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Equilibrium Price and Quantity Demand

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Show the equilibrium price and quantity for a given supply and demand curve and graph their relationship.

Annual demand and supply for the Electronic firm is given by:
QD = 5,000 + 0.5 I + 0.2 A - 100P, and
QS = -5000 + 100P
Where, Q is the quantity per year, P is price, I is income per household, and A is advertising expenditure.

a. If A = $10,000 and I = $25,000, what is the demand curve?
b. Given the demand curve in part a., what is equilibrium price and quantity?
c. If consumer incomes increase to $30,000, what will be the impact on equilibrium price and quantity?

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Solution Preview

Please view the attached Word document for the required graph.

Qd = 5,000 + 0.5I + 0.2A - 100P
Qs = -5,000 + 100P

a) If A = $10,000 & I = $25,000
Qd = 5,000 + 0.5 (25,000) + 0.2 (10,000) - 100P
= 5,000 + 12,500 + 2,000 - 100P
= 19,500 - 100P

b) Qd = 19,500 - 100P
Qs = -5,000 + 100P
At equilibrium: Qd = Qs

Therefore,
19,500 - 100P = -5,000 +100P
200P = ...

Solution Summary

This posting provides a thorough, step by step analysis illustrating how to solve for this equilibrium price problem. All required work is provided, along with a Word attachment with the required graphing.

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Similar Posting

Equilibrium price and quantity, elastic demand, inelastic supply

1. Suppose the demand is Q = 10 - P and the supply is Q = P + 4. Please verify that the following table gives the quantity demanded and supplied at each given prices. What is the equilibrium price and quantity sold under perfect competition?

Price Quantity Quantity
Supplied Demanded
1 5 9
1.5 5.5 8.5
2 6 8
2.5 6.5 7.5
3 7 7
3.5 7.5 6.5
4 8 6
4.5 8.5 5.5
5 9 5
5.5 9.5 4.5

2. Suppose a $1 per unit tax is levied on consumers so that the buyers pay $1 higher than the sellers, fill in the following table and derive the equilibrium quantity sold as well as the price a buyer pays and the price a seller receives.

Tax Buyer
Buyer Seller Quantity Quantity
Price Price Supplied Demanded
2 1
2.5 1.5
3 2
3.5 2.5
4 3
4.5 3.5
5 4
5.5 4.5
6 5
6.5 5.5

3. Suppose a $1 per unit tax is levied on producers so that the sellers receive $1 less than the buyers pay, fill in the following table and derive the equilibrium quantity sold as well as the price a buyer pays and the price a seller receives.

Tax Seller
Buyer Seller Quantity Quantity
Price Price Supplied Demanded
1 0
1.5 0.5
2 1
2.5 1.5
3 2
3.5 2.5
4 3
4.5 3.5
5 4
5.5 4.5

Exercise 1: Tax Burden

1. Suppose the demand is Q = 10 - P and the supply is Q = P + 4. Please verify that the following table gives the quantity demanded and supplied at each given prices. What is the equilibrium price and quantity sold under perfect competition?

Price Quantity Quantity
Supplied Demanded
1 5 9
1.5 5.5 8.5
2 6 8
2.5 6.5 7.5
3 7 7
3.5 7.5 6.5
4 8 6
4.5 8.5 5.5
5 9 5
5.5 9.5 4.5

2. Suppose a $1 per unit tax is levied on consumers so that the buyers pay $1 higher than the sellers, fill in the following table and derive the equilibrium quantity sold as well as the price a buyer pays and the price a seller receives.

Tax Buyer
Buyer Seller Quantity Quantity
Price Price Supplied Demanded
2 1 5 8
2.5 1.5 5.5 7.5
3 2 6 7
3.5 2.5 6.5 6.5
4 3 7 6
4.5 3.5 7.5 5.5
5 4 8 5
5.5 4.5 8.5 4.5
6 5 9 4
6.5 5.5 9.5 3.5

3. Suppose a $1 per unit tax is levied on producers so that the sellers receive $1 less than the buyers pay, fill in the following table and derive the equilibrium quantity sold as well as the price a buyer pays and the price a seller receives.

Tax Seller
Buyer Seller Quantity Quantity
Price Price Supplied Demanded
1 0 4 9
1.5 0.5 4.5 8.5
2 1 5 8
2.5 1.5 5.5 7.5
3 2 6 7
3.5 2.5 6.5 6.5
4 3 7 6
4.5 3.5 7.5 5.5
5 4 8 5
5.5 4.5 8.5 4.5

Exercise 2: Tax Burden (Continued)

Draw two diagrams to show the effect of a tax on the equilibrium buyer and seller prices as well as the equilibrium quantity sold. One with a relatively elastic demand and an inelastic supply. The other with a relatively inelastic demand and an elastic supply. Compare these two cases in terms of the impact on the buyer price and the seller price.

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