The given questions have been answered below.
1. Is there a valid enforceable contract between Chen and John?
Issue: The question that has been given, itself is the issue, which is, if the contract between Chen and John is a valid one?
Rule: “contract (or informally known as an agreement in some jurisdictions) is an agreement having a lawful object entered into voluntarily by two or more parties, each of whom intends to create one or more legal obligations between them. The elements of a contract are "offer" and "acceptance" by "competent persons" having legal capacity who exchanges "consideration" to create "mutuality of obligation."”- Common Law Legal System.
Analysis: the common law system and the contract law of Australia tell us that contract can be formed when certain conditions are fulfilled. When two or more parties (Chen and John), have a lawful object (building of the house extension), where john agrees to build the extension of Chen’s house (legal work) on a payment of certain sum (consideration) within the given period of time. When the definition of the contract is analyzed and the given situations is considered it can be seen that it lies parallel to one another. It also creates a mutual obligation between them which is that John would build the extension of the house within the given period of time and Chen in return will give him the payment they have agreed upon.
Conclusion: the contact law and the common law give a definition of how a valid enforceable contract can be formed. And the situation given fulfills all the given criteria; hence the contract between John and Chen is a valid enforceable contract.
Case law where the offer was a valid one: Carlill v Carbolic Smoke Ball Co  1 QB 256
2. Issue: What arguments could Chen use to support his refusal to pay John more than the
Original agreed price?
Rule: a contract is formed on agreed terms between the parties who are getting into the agreement. Here the terms and the considerations has already been decided and no clause has been put in, as to change in either because of unforeseen circumstances, and since when entering into a contract the parties are into a mutual obligation to complete the given work within the stipulated time, Chen can refuse to pay on the basis of breach of duty or the mutual obligation by the other part (John) - Contract Law
Analysis: when we refer to the issue we see that there was a particular compensation that Chen had agreed to pay to John for building up the extension of his house within the given period of time, because his family needed accommodation after that time. what is seen after that is that there is an increase in the labor costs while there is a decrease in the price of the materials required for the building up of the extension, and because of this john asks an increase in the labor price, or else he would not work for Chen, to which Chen ‘reluctantly’ agreed because he wanted the work to be complete within the given period of time. But the work though is completed has taken one and a half more months, and because of this Chen had to face difficulties and pay extra for his family’s accommodation. What we see is that Chen had agreed to pay the given price only on one condition that is the extension should have been completed by June, which certainly has not been done. When the only reason on which the extra payment was agreed upon is not kept in mind by John, Chen can hence deny the payment on ground of breach of duty of John, and can therefore refuse to pay the extra charges that John had asked for.
Conclusion: the Contract Law provides provisions for the plaintiff if there is a breach of duty by the defendant, and hence gives provisions for the plaintiff to act in a certain manner when the duty has not been fulfilled. Hence there are reasons which Chen can when he refuses to pay the extra amount of labor cost as his work was not done according to the terms of the contract.
Case law: for breach of duty when a contract have been formed- Payless Travel v Baba Krupa Holidays  All ER (D) 503
3. Issue: What arguments could Chen use to support his claim for compensation for the hotel?
Rule: “Damages for breach of contract are viewed as a 'substitute' for performance - consequently, they are designed to put the plaintiff in the position they would have been in had the contract been performed properly. Punitive damages are not available. The loss claimed must not be too remote from the breach and the non-breaching party must do what is reasonable to reduce (mitigate) the damage they suffer.”- Australian Contract Law.
analysis: what has been discussed earlier is the part where John has delayed the making of the extension of the house by one and a half months which in a way is breach of duty because the terms of the contract which John and Chen had got into clearly stated that the extension of the house was to be completed by June because Chen needed the accommodation for his family who would arrive by then. And this was the only reason why eventually and reluctantly Chen had agreed on paying more labor cost to John. But since this term was ignored and the work took longer, Chen had to find accommodation for his family in the hotel for which he had to incur a cost of $3000 which could have been uncalled for if the house would have built on time.
Conclusion: ‘award for damages are compensatory’ states the central principle which is governing this law, hence Chen can claim his incurred cost from John.
Case law regarding award for damage/loss: (HLA [110-11060] eg. Johnson v Perez (1988) 166 CLR 351 at 355).
Rule: “This is a rule of evidence that precludes a person from denying the truth of some promise made by him or her of the existence of facts whether existing or not which he or she has by words or conduct led another to believe in.”- promissory/equitable/estoppels under the Contract Law.
Analysis: when the given case is considered it is seen that though John took more than the required time, he actually built the house extension, putting in the labor which was required in spite of the increased labor price (after Chen had agreed), and also that the materials had been used, for which Chen should pay., moreover Chen had agreed on paying the extra cost that was required by John for the labor and material input. By brining in the estoppels method, John can claim that Chen had actually promised him to pay the increased amount of labor cost and the material cost which on completion of the house extension, he cannot refuse to pay. It was only after Chen had agreed to pay for the increased prices that John had started working. This case may also see the reference where the third party (labor force used by John to complete the completion of the house) is used, and thus their payment has to be made as well from the payment that comes from Chen. Though the time taken by John to complete the house extension was more than promised, but he can also claim that the house extension wasn’t left incomplete, but was completed over the period of time. moreover if Chen was to refuse the payment which included the extra labor cost and also the price of the materials which have been used by John for completing the extension of the house, he could have said that when John asked for the extra payment or maybe just as the due date for building the house extension was crossed, without waiting for the completion to take place on a full and final basis. No earlier notice had been given to John regarding the nonpayment of the labor costs or the material costs, which had already been spent from John’s side for completing the extension of Chen’s house.
what can be concluded after looking aspects of the contract law is that estoppels can be used as an argument by John in order to get the $10,000 from Chen which had been earlier promised by him, because of the increased labor cost and since, the house had been already completed, and that Chen had not given any notice regarding the nonpayment of labor costs earlier, John can actually go ahead and claim the money with the help of the given branch of contract law.
Case laws: where estoppels has been used as a defense or as an argument to get the other party to act in a certain way- Walton’s case, Walton’s Stores (Interstate) Ltd v Maher (1988) 164 CLR 387 and Central London Property Trust v High Trees House Ltd  1 KB 130.
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