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a. Cross elasticity (4pts): Suppose that when the price of good X rises by 50%, the quantity of good Y demanded rises by 40%.

i) calculate the cross elasticity between goods X and Y.

ii) Determine whether good X and Y are substitutes or compliments. How do you know?



Please show all work and please explain it.Thank you.

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Tod Thiel
Tod ThielLv2
29 Sep 2019

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Related questions

(a) Explain why the cross elasticity of demand for substitute goods is positive and the cross elasticity of demand for complements is negative.

(b) Explain why the price elasticity of demand changes along a linear demand curve.

(c)

Income Px Py Quantity of good x Quantity of good y
$30,000 $6 $3 2  20 
$50,000 $6 $4  5 10

(i) Using the information in the table, calculate the income elasticity of demand for good X and characterize the good. Use the midpoint formula.

(ii) Can you calculate the income elasticity of demand for good Y? If you can, show your calculation and characterize the good. If you cannot, explain 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?

1. Calculate the price elasticity for the following good. State whether the price elasticity of demand is elastic, unit elastic, or inelastic. Will revenue rise, decline, or stay the same with the given change in price? Be sure to show your work. The price of water beds rises from $500 to $600. Quantity demanded falls from 100,000 to 80,000.

2. Calculate the income elasticity of demand for the following good. State whether it is a luxury, a necessity, or an inferior good. Explain. Show your work. As income decreases from $20,000 to $18,000 per year, demand for summer cottages in Vermont decreases from 80 to 75.

3. When the price of ketchup rises by 15 percent, the demand for hot dogs falls by 10 percent. Calculate the cross-price elasticity of demand. Are the goods complements or substitutes?

4. Use the accounts listed below to answer the following questions about the profit of a retail business.

Total Revenue

$80,000

Hired Labor

$30,000

Inventory purchased for resale

$20,000

Interest that the owner could have earned on an alternative investment

$2,000

Income that the owner could have earned by renting the firm

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