Braucher, J.
We are asked to reconsider the remedy available to a taxpayer who is a victim of disproportionate assessment. Under our decisions "a taxpayer has a right to have his assessment reduced so that it is 'proportional to the assessments of the class of property valued at the lowest percentage of fair cash value.’ ” Assessors of Weymouth v. Curtis, 375 Mass. 493, 501 (1978), quoting Shoppers’ World, Inc. v. Assessors of Framingham, 348 Mass. 366, 377-378 n.10 (1965). The Appellate Tax Board (board) applied that rule to the present cases, but expressed a preference for reduction of the assessment only to a level proportional to the average percentage of fair cash value computed for the assessments of all taxable property in the taxing district. We affirm the decisions of the board.
[603]*603In the principal case the assessors of Boston valued land and an office building owned by the taxpayer at $320,000 and assessed a real estate tax for the 1977 fiscal year of $80,928. The taxpayer made timely application for abatement and appealed to the board from the assessors’ denial of his application. The board granted an abatement based on $87,904 as the "ultimate value” of the taxpayer’s property, and the assessors appealed.
The parties stipulated that the appropriate method of determining the fair cash value of the property was the capitalization of income method, that the net income of the property before taxes was $55,000, and that the proper capitalization rate was 10% to account for return on investment and for depreciation. They left to the board the determination of the appropriate "tax factor.”
The parties further stipulated that the class of property assessed at the lowest percentage of fair cash value in Boston was single-family residential property, which was assessed at an average rate of 26.8% of fair cash value as determined from figures reported by the Commissioner of Corporations and Taxation. The average for all taxable real and personal property in the city was 50.2%. The parties stipulated that these 1976 percentages "may apply” to the 1977 fiscal year for the purposes of the proceedings before the board.
The board computed the "tax factor” by multiplying the current tax rate ($252.90 per $1,000 assessed valuation) by the assessment percentage of the most favored class (26.8%), yielding a tax factor of .0678. The stipulated net income ($55,000) was divided by the combined factor for return, depreciation and taxes (.10 + .0678 = .1678), yielding a fair cash value of $327,771, rounded to $328,000. Application of the single-family residence percentage then produced an assessed value proportional to that of the most favored class ($328,000 X 26.8% = $87,-904). The tax on that value ($87,904 X .25290 = $22,-230.92), subtracted from the income ($55,000 — $22,230.92 = $32,769.08), yields approximately 10% of [604]*604the fair cash value ($32,777.10) to cover return and depreciation. See Assessors of Lynn v. Shop-Lease Co., 364 Mass. 569, 571-572 (1974).
1. The requirement of full valuation. Our Constitution empowers the Legislature to impose "proportional and reasonable assessments, rates and taxes, upon all the inhabitants of, and persons resident, and estates lying, within the said Commonwealth.” Part II, c. 1, § 1, art. 4, of the Massachusetts Constitution. Cf. art. 10 of the Declaration of Eights: "Each individual of the society has a right to be protected by it in the enjoyment of his life, liberty and property, according to standing laws. He is obliged, consequently, to contribute his share to the expense of this protection” (emphasis supplied). The former provision forbids the imposition of taxes "upon one class of persons or property at a different rate from that which is applied to other classes, whether that discrimination is effected directly in the assessment or indirectly through arbitrary and unequal methods of valuation.” Cheshire v. County Comm’rs of Berkshire, 118 Mass. 386, 389 (1875), quoted in Bettigole v. Assessors of Springfield, 343 Mass. 223, 230-231 (1961).
Pursuant to the Constitution, our statutes require assessors to assess property at its "fair cash valuation.” G. L. c. 59, § 38. Cf. G. L. c. 41, § 29 (assessors’ oath). But "illegal assessments have long been the rule rather than the exception throughout much of the Commonwealth.” Sudbury v. Commissioner of Corps. & Taxation, 366 Mass. 558, 563 (1974), and cases cited.
The present cases are not affected by art. 112 of the Amendments to the Constitution, ratified in November, 1978. The Amendment authorizes the Legislature to classify property according to its use for the purposes of taxation, and G. L. c. 59A, inserted by St. 1978, c. 580, § 38, provides for such a classification. But the statute is to be applicable to property taxes assessed for the fiscal year beginning 1980. St. 1978, c. 580, § 40. We decide no question with respect to the Amendment or the statute.
