true or false, and explain why ?

1. Total revenue is maximized at the midpoint of a downward sloping linear demand curve where the price elasticity of demand is -1.
2. A good whose income elasticity of demand is negative is called an inferior good.
3. An increase in the price of corn results in a downward shift in the demand curve for corn.
4. When the demand curve shifts, the change in equilibrium price will be smaller the closer the price elasticity of supply is to 0.
5. If a doubling of income results in a halving of the quantity demanded of a good the good must be a normal good.