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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?

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Darryn D'Souza
Darryn D'SouzaLv10
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?

Quantities Purchased Quantities Purchased Income Prices Good X Good Y $30,000 Px = $6, Py = $3 2 20 50,000 Px = $6, Py = $4 5 10

Ā  Ā  Quantity Purchased Quantity Purchased
Income Price Good X Good Y
$30,000 Px = $6; Py = $3 2 20
$50,000 Px = $6; Py = $4 5 10

Refer to Table.

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

B. 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.

A firm's demand function for product X has the following question:
Qx = 1420 -20Px- 10Py + 0.02M + 0.04A
where Qx is the quantity purchased, Px is the price of X, Py is the price charged for a related good, M is per capita income, and A is the dollar spent on advertising.

Suppose the firm spends $1200 per week on advertising, that Py=$40and that income is $8,000 per capita.

a.) Write the equation of the demand curve for product X.
b.) Briefly explain how product X is related to product Y. (Is Y a substitute or a compliment, and how can you tell?)
c.) Given the stated values of the other independent variables, calculate the point price elasticity of demand for X at Px =$50.
d.) Given the stated values of M, A, and Py at what price and quantity demanded will total revenue maximized? What will the maximum revenue be?

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