There are two types of consumers of potatoes: 10 are rich and 50 are poor. Every rich consumer has a demand of 0 for a price of $500/ton; and his/her demand decreases by 1 ton each time the price increases by $1/ton. Every poor consumer has a demand of 0 for a price of $280/ton; and his/her demand decreases by 2 tons each time the price increases by $1/ton. Interpret the differences between the demand of the rich and the demand of the poor. What is the total market demand for potatoes? Give the equation of the demand curve Q = D(P)?
To interpret the differences between the demand of the rich and the demand of the poor consumers, we need to analyze their demand functions and how they respond to changes in price.
For the rich consumers, the demand function is given by:
Q_rich = 0 - (P - 500)
Where Q_rich is the quantity demanded by the rich consumers and P is the price in dollars per ton.
This demand function indicates that for every $1 increase in price, the quantity demanded decreases by 1 ton. The initial demand at a price of $500 per ton is 0. This implies that the rich consumers are not willing to purchase any potatoes at this high price.
For the poor consumers, the demand function is given by:
Q_poor = 0 - 2(P - 280)
Where Q_poor is the quantity demanded by the poor consumers and P is the price in dollars per ton.
In this case, for every $1 increase in price, the quantity demanded decreases by 2 tons. The initial demand at a price of $280 per ton is 0.
The differences between the demand of the rich and the demand of the poor consumers can be summarized as follows:
1. Price sensitivity: The rich consumers are less price-sensitive compared to the poor consumers. The demand of the rich consumers decreases by only 1 ton for every $1 increase in price, while the demand of the poor consumers decreases by 2 tons for the same price increase.
2. Initial demand: The rich consumers have a higher initial demand of 0 at a higher price ($500 per ton), while the poor consumers have a lower initial demand of 0 at a lower price ($280 per ton).
The total market demand for potatoes can be obtained by summing the individual demands of the rich and poor consumers:
Q_total = Q_rich + Q_poor
= (0 - (P - 500)) + (0 - 2(P - 280))
= 500 + 560 - 3P
So, the equation of the demand curve Q = D(P) is:
Q = 1060 - 3P