*39 OPINION OF THE COURT

JAMES HUNTER, III, Circuit Judge.

This is an appeal from an order dismissing appellant Hahnemann University’s (“Hahnemann”) complaint under section 301 of the Labor Management Relations Act of 1947, 29 U.S.C. § 185 (1982), for injunctive and declaratory relief against District 1199C, National Union of Hospital and Health Care Employees (“District 1199C”). 596 F.Supp. 443 (D.C.Pa.1983). Hahnemann sought an order both enjoining District 1199C from proceeding to arbitration over a dispute concerning Hahne-mann’s dietary department, and defining the scope of Hahnemann’s duty to arbitrate under the collective bargaining agreement between Hahnemann and District 1199C. Because we believe that federal court interference in the parties’ dispute at this time would be inconsistent both with the parties’ agreement and with federal labor policy, we will affirm the order dismissing Hahne-mann’s complaint.

Hahnemann operates a medical school and teaching hospital in Philadelphia, Pennsylvania. District 1199C is a labor organization that is the certified bargaining representative of service and maintenance employees of Hahnemann, including all dietary department employees who regularly work twenty or more hours per week. The relationship between the parties is governed by a collective bargaining agreement, which, inter alia, provides for the resolution of disputes between the parties through a grievance and arbitration procedure.

Prior to July, 1983, Hahnemann operated and managed its dietary department with its own staff of supervisors. During this time, Hahnemann employed approximately fourteen full-time employees in the dietary department. In July, 1983, however, Hah-nemann hired ARA Services, Inc. to reorganize and manage its dietary department. As part of this reorganization, Hahnemann laid off two full-time employees, reduced the hours of the other twelve full-time employees to below twenty hours per week, and hired approximately thirty part-time employees. The effect of this reorganization was to remove the dietary department from coverage under the collective bargaining agreement by employing only workers who logged less than twenty hours per week.

The union then filed a grievance under the collective bargaining agreement, characterizing the reduction in hours and subsequent removal from the bargaining unit as a lay-off subject to Article IX of that agreement. 1 When the parties failed to settle the grievance in the first steps of the grievance procedure, the union submitted the dispute to arbitration. The parties appointed an arbitrator, and, after a postponement, scheduled the arbitration hearing for July 30, 1984. On the morning of the hearing, Hahnemann objected to the arbitration on the grounds that the collective bargaining agreement did not give the arbitrator “jurisdiction” to hear the dispute. After settlement negotiations failed, Hahnemann brought this action in the federal district court for the Eastern District of Pennsylvania.

Hahnemann’s position centers on the contractual language outlining the grievance-arbitration procedure in the parties’ collective bargaining agreement. Article VI of that agreement, entitled “GRIEVANCE PROCEDURE,” requires the parties to fol *40 low a three-step procedure for any grievance concerning the interpretation of or alleged violation of the agreement, 2 Step three of that procedure provides that “[i]f no satisfactory settlement [at steps one or two] is reached the grievance may be appealed to arbitration by the Union----” Thus, the grievance-arbitration procedure seemingly covers a broad range of disputes under the contract, i.e., any dispute involving the interpretation of or alleged violation of the agreement.

Hahnemann contends, however, that the next article in the collective bargaining agreement, entitled “ARBITRATION,” limits the broad scope of Article VI. Article VII provides in relevant part:

Authority of Arbitrator. The arbitrator will make his findings and render his decision to resolve the disagreement. The arbitrator shall not have jurisdiction to add to, modify, vary, change or remove any terms of this Agreement or to determine that any provision of this Agreement establishes an implied limitation upon Hahnemann which is not herein specifically set forth. The scale of wages established by this Agreement shall not be changed by any arbitration decision.

Hahnemann argues that this clause, particularly the phrase “shall not have jurisdiction ... to determine that any provision of this Agreement establishes an implied limitation upon Hahnemann ...” divests the arbitrator of jurisdiction over the dispute concerning the dietary department. Hah-nemann argues that because no express limitation on Hahnemann’s right to reorganize departments exists in the agreement, and indeed because the agreement’s Management Rights clause provides Hah-nemann with the authority to reorganize departments, the arbitrator cannot as a matter of contract find for the union. 3

*41 In essence, then, Hahnemann’s position is that because the arbitrator could not find for the union in this dispute without implying a limitation on Hahnemann, the arbitrator does not have jurisdiction over the dispute. This argument is untenable, however, both as a matter of contract, and as a matter of federal labor law. For these reasons, we affirm the district court’s order dismissing Hahnemann’s action.

