Question

14. Effect of a tax on buyers and sellers The following graph shows the daily market for jeans when the tax on sellers is set at $0 per pair Suppose the government institutes a tax of $5.80 per pair, to be paid by the seller. (Hint: To see the impact of the tax, enter the value of the tax in the Tax on Sellers field and move the green line to the after-tax equilibrium by adjusting the value in the Quantity field. Then, enter zero in the Tax on Sellers field. You should see a tax wedge between the price buyers pay and the price sellers receive.) Use the graph input tool to help you answer the following questions. You will not be scored on any changes you make to this graph. Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will change accordingly. Graph Input Tool Market for Jeans 50 S + Tax Quantity (Pairs of jeans) Demand Price (Dollars per pair) Supply 75.00 Supply Price (Dollars per pair) 22.80 PRICE (Dollars per pair) Supply Shifter Tax on Sellers (Dollars per pair) 5.80 Demand 0 50 100 150 200 250 300 350 400 450 500 QUANTITY (Pairs of jeans)

Answer 1

	Quantity	Price buyers pay	Price Sellers Receive
Before Tax	250	$ 25	$ 25
After Tax	230	$ 30	$ 24.20

Here I don't have access to graph tool so I have derived the equation of supply as well as demand curve.

Demand function, P = a - bQ

As we can see when P = 0, Q = 350

0= a - 3506

a=3506

When P = $ 25, Q = 250

+ 25 = a - 2506

+ 25 = 3500 - 250

+ 25 = 1006

=b= 0.25

Therefore, a = 350 × 0.25 = 87.5

Demand, P = 87.5 - 0.25Q

Now deriving supply function, P = 15 + cQ

When P = 25 , Q = 250

25 = 15 + 250c

=> 250c = 10

=> C = 0.04

Supply, P = 15 + 0.04Q

When a tax of $ 5.80 / pair is imposed then the buyers will pay a price that is Pb = Ps + 5.80

Demand, P + 5.8 = 87.5 - 0.25Q

P = 81.7 - 0.25Q

Supply, P = 15 + 0.04Q

Equate both, 81.7 - 0.25Q = 15 + 0.04Q

=> 0.29Q = 66.7

=> Q = 230 units

P = 15 + 0.04Q = 15 + 0.04×230 = $ 24.2

Price paid by buyer, P = 87.5 - 0.25Q = $ 30

Calculating the tax burden

Burden on buyers = $ 30 - $ 25 = $ 5 / pair

Burden on sellers = $ 25 - $ 24.2 = $ 0.80 / pair

	Tax burden	Elasticity
Buyers	$ 5	Inelastic
Sellers	$ 0.80	Elastic

Calculation of elasticity

器可

E - (Q2 – Qı)(P2 + Pi) (Q2 +Qi)(P2 - P1)

When P1 = 25 , Q1 = 250

P2 = 30, Q2 = 230

(230 - 250)(30 + 25) (2304 250)(30-25)

Elasticity of demand = -0.46

Now calculating elasticity of supply

P1 = 25 , Q1 = 250

P2 = 24.2, Q2 = 230

(230 – 250) (24.2 + 25) E, = (230+ 250) (24.2 – 25)

Elasticity of supply = 2.56

The burden of tax falls more heavily on the less elastic side of the market.

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