About Law

Is there any contract between Ann and Joe?
No, because Joe did not reply Ann, and Joe did not say that he give Ann the lowest cash price.
If Joe did not reply, there may be a chance that he did not receive the fax.
A contract must be agreed by both sides, but Joe did not reply, so there is no contract between Ann and Joe.

No contract formed since acceptance must exactly coincide with offer (Hyde v Wrench)

Joe's reply was merely an answer to the query of Ann; there was no response as to the offer of Ann made. As there is no acceptance, Ann cannot assume that the contract is concluded by silence of the offeree (Felthouse)

if there is a contract,we need to have both 5 elements,
offer,
acceptance ,
consideration ,
intenal to create legal relationship,
contractual capacity.

in this case,Joe relied the lowest price is giving additional information,not giving out the offer to Ann, that is no definate proposal that be intent to bound.

And Ann's Fax," I agree to buy XYZ bag for HK$600 asked by you'
it is making an offer to Joe ,she would buy the bag is HK$600.
However,Joe had not relied.An offer can not accept by the offeree unless it has been communicated to the offeree.R V. Clark.

So,there is no acceptance.This means,there is no blinding contract.

The fax messages only indicated an inquiry. Although Ann agreed with the price of
HK$600 for the XYZ bag, Joe has not yet confirmed the order by fax message.
So, it is not an order. There should be an agreement/contract for the goods descrption,
price, delivery and payment method, etc, between Ann and Peter for the guarantee of
the order.