The principal issue on this appeal is the constitutionality of the Connecticut tax on the net income of unincorporated businesses that was enacted in 1981. Forty-two named plaintiffs brought a class action, on behalf of themselves and others similarly situated, against the commissioner of revenue services and the treasurer of the state of Connecticut challenging the constitutionality of Public Acts 1981, No. 81-255, §§ 2 through 22, as amended by Public Acts 1981, No. 81-411, §§ 7, 8.1 The plaintiffs sought injunctive, *286declaratory and monetary relief from tax liability under the act as well as from the penalties imposed by the act for failure to comply with its provisions. The trial *287court, Hon. Irving Levine, state trial referee, found the issues for the defendants and the plaintiffs appealed. We find no error.
The act, which is entitled “An Act Concerning State Tax Revenue for the Fiscal Year Commencing July 1, 1981,” imposes a net income tax on unincorporated *288businesses and institutes a fourth method for computing the previously enacted corporate business tax. Although the act did not become effective until July 1, 1981, the provisions at issue were expressly made applicable to tax years beginning on or after January 1, 1981. Public Acts 1981, No. 81-255, § 37. Both taxes were subsequently repealed for tax years beginning on or after January 1,1983.2 As the trial court noted, the repeal does not render this case moot since the plaintiffs continue to have the right to seek refunds and to avoid liability for the two years during which the tax was in effect.
The principal provisions of the act impose a tax on an unincorporated business3 whose gross income exceeds $50,000 and whose net income exceeds $15,000. Public Acts 1981, No. 81-255, § 3 (b); Public Acts 1981, No. 81-411, §§ 7, 42; General Statutes (Rev. to 1983) § 12-611 (b) (1), (b) (2). Such a business is liable for a minimum tax of $250. In the alternative, the tax is calculated at 5 percent of taxable net income. Public Acts 1981, No. 81-255, § 3 (a); General Statutes (Rev. to 1983) § 12-611 (a).4 Any business that meets the threshold test for liability must pay whichever of these two alternate amounts is the greater.
*289In addition to establishing the unincorporated business tax, Public Acts 1981, No. 81-255, adds a fourth base of taxation for incorporated businesses. Public Acts 1981, No. 81-255, § 22; Public Acts 1981, No. 81-411, § 8; General Statutes (Rev. to 1983) § 12-219. The act imposes a 5 percent tax on those corporations with gross incomes in excess of $50,000 that would have been taxed in a lesser amount under the previously existing three bases for taxation of corporate income.5
In their complaint, the plaintiffs attacked the constitutionality of Public Acts 1981, No. 81-255, as amended, on three grounds. They claimed that it impermissibly: (1) establishes arbitrary and unreasonable classifications in violation of the equal protection clauses of the United States and the Connecticut constitutions; (2) defines liability in language which is so vague as to be void for vagueness under the due process clauses of the United States and the Connecticut constitutions; and (3) imposes retroactive liability in violation of the due process clauses of the United States and the Connecticut constitutions. The same claims are renewed upon this appeal. Like the trial court, we find them unpersuasive.
I
In their first assignment of error, the plaintiffs focus on the classification of exemptions under the unincorporated business tax. The plaintiffs claim that the act establishes classifications that are unreasonable and *290arbitrary under the equal protection clauses of our federal and state constitutions,6 principally because the act provides for notch exemptions rather than for total exemptions. In contrast to a total exemption, which “leaves a specified amount of income untaxed for all taxpayers . . . the notch exemption essentially designates the class of taxpayers subject to the tax. For those taxpayers within the taxed class, all income denoted . . . is subject to the tax without any threshold exemption.” Miller v. Heffeman, 173 Conn. 506, 513, 378 A.2d 572 (1977), appeal dismissed, 434 U.S. 1057, 98 S. Ct. 1226, 55 L. Ed. 2d 758 (1978). The notch exemptions of which the plaintiffs complain are the statutory thresholds of $50,000 of gross income and $15,000 of net income,7 below which no tax at all is payable and above which the minimum tax of $250 is due and owing.
