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Suppose the demand function is Qd/x = 10,000 - 2Px + 3Py - 4.5M where Px = $100, Py =$50, and M = $2000. Determine the following elasticities and explain whether the respective elasticity is elastic, inelastic, or unitary:

1. Own Price elasticity of good X.

2. Cross price elasticity with good Y.

3. Income elasticity.

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Kritika Krishnakumar
Kritika KrishnakumarLv10
28 Sep 2019
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Related questions

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?

5. The demand curve for a product is given by Qdx = 1,000 - 2Px + .02Pz where Pz = $400. (Hint: If you're not comfortable with the calculus alternatives, compute Q at the given prices, then again with a 1% increase in price. Then figure percentage change in Q over the percentage change in P, %Q/%P).

a. What is the own-price elasticity of demand when Px = $154? Is the demand elastic or inelastic? What would happen to the firm's revenue if it decided to charge a price below $154?

b. What is the own-price elasticity of demand when Px = $354? Is the demand elastic or inelastic? What would happen to the firm's revenue if it decided to charge a price below $354?

c. What is the cross-price elasticity of demand between good X and good Z when Px = $154? Are good X and good Z substitutes are complements?

the demand curve for a product is given by qxd = 1,200 - 3px - 0.1pz where pz = $300.

a. What is the own-price elasticity of demand when Px = $140? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $140?

Own price elasticity:

If the firm prices below $140, revenue will: (increase, decrease or not change)

b. What is the own-price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price above $240?

Own price elasticity:

If the firm prices above $240, revenue will:

c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z substitutes or complements?

Cross-price elasticity:

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