<PAGE>   1
THIS WARRANT AND ANY SHARES ACQUIRED UPON THE EXERCISE OF THIS WARRANT HAVE NOT
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR UNDER ANY
STATE SECURITIES LAWS, AND MAY BE OFFERED AND SOLD ONLY IF SO REGISTERED OR AN
EXEMPTION FROM REGISTRATION IS AVAILABLE.  THE HOLDER OF THIS WARRANT OR ANY
SUCH SHARES MAY BE REQUIRED TO DELIVER TO THE COMPANY, IF THE COMPANY SO
REQUESTS, AN OPINION OF COUNSEL (REASONABLY SATISFACTORY IN FORM AND SUBSTANCE
TO THE COMPANY) TO THE EFFECT THAT AN EXEMPTION FROM REGISTRATION UNDER THE
SECURITIES ACT (OR QUALIFICATION UNDER STATE SECURITIES LAWS) IS AVAILABLE WITH
RESPECT TO ANY TRANSFER OF THIS WARRANT OR THESE SHARES THAT HAS NOT BEEN SO
REGISTERED (OR QUALIFIED).

THIS WARRANT AND ANY SHARES OF THE COMPANY ACQUIRED UPON THE EXERCISE OF THIS
WARRANT ALSO ARE SUBJECT TO ADDITIONAL RESTRICTIONS ON TRANSFER AND
OBLIGATIONS, TO WHICH ANY TRANSFEREE AGREES BY HIS ACCEPTANCE HEREOF, AS SET
FORTH HEREIN AND IN THE STOCKHOLDERS AGREEMENT OF THE COMPANY, DATED AS OF
MARCH 22, 1995, COPIES OF WHICH MAY BE OBTAINED FROM THE COMPANY.  NO TRANSFER
OF THIS WARRANT OR SUCH SHARES WILL BE MADE ON THE BOOKS OF THE COMPANY UNLESS
ACCOMPANIED BY EVIDENCE OF COMPLIANCE WITH THE TERMS HEREOF AND OF SUCH
STOCKHOLDERS AGREEMENT AND BY AN AGREEMENT OF THE TRANSFEREE TO BE BOUND BY THE
RESTRICTIONS SET FORTH HEREIN AND IN THE STOCKHOLDERS AGREEMENT.



                         DOMINICK'S SUPERMARKETS, INC.

                     Class A Common Stock Purchase Warrant

No . W-1                                                         264,688 shares
                                                                 March 22, 1995


     DOMINICK'S SUPERMARKETS, INC., a Delaware corporation (together with any
corporation that shall succeed to or assume the obligations of the Company
hereunder in compliance with Section 4, the "Company"), for value received,
hereby certifies that THE YUCAIPA COMPANIES, a California general partnership,
or its registered permitted assigns (the "Holder"), is entitled to purchase
from the Company an aggregate of 264,688 shares of Class A Common Stock (as
defined below), at the Exercise Price (as defined below) per share, subject to
the terms, conditions and adjustments set forth below, (i) in whole or in part,
at any time or from time to time from and after the occurrence of a Qualified
IPO (as defined below) and on or prior to 5:00 P.M., New York 


<PAGE>   2


City  time, on the Expiration Date (as defined below) or (ii) in whole,
concurrently with any Qualified Sale Event occurring on or prior to the
Expiration Date.


     1. Definitions.  Capitalized terms used herein and not otherwise defined
herein have the meanings ascribed to them in the Stockholders Agreement (the
"Stockholders Agreement"), dated as of March 22, 1995, among the Company, DFF
Supermarkets, Inc., a Delaware corporation, Dominick's Finer Foods, Inc., a
Delaware corporation, and certain stockholders of the Company.  In addition,
the following terms shall have the meanings ascribed to them below:

     "Class A Common Stock" shall mean the Class A Common Stock, par value $.01
per share, of the Company and any stock into which such Class A Common Stock
shall have been changed or any stock resulting from any reclassification of
such Class A Common Stock.

