Question

Given the demand and supply functions for a good, Pa = 120 – 3Q and Ps = 2Q + 25, respectively. If a tax of $15 per unit is imposed, outline the distribution of the tax, that is, calculate the tax paid by the consumer and the producer. A. The consumer now pays $69, an increase of $6 on the original equilibrium price with no tax ($63) while the producer now receives $54, a reduction of $9 on the original equilibrium price with no tax B. The consumer now pays $72, an increase of $9 on the original equilibrium price with no tax ($63) while the producer now receives $57, a reduction of $6 on the original equilibrium price with no tax

How is the answer B? (with working out please)

Answer 1

Pd = 120 - 3Q

Ps = 2Q + 25

At equilibrium,

120 - 3Q = 2Q + 25

120 - 25 = 5Q

95 = 5Q

Q = 19

P = 63   

As the slope of demand curve is 3 and slope of supply curve is 2 which means that demand curve is more inelastic then supply which makes taxes falls more on consumers than producers.

The difference between the maximum price the consumer would pay (120 when 0 units are purchased) and the equilibrium price is 57. The lowest price the seller would receive when 0 units are sold and the equilibrium price is 38. Thus the ratio 57 / 38 = 3 / 2 makes consumers paying 3/5 of the tax while producers paying 2/5 of tax.

Thus consumers would pay (3/5) * 15 = $9 while producer would pay (2/5) * 15 = $6.

Thus option B is correct.

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