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Marshall's Tax Bounty Analysis Of Aggregate Welfare

 Marshall's Tax Bounty Analysis of Aggregate Welfare

            The above analysis relates to the individual consumer’s surplus or welfare. In order to arrive at the aggregate consumer’s surplus, Marshall adds the individual consumer’s surpluses in a market. This he does by assuming that most markets are standardised with respect to the income class of the buyers and regards the individual buyer as a model representatives of the group. To get rid of the problem of interpersonal utility comparisons and value judgements, Marshall says that for practical purposes the area between the demand curve and the price is taken to be good approximation of the sum of the individual consumer’s surpluses.

            Marshall uses his tax boundary analysis to explain the aggregate economic welfare. According to Marshall, aggregate economic welfare can be increased by taxing diminishing returns industries and using the tax receipts to subside increasing returns industries. To arrive at this conclusion, he describes the following three possible cases.

            Constant Returns – Marshall shows that a tax imposed on a commodity obeying the law of constant costs or constant returns results in a loss of consumer’s surplus greater than the amount of tax receipts and conversely a subsidy in this case exceeds the gain in consumer’s surplus. This is represented in the diagram where SS is the supply price is the same for the commodity. Thus the supply curve is perfectly elastic. DD1 is the demand curve for the commodity. E is the initial equilibrium point where the consumer’s surplus is SDE.

                                         

If, a uniform tax TE per unit of the commodity bought is levied. The supply curve shifts up by the amount of tax to S1S1 parallel to the old supply curve SS. Consequently the loss of consumers’ surplus is the area SS1 AE (=SDE – S1DA). The tax receipts to the government are equal to the area SS1AB.

                       

Thus the loss of consumer’s surplus is greater than the gain to the government for the reason that SS1AE > SS1AB. The net loss of consumer’s surplus is the shaded portion ABE. In the same way, if a subsidy shifts the long run supply curve down from S1S1 to SS (whereby supply increases) the triangle ATE above the demand curve means the excess of subsidies paid out over consumer’s surplus gained.

Diminishing Returns – When the industry is operating under diminishing returns to scale or increasing costs, the effects to a tax are not so certain. Whether the tax receipts will exceed the loss in consumers’ surplus will depend upon the steepness of the long run supply curve. This case is represented in the below diagram where initial supply curve is SS. After the imposition of tax, it shifts to S1S1.

The demand curve DD1 intersects the supply curve SS at point E and the new supply curve at point A. TA per unit of tax is levied on OX1 quantity of the product purchased and the total tax receipts are equal to area CRAT and the loss in consumers’ surplus is RAEP. The receipts from tax shown as the shaded rectangle CPBT are greater than the net loss in consumers’ surplus shown as the shaded triangle AEB.

Increasing Returns – When the industry is operating under increasing returns to scale or diminishing costs the long run supply curve slopes downward as SS in the diagram. With the DD1 demand curve, OX commodity is produced at the equilibrium point E. If a tax is levied, the cost of production will increase, the price of the commodity will rise there will be loss consumer’s surplus.

Nevertheless, the effect of a subsidy on a decreasing cost industry depends on the incline of the supply curve. If the supply curve is less elastic as represented the grant of AT amount of subsidy per unit of output to this industry will increase its output to OX1.

The total amount of subsidy is RTAK and the gain in consumer’s surplus is RPET. As the region RPET > RTAK, the gain consumer’s surplus is greater than the amount of subsidy payment by the government. If the long run supply curve is more elastic, as in the case of constant cost industry, subsidy payment will exceed consumer’s surplus even in diminishing cost industry.

Conclusion

            Marshall concludes that aggregate welfare can be increased if the government imposes a tax on diminishing returns or increasing cost industries where tax receipts are greater than the loss in consumer’s surplus and spends the proceeds to subsidise increasing returns or diminishing cost industries where the gain in consumer’s surplus is more than subsidy payments.

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