     "Enterprise Value" shall mean (without duplication) the sum of (a) the
aggregate value of the fully diluted common equity of the Company, based on an
assumed price per Share equal to the Exercise Price, net of the exercise,
exchange or conversion price, if any, with respect to any security exercisable
or exchangeable for or convertible into Common Stock of the Company, plus (b)
the aggregate principal amount of all Indebtedness of the Company and its
consolidated Subsidiaries and the aggregate liquidation preference of all
preferred stock of the Company (other than preferred stock included in clause
(a) above), in each case as reflected on the most recent balance sheet of the
Company and its consolidated Subsidiaries that was (or was required to be)
provided pursuant to Section 4.4 of the Stockholders Agreement on or prior to
March 22, 2000, less (c) all cash and cash equivalents of the Company and its
consolidated Subsidiaries as reflected on such balance sheet.

     "Expiration Date" initially shall mean March 22, 2000; provided, that if,
on such date, the product of (i) 6 times (ii) EBITDA for the latest four fiscal
quarters of the Company for which information was (or was required to be)
provided pursuant to Section 4.4 of the Stockholders Agreement exceeds the
Enterprise Value, then "Expiration Date" shall mean March 22, 2002.

     "Market Price" shall mean the average closing sale price of a share of
Class A Common Stock, regular way, for the period of 20 consecutive trading
days ending on the trading day immediately preceding the date of such exercise
or, in case no such sale takes place on any such day, the average of the
reported closing bid and asked prices, regular way, in each case on a Permitted
Exchange or, if not so available, as such Market Price may be determined by a
nationally recognized investment bank selected by a majority of the
disinterested members of the Board of Directors of the Company that are neither
Affiliates of the Holder nor designated or nominated by the Holder or any of
its Affiliates (the "Disinterested Directors"); provided, that if the Warrant
is exercised (i) on or prior to the 20th trading day following consummation of
a Qualified IPO, "Market Price" shall mean the price for the public in such
Qualified IPO or (ii) concurrently with a Qualified 


                                      2
<PAGE>   3
Sale Event, "Market Price" shall mean the price per share of Class A Common
Stock paid in such Qualified Sale Event.
        
     "Qualified Sale Event" shall mean a sale of all, but not less than all,
of the issued and outstanding shares of capital stock of the Company to a Third
Party in a bona fide transaction; provided, that from and after March 22, 2000,
such term shall only include a Compelled Sale.

     2.  Exercise of Warrant.

     2.1 Manner of Exercise.  Subject to the foregoing, this Warrant may be
exercised by the Holder hereof, in whole or in part, during normal business
hours on any day other than a Saturday or a Sunday or a day on which commercial
banking institutions in the City of New York are authorized by law to be closed
(a "Business Day"), by surrender of this Warrant to the Company at its office
maintained pursuant to Section 9.2, accompanied by a subscription in
substantially the form attached to this Warrant (or a reasonable facsimile
thereof), duly executed by such Holder.  Payment of the aggregate Exercise
Price of the number of shares of Class A Common Stock designated in such
subscription shall be made by the Company withholding therefrom that number of
shares of Class A Common Stock with an aggregate Market Price as of the date of
exercise equal to such aggregate Exercise Price.

     2.2 When Exercise Effective.  Each exercise of this Warrant shall be deemed
to have been effected immediately prior to the close of business on the
Business Day on which this Warrant and the accompanying subscription shall have
been duly surrendered to the Company as provided in Section 2.1, and at such
time the Holder shall be deemed to have become the holder or holders of record
of a number of shares of Class A Common Stock equal to the number of shares
designated in such subscription less the number of shares withheld by the
Company as payment therefor.

     2.3 Delivery of Stock Certificates, etc.  As soon as practicable after each
exercise of this Warrant, in whole or in part, in accordance with the terms of
Section 2.1, the Company will cause to be issued in the name of, and delivered
to the Holder hereof,

           (a) a certificate or certificates for the number of duly authorized,
      validly issued, fully paid and nonassessable shares of Class A Common
      Stock to which such Holder shall be entitled upon such exercise plus, in
      lieu of any fractional share to which such holder would otherwise be
      entitled, cash in an amount equal to the same fraction of the Market
      Price per share on the date of such exercise, and

           (b) in case such exercise is in part only, a new Warrant of like
      tenor, calling in the aggregate on the face or faces thereof for the
      number of shares of Class A Common Stock equal to the number of such
      shares called for on the face of this Warrant (after giving effect to any
      adjustment thereof after the date 

                                      3
<PAGE>   4
     hereof) minus the number of such shares designated by the Holder upon
     such exercise as provided in Section 2.1.
        