*291In our assessment of this claim, we must begin with the established principle that those who challenge the constitutionality of a state statute bear the heavy burden of demonstrating beyond a reasonable doubt that the presumption of its validity has been overcome. See, e.g., Kellems v. Brown, 163 Conn. 478, 486, 313 A.2d 53 (1972), appeal dismissed, 409 U.S. 1099, 93 S. Ct. 911, 34 L. Ed. 2d 678 (1973); Adams v. Rubinow, 157 Conn. 150, 152-53, 251 A.2d 49 (1968). A party challenging a tax statute on the grounds of equal protection bears an even greater burden because “[a]s this court emphasized in Kellems v. Brown, supra, 487, quoting Madden v. Kentucky, 309 U.S. 83, 88, 60 S. Ct. 406, 84 L. Ed. 590 [1940], ‘ “in taxation, even more than in other fields, legislatures possess the greatest freedom in classification. Since the members of a legislature necessarily enjoy a familiarity with local conditions which this Court cannot have, the presumption of constitutionality can be overcome only by the most explicit demonstration that a classification is a hostile and oppressive discrimination against particular persons and classes. The burden is on the one attacking the legislative arrangement to negative every conceivable basis which might support it.” ’ ” Miller v. Heffernan, supra, 509-10. Nonetheless, even for the purposes of taxation, the legislature does not have an unlimited power to create classifications. The classifications that it selects cannot be arbitrary but “ ‘must rest upon some ground of difference having a fair and substantial relation to the object of the legislation.’ ” (Citations omitted.) Allied Stores v. Bowers, 358 U.S. 522, 527, 79 S. Ct. 437, 3 L. Ed. 2d 480 (1959); see United Illuminating Co. v. New Haven, 179 Conn. 627, 636-37, 427 A.2d 830 (1980); Kellems v. Brown, supra, 490. Recognizing that any plan of taxation necessarily has some discriminatory impact; San Antonio Independent *292School District v. Rodriguez, 411 U.S. 1, 41, 93 S. Ct. 1278, 36 L. Ed. 2d 16, reh. denied, 411 U.S. 959, 93 S. Ct. 1919, 36 L. Ed. 2d 418 (1973); United Illuminating Co. v. New Haven, supra, 641; we have previously stated the operative test for the validity of a tax statute to be the following: “ ‘As long as some conceivable rational basis for the difference exists, “a classification is not offensive merely because it is not made with mathematical nicety.” ’ ” (Emphasis in original.) (Citations omitted.) United Illuminating Co. v. New Haven, supra, 640-41.
The trial court found a rational basis for the notch exemptions in Public Acts 1981, No. 81-255, as amended, in the distinction between those unincorporated businesses that functionally resemble incorporated businesses and those that are essentially “Mom and Pop” enterprises. The legislature intended to tax the former category because incorporated businesses were already being taxed, but intended to continue to exempt the latter group of smaller businesses.
The plaintiffs do not disagree with this statement of the legislature’s original intentions nor do they contest the legitimacy of such a plan in principle. They argue, however, that the legislature abandoned this rational plan when the first notch exemption, which had originally been set at $150,000 of gross income, was subsequently reduced to $50,000. In their view, the ultimate reach of the statute became too sweeping to accomplish its valid purpose of exempting the small businesses which had originally been targeted for speciál treatment. Furthermore, with respect to the second notch exemption, the plaintiffs argue that the exemption of businesses with a net income below $15,000 fails to leave the average family budget intact, as the legislature may have intended. The plaintiffs rely, for this *293argument, on statistical evidence before the trial court8 that showed the average budget of an urban family of four in 1979 ranging from a low of $13,623 to a high of $36,891.
The plaintiffs’ position is untenable. It is not part of the judicial function to fine tune the legislature’s definition of what constitutes a “Mom and Pop” business enterprise or an average family budget for tax purposes. “[A] legislature is not bound to tax every member of a class or none, as long as some rational basis for the designated distinction exists.” Miller v. Heffernan, supra, 511; see Carmichael v. Southern Coal & Coke Co., 301 U.S. 495, 509-10, 57 S. Ct. 868, 81 L. Ed. 1245 (1937). At most, the plaintiffs have shown that the plan selected by the legislature “resulted in some inequities to individual taxpayers.” Proof of the existence of the inequities that inevitably follow from every legislative decision of inclusion and exclusion does not suffice to meet the plaintiffs’ burden of establishing that the plan is unconstitutionally irrational and arbitrary.