[605]*6052. Boston assessments. The stipulation of the parties incorporates a report of the Commissioner of Corporations and Taxation for the year 1976. That report describes a pattern of assessment in the city of Boston in flagrant disregard of constitutional and statutory mandates. Assessments of various classes of real and personal property are shown at average percentages of full value ranging from 26.8% to 100%. The board listed separate percentages for single-family residential property in various wards, showing a range from 17% and below for Wards 1 and 2 to 79.2% and above for Ward 12. Compare Sudbury v. Commissioner of Corps. & Taxation, 366 Mass. 558, 567 (1974), where, on the basis of a narrower range for Boston districts, we said, "The process has lost contact with reality.”
The city does not now dispute the fact that the taxpayer is aggrieved by a disproportionate assessment. It contends only that the appropriate remedy is reduction of the taxpayer’s assessment to a level proportional to the average of assessments of all classes of property throughout the city.
3. Remedies. On application of a taxpayer the assessors are to make a "reasonable abatement” of his taxes "if they find him taxed at more than his just proportion, or upon an assessment of any of his property in excess of its fair cash value.” G. L. c. 59, § 59, as amended through St. 1977, c. 198. For many years, however, this court denied abatements in cases like the present one: "Whatever may be the remedy, if there be any, when it is shown that the assessors have intentionally assessed the property of a part or all of the inhabitants at less than its fair cash value, we are of opinion that, in a petition for the abatement of taxes on the ground of the overvaluation of the property of the petitioner, and the disproportionate taxation arising from such overvaluation, the question is, whether the property has been valued at more than its fair cash value, and not whether it has been valued relatively more or less than similar property of other per[606]*606sons.” Lowell v. County Comm’rs of Middlesex, 152 Mass. 372, 375 (1890). See Stone v. Springfield, 341 Mass. 246, 250-251 (1960), and cases cited.
Bettigole v. Assessors of Springfield, 343 Mass.
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Braucher, J.
We are asked to reconsider the remedy available to a taxpayer who is a victim of disproportionate assessment. Under our decisions "a taxpayer has a right to have his assessment reduced so that it is 'proportional to the assessments of the class of property valued at the lowest percentage of fair cash value.’ ” Assessors of Weymouth v. Curtis, 375 Mass. 493, 501 (1978), quoting Shoppers’ World, Inc. v. Assessors of Framingham, 348 Mass. 366, 377-378 n.10 (1965). The Appellate Tax Board (board) applied that rule to the present cases, but expressed a preference for reduction of the assessment only to a level proportional to the average percentage of fair cash value computed for the assessments of all taxable property in the taxing district. We affirm the decisions of the board.
[603]*603In the principal case the assessors of Boston valued land and an office building owned by the taxpayer at $320,000 and assessed a real estate tax for the 1977 fiscal year of $80,928. The taxpayer made timely application for abatement and appealed to the board from the assessors’ denial of his application. The board granted an abatement based on $87,904 as the "ultimate value” of the taxpayer’s property, and the assessors appealed.
The parties stipulated that the appropriate method of determining the fair cash value of the property was the capitalization of income method, that the net income of the property before taxes was $55,000, and that the proper capitalization rate was 10% to account for return on investment and for depreciation. They left to the board the determination of the appropriate "tax factor.”
The parties further stipulated that the class of property assessed at the lowest percentage of fair cash value in Boston was single-family residential property, which was assessed at an average rate of 26.8% of fair cash value as determined from figures reported by the Commissioner of Corporations and Taxation. The average for all taxable real and personal property in the city was 50.2%. The parties stipulated that these 1976 percentages "may apply” to the 1977 fiscal year for the purposes of the proceedings before the board.
The board computed the "tax factor” by multiplying the current tax rate ($252.90 per $1,000 assessed valuation) by the assessment percentage of the most favored class (26.8%), yielding a tax factor of .0678. The stipulated net income ($55,000) was divided by the combined factor for return, depreciation and taxes (.10 + .0678 = .1678), yielding a fair cash value of $327,771, rounded to $328,000. Application of the single-family residence percentage then produced an assessed value proportional to that of the most favored class ($328,000 X 26.8% = $87,-904). The tax on that value ($87,904 X .25290 = $22,-230.92), subtracted from the income ($55,000 — $22,230.92 = $32,769.08), yields approximately 10% of [604]*604the fair cash value ($32,777.10) to cover return and depreciation. See Assessors of Lynn v. Shop-Lease Co., 364 Mass. 569, 571-572 (1974).
