Revenue Functions Of A Monopoly

L r q λ r q c q π and kuhn tucker conditions are.

Revenue functions of a monopoly. Marty s marginal revenue for the first 40 passes is 50 per pass. Since revenue is represented by pq and cost is c profit is the difference between these two numbers. The revenue functions of a monopoly at the opposite end of the market spectrum from perfect competition is monopoly. The level of output that maximizes a monopoly s profit is calculated by equating its marginal cost to its marginal revenue.

Setting marginal revenue equal to zero we have. The cost to the firm at quantity q is equal to c q. Download the revenue functions of a monopoly econedlink book pdf free download link or read online here in pdf. π p q q c q in this formula p q is the price level at quantity q.

Demand and marginal revenue curves for marty s ski park monopoly if he charges 50 for a day pass marty can sell 40 passes per day for a total daily revenue of 2 000. When the manager of a monopoly firm expands his output to 4 units price falls to rs. The slope of the total revenue function is marginal revenue. Marginal revenue is the difference in total revenue at 3 units of output and at 4 units of output which is rs.

So the revenue maximizing quantity and price occur when mr 0. The total revenue function would be tr 50q 2q 2 and marginal revenue would be 50 4q. All books are in clear copy here and all files are secure so don t worry about it. We now form the lagrange function.

If the monopoly produces a lower quantity then mr mc. If the cost function is convex the profit function is also concave. We know that the revenue function of a price maker is concave. If marty reduces the price to 40 he can sell 80 passes per day for a total daily revenue of 3 200.

For a monopoly like healthpill marginal revenue decreases as it sells additional units of output. It is less than the price which is rs. 48 42 rs. If the monopolist wants to sell more of its product.

Profits are represented by π. This means the monopolist faces the market demand curve since it has no competition from other firms. That is mr mc. The profit maximizing choice for the monopoly will be to produce at the quantity where marginal revenue is equal to marginal cost.

Key takeaways a monopolistic market is where one firm produces one product. So we can apply the kuhn tucker analysis to throw light on the monopolist s maximisation problem. The monopoly s profits are given by the following equation. The marginal cost curve is upward sloping.

12 and total revenue is rs.