The marginal revenue function of a monopolistic producer is MR = 10 – 4Q.
a) Find the total revenue function and deduce the corresponding demand equation
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.