1. The requirement of full valuation. Our Constitution empowers the Legislature to impose "proportional and reasonable assessments, rates and taxes, upon all the inhabitants of, and persons resident, and estates lying, within the said Commonwealth.” Part II, c. 1, § 1, art. 4, of the Massachusetts Constitution. Cf. art. 10 of the Declaration of Eights: "Each individual of the society has a right to be protected by it in the enjoyment of his life, liberty and property, according to standing laws. He is obliged, consequently, to contribute his share to the expense of this protection” (emphasis supplied). The former provision forbids the imposition of taxes "upon one class of persons or property at a different rate from that which is applied to other classes, whether that discrimination is effected directly in the assessment or indirectly through arbitrary and unequal methods of valuation.” Cheshire v. County Comm’rs of Berkshire, 118 Mass. 386, 389 (1875), quoted in Bettigole v. Assessors of Springfield, 343 Mass. 223, 230-231 (1961).
Pursuant to the Constitution, our statutes require assessors to assess property at its "fair cash valuation.” G. L. c. 59, § 38. Cf. G. L. c. 41, § 29 (assessors’ oath). But "illegal assessments have long been the rule rather than the exception throughout much of the Commonwealth.” Sudbury v. Commissioner of Corps. & Taxation, 366 Mass. 558, 563 (1974), and cases cited.
The present cases are not affected by art. 112 of the Amendments to the Constitution, ratified in November, 1978. The Amendment authorizes the Legislature to classify property according to its use for the purposes of taxation, and G. L. c. 59A, inserted by St. 1978, c. 580, § 38, provides for such a classification. But the statute is to be applicable to property taxes assessed for the fiscal year beginning 1980. St. 1978, c. 580, § 40. We decide no question with respect to the Amendment or the statute.
[605]*6052. Boston assessments. The stipulation of the parties incorporates a report of the Commissioner of Corporations and Taxation for the year 1976. That report describes a pattern of assessment in the city of Boston in flagrant disregard of constitutional and statutory mandates. Assessments of various classes of real and personal property are shown at average percentages of full value ranging from 26.8% to 100%. The board listed separate percentages for single-family residential property in various wards, showing a range from 17% and below for Wards 1 and 2 to 79.2% and above for Ward 12. Compare Sudbury v. Commissioner of Corps. & Taxation, 366 Mass. 558, 567 (1974), where, on the basis of a narrower range for Boston districts, we said, "The process has lost contact with reality.”
The city does not now dispute the fact that the taxpayer is aggrieved by a disproportionate assessment. It contends only that the appropriate remedy is reduction of the taxpayer’s assessment to a level proportional to the average of assessments of all classes of property throughout the city.
3. Remedies. On application of a taxpayer the assessors are to make a "reasonable abatement” of his taxes "if they find him taxed at more than his just proportion, or upon an assessment of any of his property in excess of its fair cash value.” G. L. c. 59, § 59, as amended through St. 1977, c. 198. For many years, however, this court denied abatements in cases like the present one: "Whatever may be the remedy, if there be any, when it is shown that the assessors have intentionally assessed the property of a part or all of the inhabitants at less than its fair cash value, we are of opinion that, in a petition for the abatement of taxes on the ground of the overvaluation of the property of the petitioner, and the disproportionate taxation arising from such overvaluation, the question is, whether the property has been valued at more than its fair cash value, and not whether it has been valued relatively more or less than similar property of other per[606]*606sons.” Lowell v. County Comm’rs of Middlesex, 152 Mass. 372, 375 (1890). See Stone v. Springfield, 341 Mass. 246, 250-251 (1960), and cases cited.
