Is Faraj legally required to pay this additional amount in this case?

Melissa Faraj owns a lot and wants to build a house according to a particular set of plans and specifications. She solicits bids from building contractors and receives three bids: one from Carlton for $160,000, one from Feldberg for $158,000, and one from Siegel for $153,000. She accepts Siegel's bid. One month after beginning construction of the house, Siegel contacts Faraj and tells her that because of inflation and a recent price hike for materials, his costs have gone up. He says he will not finish the house unless Faraj agrees to pay an extra $13,000. Faraj reluctantly agrees to pay the additional sum.