Host posted a flyer on the bulletin board of a local music school, stating that he was

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Question:

Host posted a flyer on the bulletin board of a local music school, stating that he was hosting an event next month, for which he planned to hire a DJ. The flyer invited interested students to contact him with their hourly rates and three past clients whom Host could contact for references. The flyer also gave a local mailing address for this purpose.

Leaving class one night, Student happened to notice the billboard. She immediately wrote to Host indicating that she was available on the date in question, and that her hourly rate was $150. She also listed the names and contact information of three prior clients. Three days later, Host wrote back to Student, stating that her references had all given excellent reviews, and asking whether Student would be willing to work for $100 per hour if he advertised her services in the program provided for the event. Student received the letter the day after Host sent it, and wrote back the next day that she would be willing to drop her rate to $125 per hour plus the advertisement, but no lower.

Four days later, having received no response, Student called Host on the telephone to say that, because the event was only about two weeks away, she had assumed that Host had decided to use another DJ. For that reason, Student had booked another client for the same day and time as Host’s event. Host said, “No, I sent you a letter yesterday accepting your terms—you haven’t received it yet? We have a contract, and I will expect you to perform at my event!” (Assume that Host really sent the letter when he said he did, and that he can prove it in court.) Later that day, Host’s letter arrived in Student’s afternoon mail.

Host has filed a breach of contract claim against Student, and asked the court to order Student to perform at his event. Assume that, if the court does not so order, Host can and will hire a replacement DJ, but only at a higher cost. Also assume that (1) all mailings were done properly, and (2) the common law of contracts, and not Article 2 of the Uniform Commercial Code, applies.

Student argues that she and Host are not in a binding contract, because Host waited too long to respond to her, and she withdrew her offer before Host accepted it.

Questions

Is Student’s argument correct? Explain, analyzing only the offer-and-acceptance issue, and not whether Student has breached or repudiated any contract.
Assuming that Student is in breach, having repudiated a valid and binding contract with Host, is the court likely to issue an order compelling Student to perform at Host’s event? If not, what will the court do instead? Explain.