Question

Suppose that the demand equation for widgets is Qd=10,000−25PQd=10,000−25P. At P=$150, what is the firm’s total revenue? TR=$

Suppose that the demand equation for widgets is Qd=10,000−25PQd=10,000−25P. At P=$150, what is the firm’s marginal revenue?

Suppose that the demand equation for widgets is Qd=10,000−25PQd=10,000−25P. What is the firm’s total revenue at P=$250? TR=$

Suppose that the demand equation for widgets is Qd=10,000−25PQd=10,000−25P. What is the firm’s marginal revenue at P=$250?MR=$

Answer 1

Given, Q= 10,000 - 25P

When. P = $ 150

Q = 10,000 - 25 × 150 = 10,000 - 3,750 = 6,250 units

Total revenue = PQ = 150 × 6,250 = $ 937,500

In order to determine the Marginal revenue first determine the inverse demand function

Q = 10,000 - 25P

25P = 10,000 - Q

P = 400 - 0.04Q

TR = PQ

Now differentiate TR wrt Q we get

Now plug in Q = 6,250

MR = 400 - 0.08×6,250 = - $ 100

Now when P = $ 250

Q = 10,000 - 25 × 250 = 3,750

TR = 250 ×3,750 = $ 937,500

Marginal revenue equation will be same as the inverse demand function is same in both the cases

MR = 400 - 0.08Q

Plug in Q = 3,750

MR = 400 - 0.08 × 3,750

MR = $ 100

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