The private marginal benefit associated with a product’s consumption is pmb = 540 − 6q and the private marginal cost associated with its production is pmc = 8q. furthermore, the marginal (external) damage associated with this good’s production is md = 4q. to correct the externality, the government decides to impose a tax of t per unit sold. what tax t should it set to achieve the social optimum?

Tax = 120 per unit

Explanation:

First lets calculate Socially optimum Marginal Profit,

This can be computed by factoring in the marginal external benefit in the costs.

thus,

PMB = (PMC + MD)

This gives us the socially profit maximizing level of Product Q in quantity produced terms. we solve for Q the above equation. As generally profit is maximized at Marginal cost = Marginal Revenue

540 - 6Q = 8Q + 4Q

540 = 18Q

Q = 30 units

Since the tax amount should equal the value of marginal external damage so the amount of tax at socially optimum level thus is,

MD = T,

that gives T = 4 * 30 = 120 per unit

This shall then give the revised Marginal cost function of

Revised marginal cost = 8Q + 120. This corrects the externality by making production more expensive.

Hope that helps.

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

answer; i believe the correct answer is (tall); ///good luck