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28 Dec 2018

Consider a general demand function for a good, X, that has been estimated as:

Q(d) = 200 â 8Px + 2Py + .4*M, where

Px is the price of the good being studied

Py is the price of a related good, Y

M is per capita income

a) Are X and Y complements, substitutes, or neither? How do you know?

b) Is X a normal good or an inferior good? How do you know?

c) Calculate the direct demand function, assuming that the price of Y is $6 and that per capita income is $38,000.

d) Calculate the inverse demand function, using your answer to c).

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Casey DurganLv2

31 Dec 2018

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The generalized demand and supply functions for good X are

Qd = 10 -2Px - 4P_Y + M Qs = 10 + 2P_X

Where:

Q_D = quantity demanded of good X

P_X = price of good X

M = consumer income

P_Y = price of good Y

Q_S = quantity supplied of good X

P_X = price of good X

A. Are good X and good Y substitutes or complements? Why?

B. Is good X a normal good or an inferior good? Why?

C. What is the demand function when P_Y = $4 and M = $600?

d. Use the demand function you found in part c. and solve for the equilibrium price (P_o) and the equilibrium quantity (Q_o).

e. Find the inverse demand function and the inverse supply function.

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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

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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 = ________

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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?

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M = $60,000, P_X = $100, and P_Y = $200 then Q_d^Y = ________

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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.

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1. The inverse demand function for good X.

2. Whether good Y is a substitute or complement for good X. explain why.

3. Whether doog Z is a substitute or completement for good X. explain why

4. Whether good X is a normal or inferior good. explain why