Question

Suppose that the supply and demand for good H is described by the following equations:

QS= - 150+0.40P

QD = 600-0.2P

The production of H also creates marginal external costs of $165 per unit of H. Assuming that H is sold in

a competitive market, what is the market price? How many units of good H will be produced per year at

that price? What is the socially efficient output of H? Will taxing H @12.5 percent be socially optimal?

What alternate tax policy you can suggest to achieve social efficiency? Also calculate the incidence of each

of the taxes.

Answer 1

a) We can find the market price without regulation as follows:

$$Q_s=Q_d,$$ $$-150+0.40P=600-0.2P,$$ $$P=\$1250.$$

b) Substituting price into the supply function we can find the quantity of good H produced per year at this price:

$$Q=-150+0.40\cdot1250=350\ units.$$

c) Let's first write the inverse demand and supply functions:

$$P_s=2.5Q+375,$$ $$P_d=3000-5Q.$$

So, to find the socially efficient output of H we need to set the marginal social cost equal to the marginal social benefit (which is the demand curve):

$$MSC=MSB,$$ $$2.5Q+375+165=3000-5Q,$$ $$7.5Q=2460,$$ $$Q=328\ units.$$

d) Let's find the new inverse supply function in case of 12.5% taxing:

$$P_s=2.5Q+375+\dfrac{(2.5Q+375)}{100\%}\times12.5\%=2.81Q+421.87.$$

Tnen, we get:

$$2.81Q+421.87=3000-5Q,$$ $$7.81Q=2578$$ $$Q=330\ units.$$

As we can see from the calculations, 12.5% taxing is close to socially efficient output but still wouldn't be socially optimal (we need 328 units).

e) The alternate tax policy is to impose a per-unit tax with the rate equal to the value of the marginal external costs ($165).

f) Let's calculate the tax incidence on consumers and producers in case of 12.5% tax:

$$Tax\ inc_c=(P_c-P_e)Q_{e,new}=(\$1365-\$1250)\cdot330=\$37950,$$ $$Tax\ inc_p=(P_e-P_p)Q_{e,new}=(\$1250-\$1200)\cdot330=\$16500.$$

Let's calculate the tax incidence on consumers and producers in case of per-unit tax:

$$Tax\ inc_c=(P_c-P_e)Q_{e,new}=(\$1360-\$1250)\cdot328=\$36080,$$ $$Tax\ inc_p=(P_e-P_p)Q_{e,new}=(\$1250-\$1195)\cdot328=\$18040.$$