The marginal revenue function of a monopolistic producer is MR = 10 – 4Q.

Question

a) Find the total revenue function and deduce the corresponding demand equation

Answer 1

The total revenue function can be found by integrating the marginal revenue function. Therefore, we integrate MR with respect to Q:

TR = ∫(10 - 4Q) dQ
TR = 10Q - 2Q^2 + C

C is the constant of integration. Since we are interested in finding the demand equation, we can ignore the constant of integration. So, the total revenue function is:

TR = 10Q - 2Q^2

To deduce the demand equation, we need to find the relationship between price (P) and quantity (Q). The demand equation can be derived by setting TR equal to P*Q, as total revenue is the product of price and quantity:

P*Q = 10Q - 2Q^2

Simplifying this equation, we get:

P = 10 - 2Q

So, the demand equation for this monopolistic producer is P = 10 - 2Q.