The plaintiffs’ more cogent equal protection argument focuses on the form of the exemptions that are embodied in Public Acts 1981, No. 81-255, as amended. Relying on our holding in Miller v. Heffernan, supra, they argue that the act’s notch exemptions draw an irrational distinction between tax liability and tax exemption. In Miller v. Heffernan, we upheld the constitutionality of legislation that imposed a 7 percent tax on all dividends received by taxpayers with an adjusted gross income of $20,000 or more. We acknowledged that the notch exemption meant that “a taxpayer with an adjusted gross income of $20,000 would be subjected to a $1400 tax in the unusual event that all his income *294was derived from dividends, while a taxpayer only marginally less well endowed with dividends, receiving an adjusted gross income of $19,999, would be entirely exempt from dividend taxation.” Miller v. Heffernan, supra, 513. Despite the disparate statutory treatment illustrated by these hypothetical examples, we concluded that the statute was not unreasonable, in part because few taxpayers in fact derived their incomes wholly from dividends. We cautioned, however, that “notch exemptions have the potential for leaving a taxpayer subject to the tax with a lower net income after taxes than that of a taxpayer exempt from the tax. Taken to an extreme, this disparity in the treatment of income below the designated base could lose any rational connection with proper legislative objectives. Thus notch exemptions are to be carefully analyzed in terms of the rationality of the particular base and rate of taxation. ‘The standard of what is arbitrary and unreasonable is not rigid. . . . [T]he question is usually one of degree.’ ” (Citation omitted.) Id., 515.
The plaintiffs urge us to hold that Public Acts 1981, No. 81-255, as amended, fails the Miller v. Heffernan test. They maintain that it is arbitrary to impose a tax of $250 on a business that grosses $50,001 and has a net income of $15,001, while a neighboring business whose gross and net incomes both amount to $50,000 is exempt. A similar question might be raised about the disparity between imposing a tax of $1250 on a business with gross and net incomes of $50,0019 and exempting entirely a business with gross and net income of $50,000. The plaintiffs further maintain that the arbitrariness of these distinctions is enhanced by “the common knowledge” that grocery stores, package stores, farmers and any business with a large over*295head or inventory must generate an excessive amount of gross receipts in comparison to their net income.10
These disparities undeniably may result in unfortunate distinctions in the treatment of individual taxpayers. The disparities are not, however, different in kind from those that we found constitutional in Miller v. Heffernan. The legislature’s goal of exemption for small businesses is a legitimate goal which is rationally, albeit imperfectly, advanced by the statutory scheme of liability contained in Public Acts 1981, No. 81-255 as amended. The existence of disparities is the necessary consequence of line drawing. The plaintiffs have failed to prove that the act’s exemptions operate overall in an arbitrary or unreasonable fashion.11
*296The plaintiffs advance two further equal protection claims. First, they allege that, taken as a whole, Public Acts 1981, No. 81-255, as amended, is an income tax. This claim is premised on the contention that the scope of the unincorporated business tax, taken together with the amendment to create a fourth basis for imposition of the corporate income tax, is so broad that, in effect, it constitutes an income tax. It is not clear how such a premise, even if it had been proven, would lend weight to an argument of discriminatory treatment. Second, they allege that the amendment to the corporate income tax is itself discriminatory because it arbitrarily imposes corporate tax liability on compensation paid to corporate officers and to corporate employees owning only one percent of a corporation’s stock. Since the amendment treats all corporations alike, it can hardly be said to embody arbitrary distinctions. Furthermore, the purpose and effect of the amendment was, as the trial court found, to “equalize the taxation of all businesses and prevent taxpayers from incorporating to escape the unincorporated business tax.” The amendment therefore served to make the act in its entirety more rational and less discriminatory than it might otherwise have been.12
*297In sum, we agree with the trial court that the plaintiffs have failed in any respect to sustain their argument that Public Acts 1981, No. 81-255, as amended, violates their constitutional rights to equal protection. As that court held, “[t]he [statutory] classifications are reasonable and not arbitrary and the distinctions enumerated therein bear a reasonable relationship to the object of the legislation.”
II
The plaintiffs remaining claims of error arise under the due process clauses of the state and federal constitutions.13 As was the case with regard to their claimed rights to equal protection, the plaintiffs cannot prevail on these constitutional claims unless they can prove beyond a reasonable doubt that they have overcome the presumption of the act’s validity. See, e.g., Keogh v. Bridgeport, 187 Conn. 53, 59-61, 444 A.2d 225 (1982); Kellems v. Brown, supra, 486.
A
The plaintiffs’ first due process challenge is that Public Acts 1981, No. 81-255, as amended, is void for vagueness because it is ambiguously worded, internally inconsistent, unintelligible and loosely drafted. Due process demands that a statute be sufficiently clear and precise to “afford a person of ordinary intelligence a reasonable opportunity to know what is permitted or prohibited.” McKinney v. Coventry, 176 Conn. 613, 618-19, 410 A.2d 453 (1979); see Grayned v. City of Rockford, 408 U.S. 104, 108, 92 S. Ct. 2294, 33 L. Ed. 2d 222 (1972); Keogh v. Bridgeport, supra, 60-61; *298Wiegand v. Heffernan, 170 Conn. 567, 575, 368 A.2d 103 (1976). The plaintiffs maintain that the act fails this test by its imprecision about: (1) the identity of those subject to the unincorporated business tax and (2) the objects of taxation under the fourth base of the corporate business tax. Like the trial court, we find neither of these arguments persuasive.
