1. The demand curve is given by
QD = 500 - 5PX + 0.5I + 10PY - 2PZ
where
QD = quantity demanded of good X
PX = price of good X
I = consumer income, in thousands
PY = price of good Y
PZ = price of good Z
a. Based on the demand curve above, is X a normal or an inferior good?
b. Based on the demand curve above, what is the relationship between good X and good Y?
c. Based on the demand curve above, what is the relationship between good X and good Z?
d. What is the equation of the demand curve if consumer incomes are $30,000, the price of good Y is $10, and the price of good Z is $20?
e. Graph the demand curve that you found in (d), showing intercepts and slope.
f. If the price of good X is $15, what is the quantity demanded? Show this point on your demand curve.
2. Suppose the demand and supply curves for a product are given by
QD = 500 - 2P
QS = -100 + 3P
a. Graph the supply and demand curves.
b. Find the equilibrium price and quantity.
c. If the current price of the product is $100, what is the quantity supplied and the quantity demanded? How would you describe this situation, and what would you expect to happen in this market?
d. If the current price of the product is $150, what is the quantity supplied and the quantity demanded? How would you describe this situation, and what would you expect to happen in this market?
e. Suppose that demand changes to QD = 600 - 2P.
Find the new equilibrium price and quantity,
and show this on your graph.
3. For each of the following cases, calculate the arc price elasticity of demand, and state whether demand is elastic, inelastic, or unit elastic.
a. When the price of milk increases from $2.25 to $2.50 per gallon, the quantity demanded falls from 100 gallons to 90 gallons.
b. When the price of paperback books falls from $7.00 to $6.50, the quantity demanded rises from 100 to 150.
c. When the rent on apartments rises from $500 to $550, the quantity demanded decreases from 1,000 to 950.
4. For each of the following cases, what is the expected impact on the total revenue of the firm? Explain your reasoning.
a. Price elasticity of demand is known to be -0.5, and the firm raises price by 10 percent.
b. Price elasticity of demand is known to be -2.5, and the firm lowers price by 5 percent.
c. Price elasticity of demand is known to be -1.0, and the firm raises price by 1 percent.
d. Price elasticity of demand is known to be 0, and the firm raises price by 50 percent.