Which contract type includes a provision for adjusting the contract value according to a specified price index?

The correct choice is the type of contract known as fixed price with escalation contracts. This contract structure includes a provision that allows for the adjustment of the contract value based on changes in a specific price index, such as inflation or fluctuations in the cost of materials. The inclusion of an escalation clause helps protect both parties involved in the contract: it gives contractors a degree of certainty regarding adjustments for their costs over time, while ensuring that clients are not locked into an outdated price that doesn't reflect current market conditions.

In contrast, cost-plus contracts do not specifically tie adjustments to price index fluctuations; instead, they allow the contractor to be reimbursed for costs incurred plus a profit margin. Time and materials contracts similarly base payments on the actual time spent and materials used without an adjustment linked to a price index. Lump-sum contracts set a fixed price that does not change regardless of fluctuations in costs, making them less flexible in accommodating economic changes.