The plaintiffs’ claim of indefiniteness in the unincorporated business tax arises from the act’s definition of an unincorporated business, which excludes “the performance of services by an individual as an employee . . . unless such services constitute part of a business regularly carried on by such individual.” Public Acts 1981, No. 81-255, § 2 (a); General Statutes (Rev. to 1983) § 12-610 (a) (2). The exception contained in the exclusion, according to the plaintiffs, is so broad that it might well include every salaried employee in the state. As the trial court noted, however, such a reading overlooks the significance of the statutory phrase “business regularly carried on” which indicates a statutory intent to differentiate between independent contractors, who are taxed, and ordinary employees, who are not. Cf. Costis v. Tully, 81 App. Div. 2d 997, 440 N.Y.S.2d 65 (1981). The reasonableness of the trial court’s construction is supported by the record before us which is totally devoid of any evidence of actual confusion regarding the scope of the act. “A statute is not void for vagueness . . . simply because it may be open to two possible constructions ... or ‘merely because the imagination can conjure up hypothetical situations in which the meaning of some terms may be in question.’ ” (Citations omitted.) McKinney v. Coventry, supra, 619.
The plaintiffs’ alternate claim of unconstitutional vagueness is that the amendment to the corporate business tax contains an impermissibly imprecise statement of what constitutes taxable corporate income. Under *299the formula for the fourth base, which was added by Public Acts 1981, No. 81-255, § 22; General Statutes (Rev. to 1983) § 12-219 (1) (B); a corporation’s income includes compensation paid to elected or appointed officers. The definition of an officer “include[s] the chairman, president, vice president, secretary, assistant secretary, treasurer, assistant treasurer, comptroller, and any other person, irrespective of his title, who is charged with and performs any of the regular functions of any such officer. A director shall be considered an elected or appointed officer only if he performs duties ordinarily performed by an officer.” Public Acts 1981, No. 81-255, § 22 (1); General Statutes (Rev. to 1983) § 12-219 (1) (B) (ii).
The plaintiffs’ argument that this statutory language leaves a corporate taxpayer without guidance about the extent of its tax liability is refuted by the apt analysis of the trial court. As the trial court explained, “[wjhat the challenged language clearly means is that if a person acts as president, or other appointed or elected officer his salary will be taxed, regardless of the title he gives himself. This section apparently is an attempt to prevent a person from escaping the tax by creating a new title not specifically covered by the Act, and is certainly not vague.” In context, the act is therefore sufficiently precise to pass constitutional muster.
B
The plaintiffs’ final claim of unconstitutionality is that the act denies them due process of law because of its retroactivity. They argue that the legislature in enacting a tax statute with an effective date of July 1,1981, could not constitutionally make that statute applicable to tax years beginning on or after January 1,1981.
The plaintiffs do not dispute the general proposition that the retroactive operation of a tax statute does not per se violate the due process rights of taxpayers *300adversely affected thereby. See, e.g., United States v. Darusmont, 449 U.S. 292, 297, 101 S. Ct. 549, 66 L. Ed. 2d 513 (1981) (per curiam); Welch v. Henry, 305 U.S. 134, 146, 148-50, 59 S. Ct. 121, 83 L. Ed. 87, reh. denied, 305 U.S. 675, 59 S. Ct. 250, 83 L. Ed. 437 (1938); Atlantic Coast Line R. Co. v. Daughton, 262 U.S. 413, 425, 43 S. Ct. 620, 67 L. Ed. 1051 (1923); Fein v. United States, 730 F.2d 1211, 1212 (8th Cir.), cert. denied, 469 U.S. , 105 S. Ct. 188, 83 L. Ed. 2d 121 (1984); Estate of Ceppi v. Commissioner, 698 F.2d 17, 20-22 (1st Cir.), cert. denied, 462 U.S. 1120, 103 S. Ct. 3088, 77 L. Ed. 2d 1350 (1983); Wiegand v. Heffernan, supra, 575-79; Kellems v. Brown, supra, 510; Parlato v. McCarthy, 136 Conn. 126, 130, 69 A.2d 648 (1949); see also Hochman, “The Supreme Court and the Constitutionality of Retroactive Legislation,” 73 Harv. L. Rev. 692, 706-11 (1960). Courts have traditionally upheld retroactive taxation because “[tjaxation is neither a penalty imposed on the taxpayer nor a liability which he assumes by contract. It is but a way of apportioning the cost of government among those who in some measure are privileged to enjoy its benefits and must bear its burdens. Since no citizen enjoys immunity from the burden, its retroactive imposition does not necessarily infringe due process . . . .” Welch v. Henry, supra, 146-47; Wiegand v. Hefernan, supra, 576-77.
