# Perfectly Elastic demand and Equilibrium

Assume that the weekly supply of 16 oz bottles of soda at convenience stores in the Twin Cities of Minneapolis and St. Paul is a function of price such that:

Qs = -20 + 80P

Where Q is the number of sodas sold in convenience stores (in thousands) and P is the soda price. Assume demand is perfectly elastic at a price of $ 1.

A)Derive the soda supply curve where price is expressed as a function of output. Calculate the equilibrium level of output and convenience store sales revenue.

B)Derive a second curve based upon the assumption convenience store sales become subject to a 5-cent recycling fee. Calculate the price and quantity effects of the recycling fee. With perfectly elastic demand, who pays the economic burden of such a fee?

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#### Solution Preview

Solution is attached herewith as word document also.

Solution:

Derive the soda supply curve where price is expressed as a function of output. Calculate the equilibrium level of output and convenience store sales revenue.

Qs=-20+80P

80P=20+Qs

P=(20+Qs)/80

P=0.25+0.0125Qs -------------(1)

Demand is perfectly elastic at a price of $1, A firm can sell unlimited quantity at this price. So, equilibrium Price is $1. ...

#### Solution Summary

Solution describes the steps for finding equilibrium price and quantity of soda bottles in case demand is perfectly elastic. It also studies the effect of 5 cent recycling fee on equilibrium.

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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