     3. Adjustments.

         3.1. General.  (a)  The number of shares of Class A Common Stock that
the Holder shall be entitled to receive upon each exercise hereof shall be
determined by multiplying the number of shares of Class A Common Stock that
would otherwise (but for the provisions of this Section 3) be issuable upon
such exercise, by a fraction (i) the numerator of which is the Warrant Price
(as defined below) and (ii) the denominator of which is the Exercise Price, in
each case in effect on the date of such exercise.

         Each of the "Exercise Price" and the "Warrant Price" shall initially be
$303.48 per share; provided, that the Exercise Price shall be adjusted and
readjusted from time to time as provided in Section 3 and the Warrant Price
shall be adjusted and readjusted from time to time as provided in Section
3.1(b).

              (b) From and after March 22, 2000, the Exercise Price and the
     Warrant Price shall each be increased daily at a rate of 25% per annum,
     compounded annually.

         3.2. Treatment of Stock Dividends.  If, after the date hereof, the
Company shall declare or pay any dividend on the Class A Common Stock payable
in Class A Common Stock, then, and in each such case, the Exercise Price in
effect immediately after the close of business on the record date for the
determination of holders entitled to receive such dividend, shall be reduced by
multiplying such Exercise Price by a fraction (a) the numerator of which shall
be the number of shares of Class A Common Stock outstanding at the close of
business on such record date and (b) the denominator of which shall be the sum
of such number of shares and the total number of shares constituting such
dividend or other distribution.

         3.3. Adjustments for Stock-Splits, Combinations.  If, after the date
hereof, the outstanding shares of Class A Common Stock shall be subdivided into
a greater number of shares of Class A Common Stock or combined into a smaller
number of shares of Class A Common Stock by stock split, combination,
reclassification or otherwise, the Exercise Price in effect immediately prior
to such subdivision or combination shall, concurrently with the effectiveness
of such subdivision or combination, be proportionately reduced or increased.

         3.4. Minimum Adjustment of Warrant Price.  If the amount of any
adjustment of the Exercise Price required pursuant to Sections 3.2 or 3.3 would
be less than one percent (1%) of the Exercise Price in effect at the time such
adjustment is otherwise so required to be made, such amount shall be carried
forward and adjustment with respect thereto made at the time of and together
with any subsequent adjustment which, together with such amount and any other
amount or amounts so carried forward, shall aggregate at least one percent (1%)
of such Exercise Price, provided, that all such adjustments required 


                                      4
<PAGE>   5
pursuant to Sections 3.2 and 3.3 and carried forward under this Section
3.4 shall be made upon (and in connection with) any exercise of the Warrant.

     3.5 Form of Warrants.  Irrespective of any adjustments in the Exercise
Price or the number of shares of Class A Common Stock purchasable upon the
exercise of the Warrants, Warrants theretofore or thereafter issued may
continue to express the same price and number and kind of shares as are stated
in the Warrant initially issued.

     4.  Consolidation, Merger, etc.

         If, after the date hereof, the Company shall


           (a) consolidate with or merge into any other Person and shall not be
      the continuing or surviving corporation of such consolidation or merger,
      or

           (b) permit any other Person to consolidate with or merge into the
      Company and the Company shall be the continuing or surviving Person but,
      in connection with such consolidation or merger, the Class A Common Stock
      shall be changed into or exchanged for stock or other securities of any
      other Person or cash or any other property, or

           (c) effect a capital reorganization or reclassification of the Class
      A Common Stock

(other than (i) a Qualified Sale Event or (ii) in the cases for which an
adjustment has been or is to be made pursuant to Section 3), then proper
provision shall be made so that, upon the basis and the terms and in the manner
provided in this Warrant, the holder of this Warrant, upon the exercise hereof
after the consummation of such transaction, shall be entitled to receive, in
lieu of the Class A Common Stock issuable upon such exercise, the kind and
amount of securities, cash or other property to which such holder would
actually have been entitled upon such consummation if such holder had exercised
the rights represented by this Warrant in full (giving effect to the payment of
the aggregate Exercise Price) immediately prior thereto.

