Any one know how to do this ECON Question?

Question

In 2001, Lara attends a total quality management conference where consultant Wade wise estimates that the annual demand for legal services in Sivervally is
P = 1000 – x/2, where P= hourly billable rate and x = billable hour “output”. Wade advice that the demand for legal services is the same for 2000 and 2001 and that Lara, who has monopoly for legal services due to Sivervally’s geographical remoteness, “undercharged” his clients in 2000, Is Wade correct?


In 2000, Lara’s “output” was 1400 billable hours

Charged her work out at the hourly rate of $ 300 for each client

Her marginal firm cost hourly rate of $150 with no fixed costs.

Answer 1

In a monopoly situation, the supplier can choose the price to maximize profit in isolation.

Profit = income - cost

income = price x quantity

cost = fixed cost + sum of the marginal cost for each unit.

In this case, the marginal cost is independent of quantity (strange!) and there are no fixed costs (not even rent? very strange to say the least) so:

cost = marginal cost x quantity

These equations combine to give an equation for profit in terms of price and quantity.

Wade's estimate gives an equation for quantity in terms of price.

So we have two equations in two unknowns and can solve for both quantity and price.

Then we can compare the results with the price actually charged.