II.

The question of arbitrability under a collective bargaining agreement is for the courts, and not arbitrators, to decide. See, e.g., United Steelworkers of America v. Warrior & Gulf Navigation Co., 363 U.S. 574, 582, 80 S.Ct. 1347, 1352, 4 L.Ed.2d 1409 (1960) (section 301 gives “the courts the duty of determining whether the reluctant party has breached his promise to arbitrate”). Arbitrability, however, does not turn on the parties’ use of words such as “jurisdiction” or “power,” but rather on the issue of what types of disputes the parties agreed should be resolved by private processes. See, e.g., Teamsters v. Western Pennsylvania Motor Carriers Assoc., 574 F.2d 783, 788-89 (3d Cir.), cert. denied, 439 U.S. 828, 99 S.Ct. 102, 58 L.Ed.2d 122 (1978); Boeing Co. v. UAW, 349 F.2d 412, 413 (3d Cir.1965). Further, because arbitration is favored under federal labor law, a court should order the reluctant party to submit the dispute to arbitration “unless it may be said with positive assurance that an arbitration clause is not susceptible of an interpretation that covers the asserted dispute.” Warrior & Gulf Navigation Co., 363 U.S. at 582-83, 80 S.Ct. at 1352-1353. The favored status of arbitration derives from Congress’ declared policy of promoting industrial peace through the collective bargaining process, rather than through the courts or economic warfare. See 29 U.S.C. §§ 171, 173(d) (1982).

To resolve the issue of whether Hahne-mann and District 1199C agreed to submit their dispute over the dietary department to final and binding arbitration, we need go no further than the facts and holding of the Supreme Court’s opinion in United Steelworkers of America v. Warrior & Gulf Co., 363 U.S. 574, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960). In Warrior & Gulf, the collective bargaining agreement contained both a broad definition of disputes subject to the grievance and arbitration procedure and, in the same clause, a limit on matters subject to arbitration. The agreement defined grievance as “any differences ... as to the meaning and application of the provisions ...” of the agreement, and provided that a grievance unresolved in the first four steps would be referred to arbitration. 363 U.S. at 576, 80 S.Ct. at 1349. The agreement also provided, however, that “matters which are strictly a function of Management shall not be subject to arbitration.” Id.

The grievance at issue concerned the contracting-out of work by Warrior & Gulf. Although the court recognized that contracting-out may have been “strictly a function of Management,” id. at 584, 80 S.Ct. at 1353, it refused to decide the scope of the vague exclusionary clause, particularly given the broad scope of the grievance and arbitration clause. Instead, the Court stated “[i]n the absence of any express provision excluding a particular grievance from arbitration, we think only the most forceful evidence of a purpose to exclude the claim from arbitration can prevail. ...” Id. at 584-85, 80 S.Ct. at 1353-54. Indeed, the Court warned that:

[A] court should view with suspicion an attempt to persuade it to become entangled in the construction of the substantive provisions of a labor agreement, even through the back door of interpreting the arbitration clause, when the alternative is to utilize the services of an arbitrator.

Id.

The supposed “exclusion” clause in Hah-nemann and District 1199C’s agreement is even more ambiguous than the clause in Warrior & Gulf. Rather than excluding types of disputes that an arbitrator may hear, the clause instead restricts how an *42 arbitrator may resolve disputes that reach arbitration. Thus, although the arbitrator may be restricted as to the result she may reach in the dietary department dispute, we may not say with “positive assurance” that the parties did not intend that an arbitrator hear the dispute.