The plaintiffs contend nonetheless that the act violates their rights to due process because the taxes it imposes are new, were not reasonably forseeable and could legitimately have been avoided by some of those liable therefor if they had been forewarned of their imposition.14 The aspect of this argument which is *301potentially the most persuasive is the suggestion that the act’s retroactivity is unconstitutional because the taxes it imposed were entirely new. See Milliken v. United States, 283 U.S. 15, 23-24, 51 S. Ct. 324, 75 L. Ed. 809 (1931); Fein v. United States, supra, 1213; Estate of Ceppi v. Commissioner, supra, 21; Appendrodt v. United States, 490 F. Sup. 490, 493 (W.D. Pa. 1980). The other prongs of plaintiffs’ argument depend to a great extent on the answer to this question.
In our view, neither tax is new. Since the corporate business tax was already in existence when the act was enacted, its amendment affecting the rate of taxation obviously did not create a new tax. Cf. United States v. Darusmont, supra, 300. The remaining issue is whether the unincorporated business tax was sufficiently “new” that its retroactive imposition creates constitutional problems. A brief examination of the history of Connecticut tax laws refutes such an assertion. A tax on unincorporated businesses was first enacted in 1921; see Public Acts 1921, Ch. 393; General Statutes § 12-269 et seq.; Stone v. Sullivan, 154 Conn. 498, 227 A.2d 76 (1967); and put into dormant status in 1969. See Public Acts, Spec. Sess., June, 1969, No. 1, § 47. Its revival in 1981 does not make it a new tax.
Because the taxes were not new, the plaintiffs cannot claim surprise at their imposition and thus the second prong of their argument, that the taxes were not reasonably foreseeable, necessarily fails. See Fein v. United States, supra, 1213. Moreover, the plaintiffs con*302cede that the taxpayers of Connecticut were on notice as early as February, 1981, that the governor of the state was proposing the re-enactment of an unincorporated business tax and an amendment to the corporate business tax. Cf. United States v. Darusmont, supra, 299.
In light of these considerations, the third prong of the plaintiffs’ argument, that they could have structured their transactions to avoid liability retroactively imposed if they had had warning, is no longer viable. In sum, the plaintiffs’ “position is far different from that of the individual who, as Judge [Learned] Hand stated . . . ‘has no reason to suppose that any transactions of the sort will be taxed at all.’ ” United States v. Darusmont, supra, 300, quoting Cohan v. Commissioner, 39 F.2d 540, 545 (2d Cir. 1930).15
No other feature of Public Acts 1981, No. 81-255, as amended, makes the act unconstitutionally retroactive. Its applicability to transactions occurring at the beginning of the calendar year, six months before its effective date, is no more unconstitutional than a similar period of retroactivity which we held valid in Kellems v. Brown, supra, 510. See also Wiegand v. Heffernan, *303supra, 577. “In each case it is necessary to consider the nature of the tax and the circumstances in which it is laid before it can be said that its retroactive application is so harsh and oppressive as to transgress the constitutional limitation.” Welch v. Henry, supra, 147. The plaintiffs in this case have failed to prove that the limited retroactivity of the act caused such hardship as to be unconstitutional.
There is no error.
In this opinion the other judges concurred.
The challenged provisions of the act were codified in General Statutes Chapter 228, “Unincorporated Business Tax,” §§ 12-610 through 12-629 and Chapter 208, “Corporation Business Tax,” § 12-219.
General Statutes (Rev. to 1983) Chapter 228 provided in relevant part: “Sec. 12-610. definitions. For the purposes of this chapter:
“(a) ‘Unincorporated business’ means any trade, business, profession or occupation conducted, engaged in or being liquidated by an individual, fiduciary or unincorporated entity, including a partnership, proprietorship or trust, provided unincorporated business shall not include (1) any entity subject to tax under chapters 207 to 212a, inclusive, (2) the performance of services by an individual as an employee or as an officer or director of a corporation, society, association or political entity or as a fiduciary unless such services constitute part of a business regularly carried on by such individual, (3) a trust, plan or other unincorporated entity which by reason of its purposes or activities is exempt from federal income tax regardless of whether it is subject to federal or state tax on unrelated business taxable income, or (4) any unincorporated entity all of the ownership interest in which is held by or in behalf of any political subdivision of the state, including any city, town or borough or any district as defined in section 7-324 or any metropolitan or municipal district created under section 7-330, or other district, district department of health, school board, housing authority or other authority established by law. If an individual or entity carries on two or more unincorporated businesses, all such businesses shall be treated as one unincorporated business for the purposes of this chapter.
