# Marginal Analysis - Marginal Benefit including Marginal revenue and Marginal cost

Marginal Analysis
The determination of optimal behavior by comparing benefits and costs at the margin, that is, benefits and costs that result from small (i.e., marginal) changes. Optimality requires that marginal benefit equal marginal cost, since otherwise a rise or fall could increase benefit more than cost. http://www-personal.umich.edu/~alandear/glossary/m.html

Marginal analysis is one of one of the most important managerial tools and marginal analysis states that optimal managerial decisions involve comparing the marginal benefits of a decision with the marginal costs. (Baye, 2006). Therefore, two important concepts marginal revenue and marginal cost is explained, respectively.

Marginal Revenue/Benefit
The amount by which a firm's revenue increases when it expands output by one unit, taking into account that to sell one more unit it may need to reduce price on all units. These benefits can be seen in terms of utility/satisfaction/or dollar amounts. Marginal Benefits tend to fall as consumption of a good or service increases. A generic explaination behind this curve is that as people, we enjoy variety, and too much of one thing tends to get old, so as we continue to purchase/consume we lose that variety and receive lower levels of benefit from each unit.

Marginal revenue is the extra revenue that an additional unit of product will bring a firm. It can also be described as the change in total revenue/change in number of units sold.
More formally, marginal revenue is equal to the change in total revenue over the change in quantity when the change in quantity is equal to one unit (or the change in output in the bracket where the change in revenue has occurred)
This can also be represented as a derivative. Total Revenue=Price*Quantity or TR=P*Q.

For a firm facing perfectly competitive markets, price does not change with quantity sold dP/dQ= 0 so marginal revenue is equal to price. For a monopoly, the price received will decline with the quantity sold (dP/dQ<0)), so marginal revenue is less than price. This means that the profit-maximizing quantity, for which marginal revenue is equal to marginal cost, will be lower for a monopoly than for a competitive firm, while the profit-maximizing price will be higher. When marginal revenue is positive, price elasticity of demand [PED] is elastic, and when it is negative, PED is inelastic. When marginal revenue is equal to zero, price elasticity of demand is equal to -1.

Marginal Cost
The increase in cost that accompanies a unit increase in output; the partial derivative of the cost function with respect to output.

Marginal cost is also known as incremental cost or differential cost. A simple definition of marginal cost (MC) would be, "The change in total costs arising from a change in the managerial control variable" (Baye, 2006). According to the Blackwell Encyclopedic Dictionary of Managerial Economics "The marginal cost is the change in total costs due to a unit (or incremental) change in output.

Simply put: Marginal cost is the change in total cost that arrises due to the production of one additional unit or can be seen as the derivative of total production costs with respect to the level of output.

There are several formulas for Marginal Cost:
See Marginal Cost Page

Marginal cost is the change in total cost that arises when the quantity produced changes by one unit. Mathematically, the marginal cost (MC) function is expressed as the derivative of the total cost (TC) function with respect to quantity (Q). Note that the marginal cost may change with volume, and so at each level of production, the marginal cost is the cost of the next unit produced. Marginal cost should be distinguished from average cost. For instance, suppose it costs \$100 to manufacture 10 units of ceramic mug and \$109 to produce 101 units. The average cost per unit is \$10.9, but the marginal cost of the 11th unit is \$9
In general terms, marginal cost at each level of production includes any additional costs required to produce the next unit. If producing additional vehicles requires, for example, building a new factory, the marginal cost of those extra vehicles includes the cost of the new factory. In practice, the analysis is segregated into short and long-run cases, and over the longest run, all costs are marginal. At each level of production and time period being considered, marginal costs include all costs which vary with the level of production, and other costs are considered fixed costs.
It is a general principle of economics that a (rational) producer should always produce (and sell) the last unit if the marginal cost is less than the market price. As the market price will be dictated by supply and demand, it leads to the conclusion that marginal cost equals marginal revenue. These general principles are subject to a number of other factors and exceptions, but marginal cost and marginal cost pricing play a central role in economic definitions of efficiency.
Marginal cost pricing is the principle that the market will, over time, cause goods to be sold at their marginal cost of production. Whether goods are in fact sold at their marginal cost will depend on competition and other factors, as well as the time frame considered. In the most general criticism of the theory of marginal cost pricing, economists note that monopoly power may allow a producer to maintain prices above the marginal cost; more specifically, if a good has low elasticity of demand (consumers are insensitive to changes in price) and supply of the product is limited (or can be limited), prices may be considerably higher than marginal cost. Since this description applies to most products with established brands, marginal pricing may be relatively rare; an example would be in markets for commodities.
A number of other factors can affect marginal cost and its applicability to real world problems. Some of these may be considered market failures. These may include information asymmetries, the presence of negative or positive externalities, transaction costs, price discrimination and others.

