$.$ Hardy Construction Ltd$.$ Signed a contract to build an office complex for Schtick Corp. for $$5\mathrm{.}5$ million. Under the terms of that contract, Hardy Construction was given a firm schedule for completion of the building, and there were financial penalties if they failed to finish the project on time. Hardy Construction hired Laurel Electric Co$.$ as a subcontractor to install the wiring in the building. The terms of that subcontract $($between Hardy Construction and Laurel Electric$)$ required Hardy to pay Laurel $$50,000$ on completion of the wiring and was to include all material and labour. Laurel Electric started work immediately, but they soon discovered that it had made a mistake and had underestimated the cost to them of performing the contract. Laurel therefore approached Hardy Construction and stated that unless it was promised an additional $$20,000,$ it simply would not be able to complete the job. Hardy Construction realized that it could not possibly find a replacement for Laurel Electric on short notice and that any delay in the completion of the project would trigger the penalty clause in its contract with Schtick Corp. As a result, Hardy Construction agreed to Laurel Electric's demand for an additional $$20,000.$ Although Laurel Electric completed its performance on schedule, Hardy Construction refuses to pay Laurel more than $$50,000.$

$($a$)$ How much does Hardy have to pay to Laurel for the contract? Please explain your answer fully with reference to the basic elements of a contract for each relevant contract. $(18$ marks$)$

$($b$)$ Why might Hardy Construction consider paying the extra money to Laurel even if it doesn't have to$$do$$so$$legally$?$