“(b) ‘Gross income’ means all income, from whatever source derived, of the unincorporated business and its property, or the sale or exchange thereof, includable in gross income for the income year for federal income *286tax purposes, except there shall be subtracted from federal gross income of the unincorporated business the following items attributable to the business . . .
“(c) ‘Net income’ means the excess of gross income over deductions allowed under section 12-612.
“(d) ‘Taxable net income’ means net income apportioned to Connecticut in accordance with section 12-614, less the amount of the deduction allowed under section 12-615. . . .”
“Sec. 12-611. IMPOSITION OF TAX. EXEMPTION RELATED TO GROSS OR NET income. MINIMUM tax. (a) A tax is hereby imposed for each income year, at the rate of five per cent on the taxable net income of every unincorporated business wholly or partly carried on within this state, except as provided in subsection (b) of this section, which shall be in addition to any other taxes imposed by the state. The minimum tax shall be two hundred fifty dollars.
“(b) (1) Any unincorporated business whose gross income for the income year is fifty thousand dollars or less shall be exempt from the tax imposed by this section unless subsection (c) of this section is applicable to such business, in which case the exemption allowed by this subsection shall be reduced by a proportion equal to the number of months of the income year during which such business is incorporated or discontinued to twelve.
“(2) Any unincorporated business whose net income for the income year apportioned to Connecticut in accordance with section 12-614, less the amount of the exemption allowed under section 12-613, is fifteen thousand dollars or less shall be exempt from the tax imposed by this section unless subsection (c) of this section is applicable to such business, in which case the exemption allowed by this subsection shall be reduced by a proportion equal to the number of months of the income year during which such business is incorporated or discontinued to twelve.”
“Sec. 12-615. DEDUCTIONS FROM NET INCOME IN COMPUTING TAXABLE net income. In computing taxable net income, as defined in section 12-610, there shall be allowed a deduction from (1) net income, if the entire business of the taxpayer has been conducted in this state, in an amount equal to fifty per cent of net income or fifteen thousand dollars, whichever is greater or (2) net income apportioned to this state in accordance with section 12-614, if the entire business of the taxpayer has not been conducted in this state, in an amount equal to fifty per cent of such apportioned net income or fifteen thousand dollars, whichever is greater. In addition there shall be allowed as a deduction from net income in computing taxable net income, the amount of contributions in any income year, by any proprietor or partner of a taxpayer subject to tax under this chapter for purposes of a retirement plan qualified for tax deferment in accordance with federal *287income tax requirements, in amounts not in excess of one thousand seven hundred fifty dollars with respect to any such proprietor or partner.”
General Statutes (Rev. to 1983) Chapter 208 § 12-219 provides in relevant part: “additional tax in the amount by which alternative computations EXCEED TAX UNDER SECTION 12-214. MINIMUM TAX. (1) For each income year beginning on or after January 1,1973, for which the tax calculated under subdivision (A) of this section, or subdivision (B) of this section with respect to any company the gross income of which exceeds fifty thousand dollars in such income year, whichever is higher, exceeds the tax imposed by section 12-214, each company subject to the provisions of this part. . . shall pay for the privilege of carrying on or doing business within the state, in addition to the tax imposed by section 12-214, an additional tax of the amount by which the tax calculated under subdivision (A) or subdivision (B) of this section, whichever is higher, for such income year exceeds the tax imposed by section 12-214. In the case of a company other than a regulated investment company or real estate investment trust, the tax calculated under this section shall be ... (B) A tax to be measured by fifty per cent of (i) the net income or loss of such corporation or association but only to the extent that said income or loss is allocated and apportioned to this state, which income is the entire net income as defined in this chapter received by such corporation or association from business transacted within the state during the income year and which loss is the net loss of such corporation or association related to business transacted within the state during the income year, plus (ii) salaries and other compensation paid to the elected or appointed officers of such corporation or association and to every shareholder owning in excess of one per cent of the issued capital stock of such corporation or association, apportioned to this state by means of the apportionment fraction determined under subdivision (3) of section 12-218, at the rate of five per cent. The provisions of section 12-219a shall not apply to this subdivision. For purposes of this subdivision, the term ‘elected or appointed officer’ shall include the chairman, president, vice president, secretary, assistant secretary, treasurer, assistant treasurer, comptroller and any other person, irrespective of his title, who is charged with and performs any of the regular functions of any such officer. A director shall be considered an elected or appointed officer only if he performs duties ordinarily performed by an officer. . . . The tax calculated under subdivision (A) or subdivision (B) of this section shall, in no case, be less than two hundred fifty dollars for each income year.”
