Question

Suppose that the extended (generalized) demand function for good Y is: Qd Y= 250,000 – 500 PY – 1.5 M + 240 PX

where:

Qd Y = quantity demanded of good Y

PY = Price of good Y

M = Average income of consumers

PX = Price of related good X

1.) You know that when M = $60,000, P_X= $100, and P_Y= $200 then Q_d^Y= 84,000

Now let’s suppose that the price of the related good X decreases from $100 to $50, but income remains constant (at $60,000).  Assume that the price of good Y is also constant at $200.

You also know when M = $60,000, P_X= $50, and P_Y= $200 then Q_d^Y= 34,000

Use these prices of good X and the quantities demanded of good Y to calculate the cross-price elasticity of the demand of good Y when the price of good X decreases from $100 to $50.

2) Consider your answer to part 1.  Based on the value of the cross-price elasticity of demand you just estimated, are goods X and Y substitutes, complements or unrelated?  Why?

3) You know when M = $60,000, P_X= $100, and P_Y= $200 then Q_d^Y= 84,000

Now let’s suppose that consumer income increases from $60,000 to $80,000, but the price of good X remains constant (at $100).  Assume that the price of good Y is also constant at $200.

If M = 80,000, P_X= $100 and P_Y = $200 then Q_d^Y= __________?

Use these income levels and quantities demanded of good Y to calculate the income elasticity of the demand for good Y when income increases from $60,000 to $80,000.

Show your work

4) Consider your answer to part f. Based on the value of the income elasticity of demand you just estimated, is good Y normal, inferior or income independent?

Answer 1