     5. Certain Covenants.  The Company (a) will not permit the par value of any
shares of stock receivable upon the exercise of this Warrant to exceed the
amount payable therefor upon such exercise, (b) will take all such reasonable
action as may be necessary or appropriate in order that the Company may validly
and legally issue fully paid and nonassessable shares of stock on the exercise
of the Warrants from time to time outstanding.

     6. Accountants' Report as to Adjustments.  Upon the occurrence of any event
requiring adjustment or readjustment in the Exercise Price (other than by
operation of Section 3.1(b)) or the shares of Class A Common Stock issuable
upon the exercise of this Warrant, the Company will promptly compute such
adjustment or readjustment in 


                                      5
<PAGE>   6

accordance with the terms of this Warrant and cause independent
certified public accountants of recognized national standing (which may be the
regular auditors of the Company) selected by a majority of the Disinterested
Directors to verify such computation and prepare a report setting forth such
adjustment or readjustment and showing in reasonable detail the method of
calculation thereof and the facts upon which such adjustment or readjustment is
based.  The Company will promptly mail a copy of each such report to the
Holder.

      7.  Restrictions on Transfer.



          (a) Legends.  Each Warrant shall be stamped or otherwise imprinted
      with a legend in substantially the form set forth hereon.  Each
      certificate for shares of Class A Common Stock issued upon the exercise
      of any Warrant, and each certificate issued upon the transfer of any such
      Class A Common Stock, shall be stamped or otherwise imprinted with a
      legend in substantially the form set forth in Section 2.3 of the
      Stockholders Agreement.

          (b) No Transfer.  Neither this Warrant nor any interest herein may
      be directly or indirectly transferred or assigned by the Holder other
      than to Ronald W. Burkle or a Controlling Stockholder controlled by
      Ronald W. Burkle and, the equity holders of which consist solely of
      Ronald W. Burkle and Yucaipa Individuals.

      8.  Reservation of Stock, etc.  The Company will at all times reserve and
keep available, solely for issuance and delivery upon exercise of the Warrants,
the number of shares of Class A Common Stock from time to time issuable upon
exercise of this Warrant.  All shares of Class A Common Stock issuable upon
exercise of this Warrant shall be duly authorized and, when issued upon such
exercise in accordance with the terms hereof, shall be validly issued and fully
paid and nonassessable with no liability on the part of the holders thereof.

      9.  Ownership and Transfer.

      9.1 Ownership of Warrants.  The Company shall treat the person in whose
name any Warrant is registered on the register kept at the office of the Company
maintained pursuant to Section 9.2(a) as the owner and holder thereof for all
purposes, notwithstanding any notice to the contrary.

      9.2 Office; Transfer and Exchange of Warrants.

          (a) The Company will maintain an office at 333 N. Northwest Avenue,
      Northlake, Illinois 60164, until such time as the Company shall notify
      the Holder of the Warrant of any change of location of such office.

          (b) Subject to Section 7, upon the surrender of any Warrant,
      properly endorsed, for registration of transfer or for exchange at the
      office of the Company maintained pursuant to Section 9.2(a), the Company
      will execute and 

                                      6
<PAGE>   7

      deliver to or upon the order of the Holder thereof a new
      Warrant or Warrants of like tenor, in the name of such holder or as such
      holder (upon payment by such holder of any applicable transfer taxes) may
      direct, calling in the aggregate on the face or faces thereof for the
      number of shares of Class A Common Stock called for on the face or faces
      of the Warrant or Warrants so surrendered.

     10. No Rights or Liabilities as Stockholder.  Nothing contained in this
Warrant shall be construed as conferring upon the Holder any rights as a
stockholder of the Company or as imposing any obligation on such holder to
purchase any securities or as imposing any liabilities on
such holder as a stockholder of the Company, whether such obligation or
liabilities are asserted by the Company or by creditors of the Company.

