Question

Hospitals are faced with decisions regarding pricing, when negotiating with private insurance payers. They use information about the demand curve they face to decide on prices, quantities, and to anticipate revenue and profits.

Consider a hospital that has a demand curve given by P=180-4Q. Their total cost curve is given by TC=95+2Q.
a)Please write down the expression for MR (marginal revenue) and MC (marginal cost)

Answer 1

The expressions for marginal revenue (MR) and marginal cost (MC) for the hospital are MR=180-8Q and MC=2, where Q represents the quantity.

Step-by-step explanation:

MR and MC Calculation

To calculate the marginal revenue (MR), we need to take the derivative of the total revenue function. The total revenue (TR) is found by multiplying the demand curve by the quantity (Q), which gives us TR=P*Q=(180-4Q)*Q. The derivative of TR with respect to Q will give us MR, which is MR=d(TR)/dQ=d((180-4Q)*Q)/dQ = 180-8Q.

To calculate the marginal cost (MC), we take the derivative of the total cost (TC) function with respect to Q. Given that TC=95+2Q, the MC which is the derivative d(TC)/dQ is simply MC=2.

Therefore, the expressions for marginal revenue and marginal cost are MR=180-8Q and MC=2, respectively.