Marginal Costs:

 Quantity Total Cost Marginal Cost 0 0 -- 1 5 5 2 10 5 3 17 7 4 25 8 5 34 9 6 44 10 7 58 14 8 73 15 9 90 17 10 110 20

Marginal Benefits:
 Quantity Total Benefits Marginal Benefits 0 0 -- 1 30 30 2 55 25 3 75 20 4 90 15 5 103 13 6 113 10 7 121 8 8 126 5 9 130 4 10 132 2

Economic Efficiency:

Multiple Choice Questions:
Net Benefits are maximized when:
A.) marginal benefits equal marginal costs
B.) the slopes of the total benefits curve and total cost curve are equal.
C.) All the above.
D.) None of the above.

Answer: C.) All the above. By definition the net benefits are maximized when the marginal benefits are equal to the marginal costs. The slopes of the total benefits curve and total cost curve are equal, is just another way of expressing the same view.

Marginal Analysis:
A.) Is the optimal managerial decisions involving comparing the marginal benefits with the marginal costs of a decision.
B.) Refers to the change in total benefits arrising from the change in the managerial control variable.
C.) Refers to the change in total costs arrising from a change in the managerial control variable.
D.) The additional revenues that stem from a yes-or-no decision.

Answer: A.) Is the optimal managerial decisions involving comparing the marginal benefits with the marginal costs of a decision. This is a strict definition of marginal anaylsis.

Marginal analysis can be used:
A.) In determining how long to study for a test.
B.) In determining how to get to your spring break destination (i.e. plane=faster but more expensive, car=slower but less expensive).
C.) In determining how much more to write on a wikispaces page.
D.) All the above.

Answer: D.) All the above. The reasoning behind this is simple, by determining how important an hour of free time is vs an hour of studying for a test you are using marginal analysis. Measuring the associated benefits of arriving earlier to the spring break destination vs the additional costs of getting there sooner is using marginal analysis. Lastly continuing to update the wikispaces page for a better and better grade comes at the cost of time and effort.

Questions;

1) When an economist concludes that there is not enough of some activity, the economist is suggesting that:
a) The marginal benefit of the activity exceeds its marginal cost
b) The cost of activity has increased.
c) The benefit of the activity has decreased
d) The marginal cost of activity exceeds its marginal benefit.

Answer: If the marginal benefit of an activity exceeds its marginal cost, then more of the activity is warranted. Therefore the correct answer is A.

2) A Marginal curve shows

a). the integral of the corresponding Total curve, up to the quantity at which the marginal is being calculated
b.) The inverse of the derivative of the Total curve to which it corresponds
c). the slope of the corresponding Total curve, computed at the same consumption quantity
d.) the amount of utility derived from consumption of each number of units

Answer: C is best A Marginal is the slope of a Total. The height of the marginal utility curve at a particular quantity of consumption records the slope of the corresponding total utility curve at that same quantity of consumption. Integrals come in because the height of the total curve is given by the integral under the marginal curve up to the quantity at which that total is being measured. Inverses never come into this story at all, so b. is wrong. Answer d. is incorrect because it implicitly describes total utility, not the incremental change in utility when consumption is increased by one unit.

References:
http://en.wikipedia.org/wiki/Marginal_cost
http://en.wikipedia.org/wiki/Marginal_revenue
http://www.amosweb.com/cgi-bin/awb_nav.pl?s=gls&c=dsp&k=marginal%20analysis
http://highered.mcgraw-hill.com/novella/QuizProcessingServlet
http://www.sscnet.ucla.edu/econ143/q1z6f97.prl
http://www.econ.rochester.edu/eco108/ch10/summ10.html&h=356&w=263&sz=14&hl=en&start=1&tbnid=Z8MONhxzmV7v2M:&tbnh=121&tbnw=89&prev=/images%3Fq%3DMarginal%2Bbenefit%2Bgraph%26svnum%3D10%26hl%3Den%26sa%3DN