The demand for TOMS shoes is q=104-2p and the inverse supply is given as p=q/4+33. A...

The demand for TOMS shoes is q=104-2p and the inverse supply is given as p=q/4+33. A tax of $2 per pair of shoes is imposed. The number of pairs of TOMS sold falls. By how much does it fall?

Expert Solution

Demand: Q = 104 - 2p

Supply: p = (Q / 4) + 33

or

Supply: Q = 4p - 132

At equilibrium, demand equals supply,

104 - 2p = 4p - 132

p = 39.33

At this price, q = 25.33

When a tax is imposed of $2:

At a tax of $2, tax will be shared among both buyers as well as sellers which will fall in the ratio of (demand curve touching price axis - equilibrium price) to (equilibrium price - supply curve touching price axis) which is (52 - 39.33) / (39.33 - 33) = 12.67 / 6.33

Burden on consumers would be [12.67 / (12.67 + 6.33)] of total tax which is 66.68% rounding to 0.6668 * 2 = $1.33 while burden on producer is [6.33 / (12.67 + 6.33)] which is 33.31% totaling of 0.3331 * 2 = $0.66

Price paid by buyer becomes $40.66 while seller receive $38.66. At a price of $40.66, demand would be Q = 104 - 2 * 40.66 = 22.68 units.

Thus demand fall by 25.33 - 22.68 = 2.65

Rahul Sunny answered 8 months ago

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