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Suppose the demand for good X is given by Qxd = 500 – 10Px + 2Py + 0.7I, where Px is the price of good X. Py is the price of some other good Y, and I is income. Assume that Px is currently $10, Py is currently $5, and I is currently $100. What is the elasticity of demand for good X with respect to its price at the current situation? Interpret your result. What is the cross-price elasticity of the demand for good X with respect to the price of good Y at the current situation? What can you tell about X and Y. What is the income elasticity of demand for good X at the current situation? Comment on the type of good X.

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Related questions

Suppose demand for good A is given by Qa=500-10Pa+2Pb+0.7Y where PA is the price of good A, Pb is the price of some other good b and Y is income. Assume that Pa is currently $10, Pb is currently $5 and Y is currently $100.
i) What is the elasticity of demand for good A at the current situation?

ii) What is the cross-price elasticity of demand for good A with respect to good B at the current situation?

iii) Based on what you found in ii, what can you conclude about the relationship between good A and good B?

The extended demand function of good Y is:

QdY = 1400-20PX - 10Py+ 0.1M

where: QdY= quantity demanded of good Y

PY = Price of good Y

M = Average consumer income

Px = Price of related good X (related in consumption to good Y)

a)

If M=10,000, Py=50, and Px=50then Qdx=____

If M=20,000, Py=50, and Px=60then Qdx=_____

c) Use these two prices and quantities demanded to calculate the value of the price elasticity of demand between these two points on the demand curve for good Y (use the arc elasticity formula). Show your work and interpret your answer. What will happen to revenues for the suppliers of good Y as the price of good Y decreases from Px=50 to Px=60? WHY?

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

QdY= 250,000 - 500 PY -1.5 M + 240 PX

where: QdY = quantity demanded of good Y

PY = Price of good Y

M = Average income of consumers

PX = Price of related good X

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

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

If M = $60,000, PX = $100, and PY = $200 then QdY = ________

If M = $60,000, PX = $100, and PY = $300 then QdY = ________

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, PX = $100, and PY = $200 then QdY = ________

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, PX = $50, and PY = $200 then QdY = ________

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, PX = $100, and PY = $200 then QdY = ________

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 , PX = $100 and PY = $200 then QdY = _________

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?

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