The market supply for ice cream in Helltown is 2,000 tons for a price of $200 a ton, and 5,000 tons for a price of $500 a ton. Between these two prices market supply is a straight line.

1. What is the equation of the supply curve, Q = S(P)? and of the inverse supply curve?

2. There are two types of consumers of ice cream: 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 dierences between the demand of the rich and the demand of the poor.
What is the total market demand for ice cream? Give the equation of the demand curve Q = D(P) and of the inverse demand curve.

3. Plot market demand and market supply and nd the equilibrium price. How much ice cream will the rich buy in equilibrium? and the poor?

4. A wondrous social reform makes all poor consumers rich, without even making the rich poorer. As a result, all 60 consumers now have the demand curve of the rich in 2. What is the new equilibrium?

5. Does the social reform hurt the rich? explain how and why.