What is a private Blockchain used instead of a public one?

The fundamental distinction between a public and a private blockchain is the access control mechanism. A private blockchain is a "permissioned" network, meaning an organization or consortium controls who can participate, what transactions they can submit, and which data they can access. This ability to limit user access and define specific permissions is the primary reason enterprises choose private blockchains, as it allows them to maintain confidentiality, comply with regulations (like GDPR), and manage a network of known, vetted participants for specific business processes.

A. It is less expensive to develop: This is not necessarily true. The cost depends on the complexity and scale; a sophisticated private blockchain for a large consortium can be very expensive to develop and maintain.
B. It requires less mining power that a public Blockchain: While true that private blockchains use more efficient consensus mechanisms (e.g., PoA) than PoW, this is a consequence of its permissioned nature, not the primary reason for its use.
D. It requires fewer administrators to manage it: This is incorrect. Private blockchains require a dedicated administrative function to manage identities, grant permissions, and oversee the network, which is not required in a decentralized public network.

1. University Courseware:

UC Berkeley, Blockchain Fundamentals, Decal Course. In the module "Permissioned Blockchains," it is stated: "The main difference between permissioned and permissionless blockchains is the mechanism for access control... In a permissioned blockchain, access is restricted to a group of pre-approved participants." This directly supports that limiting access is the core purpose. (See: Module on Permissioned Blockchains).

2. Academic Publications:

Narayanan, A., Bonneau, J., Felten, E., Miller, A., & Goldfeder, S. (2016). Bitcoin and Cryptocurrency Technologies: A Comprehensive Introduction. Princeton University Press. In Chapter 2, Section 2.4, "Permissioned Blockchains," the authors define these systems by their restriction on who can create blocks and participate in the consensus, contrasting them with the "permissionless" model of Bitcoin.

3. Academic Publications:

Xu, X., Weber, I., & Staples, M. (2019). Architecture for Blockchain Applications. Springer. In Chapter 2, "Blockchain Platforms," Section 2.1.1 "Permissioned vs. Permissionless Blockchains," the text highlights: "In a permissioned blockchain, the participants are known and have been given permission to join the network... This is in contrast to permissionless blockchains where anyone can join." This establishes access control as the defining feature. (DOI: https://doi.org/10.1007/978-3-030-03035-32).