Equilibrium Price - Managerial Economics

Need help understanding (need to see) how these problems are worked.

(See attached file for full problem description with equations and data table)

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1. Suppose the supply function for product X is given by Q x = -50 + 0.5 Px - 5Pz.

a. How much of product X is produced when Px = $500 and Pz = $30?
b. How much of product X is produced when Px = $50 and Pz = $30?
c. Suppose Pz = $30. Determine the supply function and inverse supply function for good X. Graph the inverse supply function.

2. The demand for good X is given by

d
Q x = 1,200 - ½ Px + 1/4Py - 8 Pz + 1/10 M

Research shows that the prices of related goods are given by Py = $5,900 and
Pz = $90, while the average income of individuals consuming this product is M = $55,000.

b. Indicate whether goods Y and Z are substitutes or complements for good X.
c. Is X inferior or a normal good?
d. How many units of good X will be purchased when Px = $4,910?
e. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X.

3. Suppose demand and supply are given by

D s
Q x = 7 - ½ Px and Q x = ¼ Px - ½

a. Determine the equilibrium price and quantity. Show the equilibrium graphically.
b. Suppose a $6 excise tax is imposed on the good. Determine the new equilibrium price and quantity.
c. How much tax revenue does the government earn with the $6 tax?

4. Suppose the demand function for a firm's product is given by

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In Q x = 3- 0.5 In Px - 2.5 In Py + In M + 2 In A

Where
Px = $10,
Py = $4,
M = $20,000, and
A = $250.

a. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic, or unitary elastic.
b. Determine the cross-price elasticity of demand between good X and good Y, and state whether these two goods are substitutes or complements.
c. Determine the income elasticity of demand, and state whether good X is a normal or inferior good.
d. Determine the own advertising elasticity of demand.

5. Suppose the own price elasticity of demand for good X is -2, its income elasticity is 3, its advertising elasticity is 4, and the cross -price elasticity of demand between it and good Y is -6. Determine how much the consumption of this good will change if:
a. The price of good X increases by 5 percent.
b. The price of good Y increases by 10 percent.
c. Advertising decreases by 2 percent.
d. Income falls by 3 percent.

6. You are the manager of a firm that sells a leading brand of alkaline batteries. The data for the product is attached. Specifically, the file contains data on the natural logarithm of your quantity sold, price, and the average income of consumers in various regions around the world. Use this information to perform a log-linear regression, and then determine the likely impact of a 3 percent decline in global income on the overall demand for your product.
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