A monopolist faces an inverse demand curve $P = 300 - 6 Q$ and has a constant marginal cost of 20. The IEPR formula for this monopolist could be stated in the following way:

Question

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The IEPR formula for a monopolist is given by:

IEPR = (P - MC) / P

Substituting the given values, we get:

IEPR = (P - 20) / P

Now, we need to manipulate the demand function to obtain an expression for P in terms of Q, so that we can substitute it in the IEPR formula.

The given demand function is:

P = 300 - 6Q

Solving for P, we get:

P = 300 - 6Q

P + 6Q = 300

P = 300 - 6Q

Now, substituting this expression for P in the IEPR formula, we get:

IEPR = [(300 - 6Q) - 20] / (300 - 6Q)

Simplifying, we get:

IEPR = (280 - 6Q) / (300 - 6Q)

Multiplying and dividing by 10, we get:

IEPR = (28 - 0.6Q) / (30 - 0.6Q)

Now, we need to express this in terms of the original demand function.

Substituting P = 300 - 6Q in the above equation, we get:

IEPR = (28 - 0.6Q) / (P - 20)

This can be rearranged as:

(P - 20) / P = (28 - 0.6Q) / (300 - P)

Simplifying, we get:

(P - 20) / P = (300 - P - 0.6Q) / (300 - P)

Multiplying and dividing by -1, we get:

(P - 20) / P = (P - 300 + 0.6Q) / (P - 300)

Multiplying and dividing by -1 again, we get:

(P - 20) / P = (300 - P + 0.6Q) / (300 - P)

This is the same as Option B:

(P - 20) / P = (300 - P) / (P + 0.6Q)

Hence, the answer is B. The IEPR formula for a monopolist is given by:

IEPR = (1/|E_d|)*(p - MC)/p

Where IEPR is the inverse elasticity of price with respect to marginal cost, |E_d| is the absolute value of the price elasticity of demand, p is price and MC is marginal cost.

In this case, we know that the demand function is given by:

P = 300 - 6Q

So, we can solve for Q as a function of P:

Q = (300 - P)/6

Taking the derivative of Q with respect to P, we get:

dQ/dP = -1/6

Using the formula for the price elasticity of demand, we get:

|E_d| = (P/Q)*dQ/dP = (P/((300-P)/6))*(-1/6) = (P/50)

Substituting into the IEPR formula, we get:

IEPR = (50/P)*(P-20)/P = (50/P)-(1000/P^2)

Simplifying, we get:

IEPR = 50/P - 0.0333

So, the correct answer is option B, as it is the only one that is equivalent to 50/P - 0.0333.

A Monopolist Faces an Inverse Demand Curve P=300−6QP = 300 - 6 QP=300−6Q

A Monopolist Faces an Inverse Demand Curve $P = 300 - 6 Q$