Suppose that the extended (generalized) demand function for good Y is:

Q_{d}^{Y}= 250,000 - 500 P_{Y} -1.5 M + 240 P_{X}

where: Q_{d}^{Y} = quantity demanded of good Y

P_{Y} = Price of good Y

M = Average income of consumers

P_{X} = Price of related good X

a) If M = $ 60,000 and P_{X} = $100, what is the reduced demand function for good Y?

b) Continue using the reduced demand equation from part a,

If M = $60,000, P_{X} = $100, and P_{Y} = $200 then Q_{d}^{Y} = ________

If M = $60,000, P_{X} = $100, and P_{Y} = $300 then Q_{d}^{Y} = ________

Use this information (prices and quantities demanded of good Y) to calculate the price elasticity of demand between these two points on the demand curve of good Y. Show your work.

c) Use your answer to part b. Between these two points on the demand for good Y, is demand elastic, inelastic, or unitary price elastic? Why? What will happen to total revenues if the price increases between these two points on the demand curve?

d) In part b, you found that when:

M = $60,000, P_{X} = $100, and P_{Y} = $200 then Q_{d}^{Y} = ________

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.

If M = $60,000, P_{X} = $50, and P_{Y} = $200 then Q_{d}^{Y} = ________

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

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

f) In part b, you found that when:

M = $60,000, P_{X} = $100, and P_{Y} = $200 then Q_{d}^{Y} = ________

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

g) 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?