     11. Notices.  All notices, demands, requests, consents, approvals or other
communications required or permitted to be given hereunder or which are given
with respect to this Warrant shall be in writing and shall be personally served
or delivered by a reputable air courier service with charges prepaid, or
transmitted by hand delivery, telegram, telex or facsimile, addressed (a) if to
any holder of any Warrant, at the registered address of such holder as set
forth in the register kept at the principal office of the Company, or (b) if to
the Company, to the attention of its Chief Executive Officer at its office
maintained pursuant to Section 9.2(a), provided that the exercise of any
Warrant shall be effective only in the manner provided in Section 2.  Notice
shall be deemed given on the date of service or confirmation of receipt of
transmission if personally served or transmitted by telegram, telex or
facsimile.  Notice otherwise sent as provided herein shall be deemed given on
the next Business Day following delivery of such notice to a reputable air
courier service.

     12. Miscellaneous.  This Warrant and any term hereof may be changed,
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or
termination is sought.  THIS WARRANT SHALL BE GOVERNED BY, INTERPRETED UNDER,
AND CONSTRUED IN ACCORDANCE WITH THE INTERNAL LAWS OF THE STATE OF NEW YORK
APPLICABLE TO AGREEMENTS MADE AND TO BE PERFORMED WITHIN THE STATE OF NEW YORK
WITHOUT GIVING EFFECT TO THE CHOICE-OF-LAW PROVISIONS THEREOF.  Titles and
headings of sections of this Warrant are for convenience only and shall not
affect the construction of any provision of this Warrant.

     13. Expiration.  The right to exercise this Warrant shall expire at 5:00
P.M., New York City time, on the Expiration Date.


                                          DOMINICK'S SUPERMARKETS, INC.


                                          By:    /s/ Mark A. Resnik
                                             -----------------------------
                                          Name:  Mark A. Resnik
                                          Title: Vice President




                                       7
<PAGE>   8


                              FORM OF SUBSCRIPTION

                 [To be executed only upon exercise of Warrant]


To:  DOMINICK'S SUPERMARKETS, INC.

     The undersigned registered holder of the within Warrant hereby irrevocably
exercises such Warrant for, and purchases thereunder, ____* shares of Class A
Common Stock of DOMINICK'S SUPERMARKETS, INC. and requests that the
certificates for such shares be issued in the name of, and delivered to the
undersigned, whose address is set forth below.  In payment therefor, the
Company may withhold therefrom, and the undersigned holder hereby surrenders
its right to, that number of shares of Class A Common Stock with an aggregate
Market Price as of the date of exercise equal to the aggregate Exercise Price
for the shares designated for purchase in the preceding sentence.


Dated:

                               ------------------------------------------------ 
                               (Signature must conform in all respects to name
                               of holder as specified on the face of Warrant)



                               ------------------------------------------------ 
                               (Street Address)



                               ------------------------------------------------ 
                               (City) (State) (Zip Code)

*Insert here the number of shares called for on the face of this Warrant (or,
in the case of a partial exercise, the portion thereof as to which the Warrant
is being exercised), in either case after making any adjustment for additional
shares of Class A Common Stock which, pursuant to the adjustment provisions of
this Warrant, may be delivered upon exercise. In the case of a partial
exercise, a new Warrant or Warrants will be  issued and delivered, representing
the unexercised portion of the Warrant, to the holder surrendering the Warrant.



                                       8

<PAGE>   9


                         DOMINICK'S SUPERMARKETS, INC.

              SUPPLEMENT TO CLASS A COMMON STOCK PURCHASE WARRANT


     This SUPPLEMENT TO CLASS A COMMON STOCK PURCHASE WARRANT, dated as of
November 1, 1996, between Dominick's Supermarkets, Inc., a Delaware corporation
(the "Company"), and The Yucaipa Companies, a California general partnership
("Yucaipa"), amends that certain Class A Common Stock Purchase Warrant No. W-1
dated as of March 22, 1995 of the Company entitling Yucaipa to purchase 264,688
shares (subject to adjustment) of Class A Common Stock of the Company (the
"Warrant").  Capitalized terms used herein without definition shall have the
meanings assigned to them in the Warrant.