Hahnemann argues, however, that it does not make sense to order the dietary department dispute to arbitration if the arbitrator is restricted to finding for Hahnemann because of the management rights clause. Despite the simplistic appeal of this argument, it ignores a central tenet of federal labor law. Regardless of the supposed strength of Hahnemann’s position in the dietary department dispute, Hahnemann contractually agreed to submit disputes to arbitration, including disputes over an arbitrator’s authority. The issue of an arbitrator’s authority to resolve a dispute properly before her, as with other issues concerning interpretation of contractual provisions, rests in the first instance with the arbitrator. See W.R. Grace & Co. v. Local Union 759, 461 U.S. 757, 765, 103 S.Ct. 2177, 2183, 76 L.Ed.2d 298 (1983) (“Because the authority of arbitrators is a subject of collective bargaining, just as is any other contractual provision, the scope of the arbitrator’s authority is itself a question of contract interpretation that the parties have delegated to the arbitrator.”). When an employer and union agree to submit their disputes to arbitration as a means of avoiding industrial strife, they agree to submit all disputes, whether or not meritorious. Because processing grievances may be an alternative to disrupting production, “[t]he objection that equity will not order a party to do a useless act is outweighed by the cathartic value of arbitrating even a frivolous grievance and by the dangers of excessive judicial intervention.” United Steelworkers of America v. American Mfg. Co., 363 U.S. 564, 568 n. 6, 80 S.Ct. 1343, 1347 n. 6, 4 L.Ed.2d 1403 (1960) (quoting Cox, Current Problems in the Law of Grievance Arbitration, 30 Rocky Mt.L. Rev. 247, 261 (1958)).

Because Hahnemann has agreed to arbitrate its disputes with District 1199C over matters arising from the collective bargaining agreement, it may not seek court determination of the contractual validity of the reorganization of the dietary department, nor court determination of the arbitrator’s authority to resolve the dispute. Subject to limited court review after arbitration, the parties have bargained for the arbitrator’s judgment, and it is with her judgment that they must live. We will affirm the judgment of the district court and order the parties to proceed to arbitration.

. Initially, the union did not identify the specific clause under which the grievance was filed. In its brief before this court, however, the union relies on the following part of Article IX:

If it becomes necessary to reduce Hahne-mann’s work force because of lack of work, funding or an emergency that curtails normal operation, the following shall apply:

1. In the event of a layoff within a job classification, all non-bargaining unit employees in the classification affected shall be laid off first.

Presumably, the union is arguing that this reduction in hours was actually a reduction in force, and that this clause both restricts reductions in force to those instances of lack of work, lack of funding, or emergencies, and specifies the order in which employees should be laid off.

. ARTICLE VI provides:

GRIEVANCE PROCEDURE

Procedure. Should any grievance arise as to the interpretation of or alleged violation of this Agreement, the employee or employees affected or the Union shall process the grievance in accordance with the following procedure:

STEP ONE. The employee or employees affected shall take the matter up with his supervisor within ten (10) days of its occurrence, either directly or through a union delegate in an attempt to effect a satisfactory settlement. The supervisor shall have five (5) days after the grievance was first presented to settle the matter. If no satisfactory settlement is reached the grievant or Union may within five (5) days after the supervisor’s answer appeal to—

STEP TWO. The grievance shall be reduced to writing by the grievant or the Union and referred to the grievant's Department Head or his authorized representative. A hearing on the grievance shall be convened if requested by either party. The Department Head or his authorized representative shall have five (5) days after receipt of the grievance to give his answer. If no satisfactory settlement is reached within five (5) days after the Department Head’s answer the grievant or the Union may appeal the matter to—

STEP THREE. The grievant or the Union will submit the written grievance to the Personnel Director who shall have ten (10) days in which to give his answer. A hearing on the grievance shall be convened if requested by either party. If no satisfactory settlement is reached the grievance may be appealed to arbitration by the Union upon written notice to Hahnemann and the American Arbitration Association by registered mail within ten (10) days of the answer of the Personnel Director, except in cases of discharge, in which the time period shall be thirty (30) calendar days. The Arbitration shall proceed in accordance with the current rules of the American Arbitration Association.

. ARTICLE XXXII provides:

MANAGEMENT RIGHTS

The management of Hahnemann and the direction of the working force is vested exclusively with Hahnemann. Except where expressly abridged by a specific provision of this Agreement, Hahnemann retains the sole right to hire, discipline or discharge for cause, lay off, promote, transfer and assign its employees: to determine or change the starting and quitting time and number of hours worked; to promulgate working rules and regulations; to assign duties to the work force; to establish new job classifications; to organize, discontinue, enlarge or reduce a department, function or division; to assign or transfer employees to other departments as operations may require; to hire temporary or part-time employees, to introduce new or improved facilities; to carry out the ordinary and customary functions of management whether or not possessed or exercised by Hahnemann prior to the execution of this Agreement.