Question

In a given market, supply is given by the equation p = q^2 + 20, and the demand is given by the equation p = 140 − 3q^2 − 6q. A tax of $42 is placed on the production of the market’s product. Find the after-tax equilibrium point for this market, that is, both the quantity and the unit price in equilibrium.

Answer 1

Supply price: p = q² + 20

Demand price: p = 140 - 3q² - 6q

A $42 tax will lower effective price received by producers by $42 at every output level, so supply curve will left leftwrd and new supply function will be:

p - 42 = q² + 20

p = q² + 62

Equating demand price and supply price,

140 - 3q² - 6q = q² + 62

4q² + 6q - 78 = 0

2q² + 3q - 39 = 0Solving this quadratic equation using online solver,

q = 3.72 or q = - 5.23 (Inadmissible, since q >= 0)

When q = 3.72,

p = (3.72)² + 62 = 13.84 + 62 = $75.84 (Price paid by consumers)

Price received by producers = $75.84 - $42 = $33.84