Bettigole v. Assessors of Springfield, 343 Mass. 223 (1961), established that a court of equity might "prevent the enforcement of the whole of an illegal city or town tax assessment for a given year,” but such extraordinary and drastic relief is narrowly confined. Leto v. Assessors of Wilmington, 348 Mass. 144, 148-149 (1964). Other remedies provided some measure of relief from disproportionate assessments, but were "not wholly satisfactory. ”Id at 147. To afford taxpayers their constitutional rights, we reconsidered and abandoned the rule of the Lowell case in Shoppers’ World, Inc. v. Assessors of Framingham, 348 Mass. 366, 373-376 (1965). Since that decision we have continued to confine alternative remedies within narrow limits. Nearis v. Gloucester, 357 Mass. 203, cert. denied, 400 U.S. 918 (1970) (injunction). Sears, Roebuck & Co. v. Somerville, 363 Mass. 756 (1973) (actioñ of contract under G. L. c. 60, § 98). But within those limits we have ordered comprehensive declaratory and injunctive relief, directing the filing of plans for orderly revaluation. Coan v. Assessors of Beverly, 349 Mass. 575 (1965) (taxpayer suit under G. L. c. 40, § 53). Bennett v. Assessors of Whitman, 354 Mass. 239 (1968) (same).
In Sudbury v. Commissioner of Corps. & Taxation, 366 Mass. 558, 565-568 (1974), we dealt with the problem of discrimination against those cities and towns whose assessors act lawfully, in favor of those whose assessors engage in the illegal practice of fractional valuation. The State Tax Commission was required to establish an "equalized valuation” for each city and town. G. L. c. 58, §§ 9-10C. Those valuations play an important part in the distribution of State funds and in the apportionment of county and other taxes. It appeared that fractional valuation made the equalization task difficult, if not impossible. We noted that such complex problems are usually solved by executive action or pursuant to express legisla[607]*607tive directions, and ordered the entry of a decree declaring the powers and duties of the Commissioner of Corporations and Taxation and the State Tax Commission.
Malden v. Appellate Tax Bd., 367 Mass. 395, 403 (1975), began as an attack on the equalized valuation established for Boston in 1974. That attack, however, was withdrawn. We upheld the constitutionality of the equalization statutes against the claim that they resulted in discrimination against cities and towns other than Boston. We did not pass on the question whether any other remedy was available to those cities and towns.
Pursuant to the decree in the Sudbury case, the Commissioner of Corporations and Taxation and the State Tax Commission have reported the progress of a continuing program to produce uniformity throughout the Commonwealth in valuation and assessments. The assessors of Boston assert that that program is in the process of implementation in Boston under the supervision of the Superior Court. In argument they estimated that comprehensive revaluation will take two to three years and cost about $7 million.
4. Abatement to the municipal average. Comprehensive remedies seek to produce uniform assessments at fair cash value. "Where every assessment has been made on a wrong basis, the defects in the scheme cannot be cured by the sporadic correction of individual assessments.” Bettigole v. Assessors of Springfield, 343 Mass. 223, 236 (1961). But no comprehensive remedy can be ordered by the Appellate Tax Board in an abatement proceeding. The Shoppers’ World case involved "a simple form of discrimination” — substantially all property was assessed at 45% of fair cash value, but one taxpayer’s property was assessed at a higher percentage. In that situation the remedy was an abatement "which will make the taxpayer’s assessment proportional to other assessments, on a basis which reaches results as close as is practicable to those which would have followed application by the assessors of the proper statutory assessment principles.” 348 Mass. at 377-378.
[608]*608That conclusion rested in part "on the principle that where it is impossible to secure both the standard of the true value, and the uniformity and equality required by law, the latter requirement is to be preferred as the just and ultimate purpose of the law.” 348 Mass. at 373, quoting Sioux City Bridge Co. v. Dakota County, Neb., 260 U.S. 441, 446 (1923). In dictum we added that if, as in the Bettigole case, several different percentages had been employed for different classes of property, the same principle "would logically require reduction of the assessment of a taxpayer against whom there had been discrimination so that such taxpayer’s assessment would be proportional to the assessments of the class of property valued at the lowest percentage of fair cash value.” 348 Mass. at 377-378 n.10.
