Question

The state of Colorado requires oil and gas companies who use fracking techniques to return the land to its original condition after the oil and gas extractions. Table $12.9$shows the total cost and total benefits (in dollars) of this policy.

Table$12.9$

Land Restored (in acres)	Total Cost	Total Benefit
0	\(0	\)0
100	\(20	\)140
200	\(80	\)240
300	\(160	\)320
400	\(280	\)380

(a) Calculate the marginal cost and the marginal benefit at each quantity (acre) of land restored. See Production, Costs and Industry Structure if you need a refresher on how to calculate marginal costs and benefits.

b. If we apply marginal analysis, what is the optimal amount of land to be restored?

Short answer

Land Restored (in acres)	Marginal Cost	Marginal Benefit
0	$0	$0
100	$0.2	$1.4
200	$0.6	$1
300	$0.8	$0.8
400	$1.2	$0.6

If we apply marginal analysis, $300$acres is the optimal amount of land to be restored.

Step-by-step solution

Formula of marginal cost and marginal benefit : 

$$\begin{gathered} MarginalCost\left(MC\right)=\frac{Changeintotal\cos t\left(dTC\right)}{Changeintotaloutput\left(dQ\right)} \\ MarginalBenefit\left(MB\right)=\frac{Changeintotalbenefit\left(dTB\right)}{Changeintotaloutput\left(dQ\right)} \end{gathered}$$

(a) Explanation : 

For $0$acres land to be restored -

$$\begin{gathered} MC=\frac{dTC}{dQ} \\ or,MC=\frac{0}{0} \\ or,MC=0 \\ MB=\frac{dTB}{dQ} \\ or,MB=\frac{0}{0} \\ or,MB=0 \end{gathered}$$

For $100$acres land to be restored -

$$\begin{gathered} MC=\frac{dTC}{dQ} \\ or,MC=\frac{\$20-\$0}{100-0} \\ or,MC=\$0.2 \\ MB=\frac{dTB}{dQ} \\ or,MB=\frac{\$140-\$0}{100-0} \\ or,MB=\$1.4 \end{gathered}$$

Foe $200$acres land to be restored -

$$\begin{gathered} MC=\frac{dTC}{dQ} \\ or,MC=\frac{\$80-\$20}{200-100} \\ or,MC=\$0.6 \\ MB=\frac{dTB}{dQ} \\ or,MB=\frac{\$240-\$140}{200-100} \\ or,MB=\$1 \end{gathered}$$

For $300$acres land to be restored -

$$\begin{gathered} MC=\frac{dTC}{dQ} \\ or,MC=\frac{\$160-\$80}{300-200} \\ or,MC=\$0.8 \\ MB=\frac{dTB}{dQ} \\ or,MB=\frac{\$320-\$240}{300-200} \\ or,MB=\$0.8 \end{gathered}$$

For $400$acres land to be restored -

$$\begin{gathered} MC=\frac{dTC}{dQ} \\ or,MC=\frac{\$280-\$160}{400-300} \\ or,MC=\$1.2 \\ MB=\frac{dTB}{dQ} \\ or,MB=\frac{\$380-\$320}{400-300} \\ or,MB=\$0.6 \end{gathered}$$

(b) Explanation : 

It is the ideal level of land to be allocated when marginal cost = marginal benefit.

The optimal amount of land is $300$acres, after which marginal revenue decreases.