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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 12.9shows the total cost and total benefits (in dollars) of this policy.

Table12.9

Land Restored (in acres)Total CostTotal 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

Expert verified
Land Restored (in acres)Marginal CostMarginal 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, 300acres is the optimal amount of land to be restored.

Step by step solution

01

Formula of marginal cost and marginal benefit : 

MarginalCost(MC)=Changeintotalcost(dTC)Changeintotaloutput(dQ)MarginalBenefit(MB)=Changeintotalbenefit(dTB)Changeintotaloutput(dQ)

02

(a) Explanation : 

For 0acres land to be restored -

MC=dTCdQor,MC=00or,MC=0MB=dTBdQor,MB=00or,MB=0

For 100acres land to be restored -

MC=dTCdQor,MC=$20-$0100-0or,MC=$0.2MB=dTBdQor,MB=$140-$0100-0or,MB=$1.4

Foe 200acres land to be restored -

MC=dTCdQor,MC=$80-$20200-100or,MC=$0.6MB=dTBdQor,MB=$240-$140200-100or,MB=$1

For 300acres land to be restored -

MC=dTCdQor,MC=$160-$80300-200or,MC=$0.8MB=dTBdQor,MB=$320-$240300-200or,MB=$0.8

For 400acres land to be restored -

MC=dTCdQor,MC=$280-$160400-300or,MC=$1.2MB=dTBdQor,MB=$380-$320400-300or,MB=$0.6

03

(b) Explanation : 

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

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

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