     WHEREAS, the parties hereto have entered into the Warrant and desire to
amend certain provisions thereof, as more fully described herein;

     NOW, THEREFORE, in consideration of the premises, the parties hereto
hereby agree as follows:

     1.  Manner of Exercise.  Section 2.1 of the Warrant shall be amended to
read in its entirety as follows:

           2.1.  Manner of Exercise.  Subject to the foregoing, this
      Warrant may be exercised by the Holder hereof, in whole or in
      part, during normal business hours on any day other than a
      Saturday or a Sunday or a day on which commercial banking
      institutions in the City of New York are authorized to be closed
      (a "Business Day"), by surrender of this Warrant to the Company at
      its office maintained pursuant to Section 9.2, accompanied by a
      subscription in substantially the form attached to this Warrant
      (or a reasonable facsimile thereof), duly executed by such Holder.
      Payment of the aggregate Exercise Price of the number of shares
      of Class A Common Stock designated in such subscription may be
      made, at the Holder's option, either (i) in cash or by certified
      or bank check in the amount of the aggregate Exercise Price at the
      office of the Company designated for such purpose or by wire
      transfer of immediately available funds in the amount of such
      aggregate Exercise Price to an account designated by the Company
      or (ii) by the Company withholding therefrom that number of shares
      of Class A Common Stock with an aggregate Market Price as of the
      date of exercise equal to such aggregate Exercise Price.

     2.  When Exercise Effective.  Section 2.2 of the Warrant shall be amended
to read in its entirety as follows:

           2.2.  When Exercise Effective.  Each exercise of this Warrant
      shall be deemed to have been effected immediately prior to the
      close of business on the Business Day on which this Warrant and
      the accompanying 


                                       9

<PAGE>   10
      subscription shall have been duly surrendered to the Company as provided
      in Section 2.1, and at such time the Holder shall be deemed to have
      become the holder or holders of record of a number of shares of Class A
      Common Stock equal to (a) in the case of "cash exercise" pursuant to
      clause (i) of Section 2.1, the number of shares designated in such
      subscription or (b) in the case of "cashless exercise" pursuant to clause
      (ii) Section 2.1, the number of shares designated in such subscription
      less the number of shares withheld by the Company as payment therefor.
                        
     3.  Form of Subscription.  The sole paragraph of the Form of Subscription
attached to the Warrant shall be amended to read in its entirety as follows:

           The undersigned registered holder of the within Warrant
      hereby irrevocably exercises such Warrant for, and purchases
      thereunder, _______* shares of Class A Common Stock of DOMINICK'S
      SUPERMARKETS, INC. and requests that the certificates for such
      shares be issued in the name of, and delivered to the undersigned,
      whose address is set forth below.  In payment therefor, the
      undersigned registered holder elects (check one):

      [ ]  the "cash exercise" pursuant to clause (i) of Section 2.1 of
      the Warrant, and the undersigned registered holder herewith
      tenders payment for such shares to the order of DOMINICK'S
      SUPERMARKETS, INC. in the amount of $__________ in accordance with
      the terms of the Warrant; or

      [ ]  the "cashless exercise" pursuant to clause (ii) of Section
      2.1 of the Warrant, and the undersigned registered holder hereby
      surrenders its right to, and authorizes the Company to withhold
      therefrom, that number of shares of Class A Common Stock with an
      aggregate Market Price as of the date of exercise equal to the
      aggregate Exercise Price for the shares designated for the
      purchase in the preceding sentence.


                                      10
<PAGE>   11


     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to Class
A Common Stock Purchase Agreement to be duly executed and delivered as of the
day and year first above written.

                                       DOMINICK'S SUPERMARKETS, INC.


                                       By:    /s/ Robert A. Mariano
                                          ----------------------------------
                                       Name:  Robert A. Mariano

                                       Title: President and Chief Executive 
                                              Officer
 

                                       THE YUCAIPA COMPANIES


                                       By:    /s/ Ronald W. Burkle
                                          ---------------------------------
                                      Name:   Ronald W. Burkle
                                      Title:  General Partner




                                      11