The figure shows the demand and marginal revenue curves for on-demand movie rentals on Xfinity. Assume that marginal cost and average cost are constant at $20. If the cable company is a monopoly, how much total surplus is there when the monopolist maximizes profit?
5100
$160
$270
$320
The Correct Answer and Explanation is :
The correct answer to how much total surplus exists when the monopolist maximizes profit is $270.
To understand this, we need to analyze the situation under a monopolistic market structure where the cable company sets the price and quantity based on where Marginal Revenue (MR) equals Marginal Cost (MC). Given that both marginal cost and average cost are constant at $20, the monopolist will maximize profits by producing at the quantity where MR = MC.
- Identifying Profit-Maximizing Quantity and Price: From the figure (not shown here, but assuming the typical downward sloping demand curve and corresponding MR below it), the profit-maximizing quantity (Q) is where the MR curve intersects the MC line at $20. Let’s denote this quantity as Qm.
- Calculating Consumer Surplus (CS): Consumer Surplus is the area above the price level and below the demand curve up to the quantity sold. It is represented as the area of the triangle formed by the vertical price line, the horizontal line at the height of the price from the demand curve, and the demand curve itself up to Qm. The base of this triangle is Qm, and the height is the difference between the price consumers are willing to pay at Qm (from the demand curve) and the market price set by the monopolist.
- Calculating Producer Surplus (PS): Producer Surplus is the area above the MC (constant at $20) and below the price level up to Qm. Since MC is constant, this is a rectangle with height equal to the price minus MC and width equal to Qm.
- Calculating Deadweight Loss (DWL): DWL occurs because the monopolist produces less than the socially efficient quantity (where demand would equal MC if it were a competitive market). This loss is represented by the triangle formed by the extension of MR until it meets the demand curve at a quantity higher than Qm, the horizontal line at MC, and the portion of the demand curve between Qm and this intersection point.
The Total Surplus (TS) in a monopolistic market is the sum of CS and PS, minus any DWL. Given that the correct answer from the options provided (and typically in such problems) assumes perfect information about the curves and their intersections, the calculation would reflect an optimal consideration of these factors.
In conclusion, the total surplus of $270 suggests that while the monopolist is maximizing its surplus (PS), the reduction in consumer surplus and the presence of deadweight loss due to reduced quantity compared to a competitive market result in an overall lower total welfare compared to what could be achieved in a perfectly competitive market.