Problem 25-6 from Chapter 25 A. What is the monopolist’s profit-maximizing outpu

Question

Problem 25-6 from Chapter 25A.    What is the monopolist’s profit-maximizing output? B.    At the profit-maximizing output rate, what are the monopolist’s average total cost and average revenue? C.    At the profit-maximizing output rate, what are the monopolist’s total cost and total revenue? D.    What is the maximum profit? Please explain to me how to solve this, I am getting confused as I read it, maybe it is due to I have surgery in the morning. Please explain to me how to solve this, I am getting confused as I read it, maybe it is due to I have surgery in the morning.

Explanation / Answer

A. The monopoly's profit maximizing output is where marginal cost (MC) equals marginal revenue (MR). This happens at a quantity of about 4.5. B. Drawing a straight line up from the intersection of MC=MR, we see that the ATC is at a price of about 5.25. The price that the monopolist can sell at is about 5.75, since that is the price on the demand curve that corresponds to a quantity of about 4.5. The demand curve is usually also the average revenue curve, as it is in this case (since average revenue is simply the revenue divided by the quantity. But what is revenue but price times quantity? So, (price*quantity) divided by quantity equals price, which is the demand curve). Thus, the average revenue is 5.75. C. Since we already have the average total cost and average revenue, we just need to multiply both by the quantity produced (4.5) to get the total cost and total revenue. Thus, the total cost is 4.5*5.25=23.625 and the total revenue is 4.5*5.75=25.875. D. So, to get the maximum profit, we just need to subtract the profit maximizing cost from the profit maximizing revenue, which is 25.875-23.625=2.25 Note: The graphic you have above is a bit weird in that maybe the points are a bit off on my screen. But I'm seeing random equilibrium points (which they give the value for in the x and y axis) that isn't really necessary or make sense where it's at. If the graphic didn't load right, let me know. The idea is the same. First find the profit maximizing quantity, which is at MC=MR, then draw an imaginary line up to see where it intersects ATC and that's your average total cost, then keep on going up until it hits demand and that's your average revenue. Then, multiply by the quantity to get the total cost and total revenue, at which point you can subtract the cost from the revenue to get profit.

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