The recent economic expansion in Japan has led to increased sales for most firms. Gerald Ltd sells laptop cases and its demand for the product is expressed through the demand equation Qd = 100 - 2P. The inverse demand P = 50 - 0.5Q.

Gerald Ltd is thinking if he must put the price higher to benefit from the rising demand caused by the increase in people's incomes due to the growth of the economy. The laptop cases are being sold at the price $20 at the moment.

Calculate the marginal revenue (from the taplet cases) of the business when it sells its 30^th unit.

I don't understand which of the 2 answers below is correct and when I have to use each method.

1st method: MR = Change in TR / Change in Q

TR = P x Q therefore TR = (50 - 0.5Q) Q = 50Q - 0.5Q^2

MR = d(TR) / dQ = 50 - Q

So, MR = 50 - 30 = 20

2nd method: Since MR is the revenue gained from selling one extra unit of output, I have to find MR by finding the difference between the TR gained when selling 29 and when selling 30 units.

So, when Q = 30, P = 35 therefore TR = 30*35=1050

When Q = 29, P = 35.5 therefore TR = 29*35.5=1029.5

Since MR = Change in TR / Change in Q = (1050-1029.5)/(30-29)= (20.5/1) = 20.5

MR=20.5

When I compare TR at Q = 30 and TR a Q = 50 I find 200 change in TR for 20 units or 20 for 1 unit, which again is confusing.

WHICH OF THE TWO IS CORRECT AND WHY? I DONT UNDERSTAND THE DIFFERENCE