Most of our cases applying the rule of the Shoppers’ World case have focused on the issue whether there was a sufficient showing of disproportionate assessment. Beardsley v. Assessors of Foxborough, 369 Mass. 855, 859 (1976). Coomey v. Assessors of Sandwich, 367 Mass. 836, 838-839 (1975). Assessors of Kingston, v. Sgarzi, 367 Mass. 840, 843 (1975). First Nat’l Stores, Inc. v. Assessors of Somerville, 358 Mass. 554, 560-562 (1971). Butler v. Assessors of Worcester, 354 Mass. 651, 654 (1968). In the First Nat’l Stores case, however, we relied on evidence of average percentages for all classes of property to show disproportion. See 358 Mass. at 556 & n.3. We think the aggrieved taxpayer may, if he chooses, claim an abatement of his assessment to the average percentage of fair cash value computed for the assessments of all taxable property in the taxing district. That remedy may be particularly appropriate when there is no apparent pattern in the disproportionate assessments. Lerner Shops of Conn., Inc. v. Waterbury, 151 Conn. 79, 87-89 (1963). Southern Bell Tel. & Tel. Co. v. County of Dade, 275 So. 2d 4, 10 (Fla. 1973). Grainger Bros. v. Board of Equalization, 180 Neb. 571, 585-586 (1966). In re Appeals of Kents 2124 Atlantic Ave., Inc., 34 N.J. 21, 30-32 (1961). Deitch Co. v. Board of Property Assessment, 417 Pa. 213, 220-221 (1965).
[609]*609We think a taxpayer makes out at least a prima facie case of disproportionate assessment if he shows that his property is assessed at a percentage of fair cash value greater than the average percentage for all taxable property in the city or town, using the fair cash value of all such property as determined by the Commissioner of Revenue (formerly the State Tax Commission) pursuant to G. L. c. 58, § 10C. See In re Appeals of Kents 2124 Atlantic Ave., Inc. 34 N.J. 21, 26-28 (1961); Ed Guth Realty, Inc. v. Gingold, 34 N.Y.2d 440, 449-451 (1974); Pittsburgh Miracle Mile Town & Country Shopping Center, Inc. v. Board of Property Assessment, 417 Pa. 243, 247-248 n.3 (1965); Barnet v. Palazzi Corp. 135 Vt. 298, 300 (1977); Note, Inequality in Property Tax Assessments: New Cures for an Old Ill, 75 Harv. L. Rev. 1374, 1392-1395 (1962). Otherwise, proof of disproportionate assessment, in the absence of a stipulation like that in the present case, imposes on the taxpayer a wasteful burden of proving the assessed values and the fair cash values of a great number of properties other than his own. See First Nat’l Stores, Inc. v. Assessors of Somerville, 358 Mass. 554, 555-556, 560 (1971); Butler v. Assessors of Worcester, 354 Mass. 651, 654 (1968); Shoppers’ World, Inc. v. Assessors of Framingham, 348 Mass. 366, 377 (1965). To require the taxpayer to revalue even a substantial fraction of the property of a large city may be tantamount to a denial of relief.
5. Abatement to the average for the most favored class. The question remains whether we should stand by the dictum in the Shoppers’ World case, which became the holding in Assessors of Weymouth v. Curtis, 375 Mass. 493, 501 (1978). In the Curtis case we upheld an abatement of the tax on commercial property to an amount based on 70% of its fair cash value, in the face of an argument much like that in the present case. We held that it was not improper to include only sales of residential properties in the study on which the 70% figure was based. A similar result was ordered as to industrial prop[610]*610erty in Kavet v. Assessors of Watertown, 376 Mass. 927 (1978). Cf. Chomerics, Inc. v. Assessors of Woburn, 6 Mass. App. Ct. 394, 396-399 (1978) (assessments of commercial and industrial property reduced to residential average).
The same problem has arisen in other jurisdictions, and in several States taxpayers have been limited to reduction to the municipal average for all taxable property. Bade v. Drachman, 4 Ariz. App. 55, 64-65 (1966). Siegal v. Newark, 38 N.J. 57, 62-64 (1962). See Chomerics, Inc. v. Assessors of Woburn, 6 Mass. App. Ct. 394, 402 n.10 (1978). Cf. Kays, Inc. v. Board of Tax Review, 170 Conn. 477 (1976) (failure of proof of municipal average); Addington v. County Comm’rs, 191 Kan. 528, 529-530 (1963) (claim based on county median); Hoerner-Waldorf Corp. v. Ontonagon, 26 Mich. App. 542, 547-548 (1970) (calculation of township average); Rich Appeal, 402 Pa. 209, 210-211 (1961) (favored class not substantial). The theory seems to be that the municipal average produces a tax approximating the tax that should have been imposed by lawful assessment practices.
