Profmax
Jan 22, 2015Limited, anyone with the link
Photo: Profit Maximization, by D. Ohmans
Photo: Good evening. This is a diagram by Kenneth Boulding. Practical economics is cost-benefit analysis. You set the buying or selling price. The result is profit. But profit does not have to maximize money: it could maximize utility.
Photo: Obviously, to compute profit simply subtract your total costs from your total revenue. Ask what quantity of widgets per day is the profit-maximizing quantity. Where the difference is GREATEST, the profit will be the most.
Photo: But there is another sort of profit maximization: marginalism. Here are four pretty girls. Their average weight is 150 pounds, for a total of 600 pounds.
Photo: Along comes Fernando and joins the group. His weight, the marginal increment, is 200. The new total is 800, the new average (800/5)=160 pounds. The average is pulled up towards the marginal.
Photo: Now for the easy part: a spreadsheet accounting for the production of five widgets. Price is average revenue. We also have marginal revenue, average cost and marginal cost. Cost is supply, revenue is demand.
Photo: Let us assume scarcity. Eventually supply costs rise: the next widget costs two dollars more to make than the previous one. In practice, the best way that an economist or a firm can figure out the value of marginal cost is to look at average variable cost (average cost net of overhead).
Photo: Let us assume diminishing returns. The price per widget for the whole batch will decrease: if you buy five, they can be obtained for $11 each.
Photo: The average cost of just one, seven dollars, is the same as the marginal cost. The average cost of two is (7+9)/2=8. Here the average is pulled up by the marginal.
Photo: Marginal revenue falls for the exact same reason that price falls: (15+13)/2=14. MR pulls the average down.
Photo: The producer faces rising costs and declining price. Should she produce and sell five widgets, she will break even at (5x11)=55 dollars total.
Photo: If we look at the marginal figures, there is a different "breakeven" point after doing only three where marginal revenue equals marginal cost.
Photo: Here are all our numbers based on the two assumptions: eventual scarcity and diminishing returns or satiation.
Photo: This grid looks like the constellation Orion. It is the general shape of any such data, including the right-hand side of cost curves U-shaped because of initial economies of scale.
Photo: Please look at the 11's in the data. You will observe that they occur at the intersection points of the averages and the marginals. But the two equilibria are at different quantities: five and three, respectively.
Photo: In 1871 William Jevons, who died by drowning at age 47, published "The Theory of Political Economy,” which systematized the discovery that maximum profit is obtained at the quantity where marginal cost is exactly equal to marginal revenue.
Photo: The other way to maximize profits was to look at total revenue and total costs. To get totals, multiply your averages or add your marginals. (2x14)=28 or (15+13)=28.
Photo: Total profit (total revenue minus total costs) does not decline until the fourth widget.
Photo: For the quantity, three, total revenue is 39 (and rises to 55) total costs are 27 and profit, the difference, is 12.
Photo: The monopolist sets her price at $13 for three, here at #5 to maximize profit, but imperfect competition might bring it down to #3. Number One, five widgets, is the unobtainable maximum.
Photo: Minimize the difference between the marginals or maximize the difference between the totals: miraculously the profit-maximizng quantity is the same either way. Thank you.