You have just been hired as manager. The previous manager was fired because the

Question

You have just been hired as manager. The previous manager was fired because the owner was not satisfied that the previous manager was maximizing profits. You are provided with the following information:

P=6.25 -1.25QD

MR = 6.25 -2.5QD

C = 0.5Q

MC = 0.5

Illustrate that the previous manager, who was charging the monopoly price per beer, was not maximizing profits as accused by the owner. That is, find an alternate pricing scheme that results in more profits per customer than the monopoly scenario.

Explanation / Answer

Any costs incurred by a firm may be classed into two groups: fixed costs and variable costs. Fixed costs, which occur only in the short run, are incurred by the business at any level of output, including zero output. These may include equipment maintenance, rent, wages of employees whose numbers cannot be increased or decreased in the short run, and general upkeep. Variable costs change with the level of output, increasing as more product is generated. Materials consumed during production often have the largest impact on this category, which also includes the wages of employees who can be hired and laid off in the span of time (long run or short run) under consideration. Fixed cost and variable cost, combined, equal total cost. Revenue is the amount of money that a company receives from its normal business activities, usually from the sale of goods and services (as opposed to monies from security sales such as equity shares or debt issuances). Marginal cost and revenue, depending on whether the calculus approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced, or the derivative of cost or revenue with respect to the quantity of output. For instance, taking the first definition, if it costs a firm 400 USD to produce 5 units and 480 USD to produce 6, the marginal cost of the sixth unit is 80 dollars. [edit]Total revenue - total cost perspective Profit Maximization - The Totals Approach To obtain the profit maximising output quantity, we start by recognizing that profit is equal to total revenue (TR) minus total cost (TC). Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph. The profit-maximizing output is the one at which this difference reaches its maximum. In the accompanying diagram, the linear total revenue curve represents the case in which the firm is a perfect competitor in the goods market, and thus cannot set its own selling price. The profit-maximizing output level is represented as the one at which total revenue is the height of C and total cost is the height of B; the maximal profit is measured as CB. This output level is also the one at which the total profit curve is at its maximum. If, contrary to what is assumed in the graph, the firm is not a perfect competitor in the output market, the price to sell the product at can be read off the demand curve at the firm's optimal quantity of output. [edit]Marginal revenue-marginal cost perspective Profit maximization using the marginal approach An alternative perspective relies on the relationship that, for each unit sold, marginal profit (Mp) equals marginal revenue (MR) minus marginal cost (MC). Then, if marginal revenue is greater than marginal cost at some level of output, marginal profit is positive and thus a greater quantity should be produced, and if marginal revenue is less than marginal cost, marginal profit is negative and a lesser quantity should be produced. At the output level at which marginal revenue equals marginal cost, marginal profit is zero and this quantity is the one that maximizes profit.[1] Since total profit increases when marginal profit is positive and total profit decreases when marginal profit is negative, it must reach a maximum where marginal profit is zero - or where marginal cost equals marginal revenue - and where lower or higher output levels give lower profit levels.[1] In calculus terms, the correct intersection of MC and MR will occur when:[1] The intersection of MR and MC is shown in the next diagram as point A. If the industry is perfectly competitive (as is assumed in the diagram), the firm faces a demand curve (D) that is identical to its marginal revenue curve (MR), and this is a horizontal line at a price determined by industry supply and demand. Average total costs are represented by curve ATC. Total economic profit are represented by the area of the rectangle PABC. The optimum quantity (Q) is the same as the optimum quantity in the first diagram. If the firm is operating in a non-competitive market, changes would have to be made to the diagrams. For example, the marginal revenue curve would have a negative gradient, due to the overall market demand curve. In a non-competitive environment, more complicated profit maximization solutions involve the use of game theory.

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