Use of the municipal average reduces the discrimination between those who do and those who do not seek abatements. But such discrimination is inherent in the abatement procedure, and the use of the municipal average affords only partial equalization between the favored taxpayer and the disfavored taxpayer. Suppose for example, four taxpayers with properties of equal value. Two are residential and are unlawfully assessed at 25% of that value; two are commercial and are unlawfully assessed at 75%. A comprehensive remedy would reassess all at 100%; reassessment of all at the 50% average would produce the same tax, in the absence of some exemption. If one of the commercial taxpayers is granted an abatement to 50%, he is treated better than the other, but he is still a victim of the discrimination in favor of residential property. Cf. Dehydrating Process Co. of Gloucester, Inc. v. Gloucester, 334 Mass. 287, 293 (1956) (assessment of only two of a much larger number of occupants of a
[611]*611pier, illegal and void). In such circumstances several courts have insisted on complete relief by reduction to the average percentage for the most favored substantial class. Kittery Elec. Light Co. v. Assessors of Kittery, 219 A.2d 728, 739 (Me. 1966) (utility assessment reduced to residential percentage). Hamm v. State, 255 Minn. 64, 67-68 (1959) (taxpayer aggrieved by assessment at municipal average). Chicago, Rock Island & Pac. Ry. v. Young, 60 S.D. 291, 293-297 (1932), and cases cited: "There being now no way to bring the favored persons up to the level where all should have been, the only way to remove the discrimination is to bring appellant down to their rate, even though it is a rate lower than any one was ever lawfully entitled to receive.” See Baken Park, Inc. v. County of Pennington, 79 S.D. 156, 160 (1961).
We do not agree with the assessors’ contention that the lowest-class remedy is punitive rather than remedial. In Assessors of Lynn v. Shop-Lease Co., 364 Mass. 569 (1974), we upheld the appeal of assessors who had stipulated that they assessed property at 30% of fair cash value. A dissenting Justice would have dismissed their appeal "out of hand,” refusing to adjudicate proportionality in the context of "a thoroughly illegal system.” Id. at 574-577. But a majority of the court refused to compel the taxpayers of the city "to suffer in effect a forfeiture to Shop-Lease of tax revenues to which the city is entitled,” although assessors who flagrantly fail to perform their duty were warned that they "may expect to receive an unsympathetic reception in this court.” Id. at 572. We adhere to that decision. But the board’s decision in the present case does not impose a forfeiture; it vindicates the rights of the aggrieved taxpayer by conforming his assessment to those of more favored taxpayers. The remedy may provide some incentive to the assessors to comply with laws they have blatantly violated for many years, but that fact does not render it punitive.
This case was presented to the board and is presented to us a choice between the municipal average of 50.2% [612]*612and the lowest-class average of 26.8%. In these circumstances we uphold the board in following our past decisions, under which the taxpayer is entitled to an abatement to the lower percentage. We have not gone behind the stipulation of the parties to review possible weaknesses in the agreed percentages, nor have we reexamined the stipulated conclusion that single-family residential property, assessed at an average rate of 26.8%, is "the lowest substantial class.” It appears that such property constituted more than $600 million out of a total of $3,600 million of full valuation. We do not now decide how large the favored category must be to bring into play the rule we now apply. Cf. Chomerics, Inc. v. Assessors of Woburn, 6 Mass. App. Ct. 394 (1978) (undisclosed amount of vacant residential property assessed at very low rate).
We are not persuaded by what the taxpayer calls "the city’s doomsday argument.” The assessors argue that the decision we now reach will result in huge total abatements, a massive rise in the "effective tax rate” and an unbearable increase in the average residential tax bill, leading to a sudden reduction in property values, an increase in mortgage foreclosures and other adverse effects. In other contexts the city has made more optimistic forecasts,1 and it seems clear to us that the adverse consequences will be far less than the assessors claim. In any event the consequences will be less burdensome than the consequences of full compliance with the law. We, like the assessors, are required to comply with the law, burdensome or not.
Decisions of the Appellate Tax Board affirmed.