Public Acts, Spec. Sess., November, 1981, No. 81-4, §§ 30 and 32 (6) (repealing fourth base of corporate taxation), §§ 31 and 32 (7) (repealing unincorporated business tax).
The act defines an unincorporated business as “any trade, business, profession or occupation conducted, engaged in or being liquidated by an individual, fiduciary or unincorporated entity, including a partnership, proprietorship or trust . . . .” Public Acts 1981, No. 81-255, § 2 (a); General Statutes (Rev. to 1983) § 12-610 (a).
The act defines taxable net income as net income minus the greater of 50 percent of net income or $15,000. Taxable net income is further reduced by permitting the deduction of contributions to an individual retirement account or a Keogh plan in an amount not in excess of $1750. Public Acts 1981, No. 81-255, §§ 2 (a) and 7; General Statutes (Rev. to 1983) § 12-615.
The additional tax was to be levied upon 50 percent of a corporation’s net income and 50 percent of the compensation paid to corporate officers and to stockholders owning more than 1 percent of the corporation’s stock. Public Acts 1981, No. 81-255, § 22; Public Acts 1981, No. 81-411, § 8; General Statutes (Rev. to 1983) § 12-219 (1). One of the previously existing bases was a minimum tax of $100. The act raised this tax to $250. Public Acts 1981, No. 81-255, § 22; Public Acts 1981, No. 81-411, § 8; General Statutes (Rev. to 1983) § 12-219 (1).
The equal protection clauses of the United States constitution, § 1, of the fourteenth amendment, and of the Connecticut constitution, article first, § 20, can be treated conjointly because “[they] have a like meaning, imposing similar constitutional limitations.” Miller v. Heffernan, 173 Conn. 506, 509, 378 A.2d 572 (1977), appeal dismissed, 434 U.S. 1057, 98 S. Ct. 1226, 55 L. Ed. 2d 758 (1978); United Illuminating Co. v. New Haven, 179 Conn. 627, 635, 427 A.2d 830 (1980); Kellems v. Brown, 163 Conn. 478, 485, 313 A.2d 53 (1972), appeal dismissed, 409 U.S. 1099, 93 S. Ct. 911, 34 L. Ed. 2d 678 (1973).
The defendants argue that the act establishes only one notch exemption. They claim it does not contain the second notch exemption for $15,000 net income. This interpretation apparently stems from a confusion over two separate sections of the act. Public Acts 1981, No. 81-255, § 7; General Statutes (Rev. to 1983) § 12-615, provides for a deduction of $15,000 or one-half of net income in computing taxable net income that is not a notch exemption. By contrast, Public Acts 1981, No. 81-411, § 7; General Statutes (Rev. to 1983) § 12-611 (b) (2), which exempts business with less than $15,000 net income from any tax liability, does fit the description of a notch exemption. This notch exemption was an amendment to the original act, Public Acts 1981, No. 81-411, § 7. When the amendment was under discussion in the House, Representative Mannix commented on its function. “[T]his amendment cleans up somewhat some perhaps ambiguous interpretations of the tax on unincorporated business. What it does is clearly state that if you have an income of $15,000 or less you are not liable for the tax or the minimum tax.” 24 H.R. Proc., Pt. 24, 1981 Sess,, p. 8151; see also id., p. 8152.
These statistics are taken from the United States Department of Labor, Bureau of Labor Statistics, Handbook of Labor Statistics, December, 1980, pp. 385-88.
See footnote 4 and accompanying text, supra, for method of calculation.
In the trial court, the plaintiffs adduced only one tax return to demonstrate the validity of this observation.
The defendants argue that the two notch exemptions are analogous to classifications found unconstitutional by courts in other jurisdictions. They rely on Kalian v. Langton, 96 R.I. 367, 192 A.2d 12 (1963), and Johnson & Porter Realty Co. v. Commissioner of Revenue Administration, 122 N.H. 696, 448 A.2d 435 (1982).
