demand is less than 1, the program will cost the consumers less than $50 million per year.
Step by step solution
Step 1. Conditions under which the program will cost the government more than $50 million or less than it
The condition under which the government cost will exceed more than $50 million per year.
Price elasticity of supply shows the extent of change in supplied quantity relative to the change in price. If the ratio of change in the supplied quantity is greater than the ratio change in price, then the elasticity of supply would be greater than 1. It will cause government costs to exceed more than $50 million.
The following graph illustrates the situation under which the government cost will exceed more than $50 million.
To support the minimum price, the government had to buy quantity q. The extent of the gap between quantity q and 100 is greater than the extent of the gap between 1 and 0.5. Thus, the government cost is more than $50 million.
The condition under which the government cost will be lower than $50 million per year.
If the ratio of change in the supplied quantity is lower than the ratio change in price, then the elasticity of supply would be less than 1. It will cause the government鈥檚 cost not to exceed more than $50 million.
The following graph illustrates the situation under which the government cost will be lower than $50 million.
To support the minimum price, the government had to buy quantity q. The extent of the gap between quantity q and 100 is lower than the extent of the gap between 1 and 0.5. Thus, the government cost will be lower than $50 million.
Step 2. Conditions under which the program will cost consumers more than $50 million or less than it
The condition under which this program would cost consumers more than $50 million per year.
Price elasticity of demand shows the extent of change in demanded quantity relative to the change in price. If the ratio of change in the demanded quantity is greater than the ratio change in price, then the elasticity of demand would be greater than 1. In this case, the program will cost more than $50 million to consumers.
The following graph illustrates the situation under which the program will cost consumers more than $50 million.
To support the minimum price, the government had to buy quantity q. The extent of the gap between quantity q and 100 is greater than the extent between 1 and 0.5. Thus, the program will cost more than $50 million to the consumers.
The condition under which this program would cost consumers less than $50 million per year.
If the ratio of change in the demanded quantity is lower than the ratio change in price, then the elasticity of demand would be less than 1. In this case, the program will cost less than $50 million to consumers.
The following graph illustrates the situation under which the program will cost less than $50 million to consumers.
To support the minimum price, the government had to buy quantity q. The extent of the gap between quantity q and 100 is lower than the extent of the gap between 1 and 0.5. Thus, the program will cost less than $50 million to the consumers.
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