In Miller v. Heffernan, we described the Rhode Island tax which the Supreme Court of Rhode Island in Kalian v. Langton, supra, held violative of equal protection as “a tax statute which immunized from taxation [unincorporated] businesses with gross receipts of less than $30,000 while subjecting businesses with gross receipts in excess of this to a tax on all but $5000 of the total receipts.” Miller v. Heffernan, 173 Conn. 506, 515, 378 A.2d 572 (1977), appeal dismissed, 434 U.S. 1057, 98 S. Ct. 1226, 55 L. Ed. 2d 758 (1978). The Rhode Island tax was a tax on gross receipts, not on net income and provided no protection for businesses whose net income fell below a certain level. It is thus arguably more arbitrary than the tax at issue in the case before us. Moreover, to the extent that the Rhode Island decision is based on the court’s perception that the protection of small businesses is not a legitimate legislative goal; see Kalian v. Langton, supra, 377; we decline to follow its reasoning. See Betts v. Zeller, 263 A.2d 290, 294-95 (Del. 1970) (declining to follow the rationale of Kalian v. Langton and upholding a tax exempting taxpayers with less than $4000 earnings from taxation). In any case, we are not any more persuaded today than we were in Miller v. Heffernan that the Rhode Island court’s view of the Rhode Island tax structure can be superimposed upon the different fact pattern of the Connecticut tax system. See Miller v. Heffernan, supra, 515.
The plaintiffs also argue that the present case is similar to Johnson & *296Porter Realty Co. v. Commissioner of Revenue Administration, supra, which held unconstitutional a minimum business profits tax that imposed a minimum tax of $250 on every business with a gross income in excess of $12,000 and business profits of less than $2753. The New Hampshire statute changed the previously existing business profits tax under which a business with no net income would not be subject to tax liability. Although the New Hampshire Supreme Court held the tax unconstitutional, the basis for its decision was not a denial of equal protection, but rather a violation of specific provisions in the New Hampshire constitution requiring uniformity and proportionality in taxation. See id., 698. The plaintiffs’ reliance on this case in their equal protection claim is therefore misplaced.
In the trial court, the plaintiffs also specifically challenged the $250 minimum tax as violative of equal protection. The plaintiffs have not briefed that issue on appeal and it is thus considered abandoned. See Pastir v. Bielski, 174 Conn. 193, 384 A.2d 367 (1978).
The due process clauses of the United States constitution, § 1, of the fourteenth amendment, and of the Connecticut constitution, article first, § 8, can be treated together because they “generally have the same meaning and impose similar constitutional limitations.” Keogh v. Bridgeport, 187 Conn. 53, 60, 444 A.2d 225 (1982); McKinney v. Coventry, 176 Conn. 613, 616, 410 A.2d 453 (1979).
In United States v. Darusmont, 449 U.S. 292, 101 S. Ct. 549, 66 L. Ed. 2d 513 (1981) (per curiam), the United States Supreme Court considered a similar three-pronged argument in a challenge to the validity of a retroactive federal income tax statute. The court rejected the third factor, whether liability could have'been avoided if it had been foreseen, as inap*301propriate to an assessment of an income tax statute as opposed to a gift tax statute. Id., 299. The court went on to address the merits of the remaining factors and concluded there was no due process violation. The court assumed arguendo that the factors were relevant, but did not specifically approve them as an appropriate way to evaluate the legislation. Id., 299-301; see Fein v. United States, 730 F.2d 1211, 1212 (8th Cir.), cert. denied, 469 U.S. , 105 S. Ct. 188, 83 L. Ed. 2d 121 (1984); Estate of Ceppi v. Commissioner, 698 F.2d 17, 21-22 (1st Cir.), cert. denied, 462 U.S. 1120, 103 S. Ct. 3088, 77 L. Ed. 2d 1350 (1983).
We do not intend our discussion of the three prongs to imply that a failure to meet one or more of the prongs of the plaintiffs proposed test would necessarily render the statute invalid. Courts have eschewed reliance on rigid standards in determining whether a retroactive tax statute violates due process in any given situation. As one court has observed, “[t]he validity of retroactive statutes, including those imposing retroactive taxes, has been challenged on many occasions in the courts of this nation. A review of United States Supreme Court decisions involving retroactive legislation does not reveal inflexible rules or immutable patterns of due process analysis with respect to such legislation. Rather, it is clear that the constitutionality of a retroactive statute depends upon a broad variety of policy considerations couched within a due process framework.” State ex rel. Van Emmerik v. Janklow, 304 N.W.2d 700, 703 (S.D. 1981), appeal dismissed, 454 U.S. 1131, 102 S. Ct. 986, 71 L. Ed. 2d 285 (1982); cf. Fein v. United States, 730 F.2d 1211, 1212-13 (8th Cir.), cert. denied, 469 U.S. , 105 S. Ct. 188, 83 L. Ed. 2d 121 (1984); Appendrodt v. United States, 490 F. Sup. 490, 493 (W.D. Pa. 1980).