1.Differentiate the following:
(a)y = 10 x3 - 10 x2 + 4x + 2(e)y = [pic]
(b)y = [pic](f)y = ( 4 + x ) ( x - 1 )
(c)y = [pic](g)2y = 3 x2 + 10
(d)y =[pic](h)x y = 2 x2 - 5 x + 4

2.Find the integral of the following:
(a) [pic](e)[pic]
(b) [pic](f) [pic]
(c) [pic](g) [pic]
(d) [pic]

3.Find the x value of the turning points on the graph of y = [pic] and determine whether it is a maximum or a minimun point.

4.Find the coordinates of the two turning points of the function y = x3 - 8 x2 + 5 x + 3

5.For a particular function, dy/dx = 4x - 3. If it is known that when x = 1, y = 5, find y in terms of x.

6.A manufacturing process costs RM 6500 to set up for one year’s use. If items cost RM 85 each to produce and other costs amount to 3.5 x2, where x is the production in hundreds, find the level of production that will minimise the cost per item over the year. What will the total cost amount to at this level of production?

7.The marketing department of Spager Ltd estimated that if the selling price of product is set at $15 per unit then the sales will be 50 units per week, while, if the selling price is set at $20 per unit, the sales will be 30 units per week. Assume that the graph of this function is linear. The production department estimates that the variable cost will be $5 per unit and that the fixed cost will be $50 per week, and special cost are estimated as $0.125x2, where x is the quantity of output. All production is sold. (a) Show that the relationship between price (Pr) and quantity sold (x) , are given by the equation Pr = 27.5 - 0.25x. (b) Find the revenue function, R.

(c) Find the total cost function (C).
(d) Advise the company on production and pricing policy if it wishes to maximize profits, and find the maximum profit.

8.A firm receives £135 for each unit sold. The costs consist of a fixed cost per month of £2500 and...

...Practice Questions and Answers from Lesson III-3: Monopoly Practice Questions and Answers from Lesson III-3: Monopoly The following questions practice these skills: Explain the sources of market power. Apply the quantity and price affects on revenue of any movement along a demand curve. Find the profit maximizing quantity and price of a single-price monopolist. Compute deadweight loss from a single-price monopolist. Compute marginal revenue. Define the efficiency of P = MC. Find the profit-maximizing quantity and price of a perfect-price-discriminating monopolist. Find the profit-maximizing quantity and price of an imperfect-price-discriminating monopolist. Question: Each of the following firms possesses market power. Explain its source. a. Merck, the producer of the patented cholesterol-lowering drug Zetia b. Chiquita, a supplier of bananas and owner of most banana plantations c. The Walt Disney Company, the creators of Mickey Mouse Answer to Question: a. Merck has a patent for Zetia. This is an example of a government-created barrier to entry, which gives Merck market power. b. Chiquita controls most banana plantations. Control over a scarce resource gives Chiquita market power. c. The Walt Disney Company has the copyright over animations featuring Mickey Mouse. This Is another example of a government-created barrier to entry that gives the Walt Disney Company market power. Question: Skyscraper City has a subway system, for which a one-way...

...Annual employment costs are $30,000 for each social service staff member (S) and $60,000 for each medical staff member (M).
(1iiia) Using the Lagrangean multiplier approach calculate the optimal (i.e., service maximizing) combination of medical and social staff. Determine the optimal amount of service provided by BF (32 points).
Objective function: Z = M + .5S + .5 MS – S2
Constraint: 30000S+60000M = 1200000
Lagrangian:
L = M + .5S + .5 MS - S2+λ[1200000-30000S-60000M]
First we need to calculate the first order conditions from the objective function:
dL/dS = 0 implies 0.5+0.5M-2S = 30000λ or 0.5+0.5M-2S-30000λ=0
dL/dM = 0 implies 1+0.5S=60000λ or 1+0.5S-60000λ=0
dL/dλ = 0 implies 30000S+60000M = 1,200,000 or 30000S+60000M-1,200,000=0
Next we need to equate dL/dS = dL/dM
60000*(0.5+0.5M-2S) = 30000*(1+0.5S)
30000+30000*M-1,200,000S = 30000+15000S
M = 4.5S
Substituting this value into the last equation of dL/dλ
30000S+60000*4.5S = 1,200,000
S= 4 = Social Staff
M* = 4.5*4 = 18 = Medical Staff
Z = M + .5S + .5 MS - S2
Z= 18+0.5*4+0.5*18*4-42 = 40 = Optimal amount of service
(1iiib) Calculate BF’s marginalcost. Explain your answer.
Dr. Ghosh…I couldn’t find much in our text regarding the interpretation of this in relation to MC. I did find that the multiplier should equate to the marginalcost from research online and inferred from the definition of the multiplier itself in...

...
The net present value of an investment represents
Selected Answer: Correct Answer:
the expected contribution of that investment to the goal of shareholder wealth maximization the expected contribution of that investment to the goal of shareholder wealth maximization
Question 8
5 out of 5 points
Generally, investors expect that projects with high expected net present values also will be projects with
Selected Answer: Correct Answer:
high risk high risk
Question 9
Which of the following would tend to make demand INELASTIC?
Selected Answer: Correct Answer:
5 out of 5 points
the proportion of the budget spent on the item is very small the proportion of the budget spent on the item is very small
Question 10
Marginal revenue (MR) is ____ when total revenue is maximized.
Selected Answer: Correct Answer:
5 out of 5 points
equal to zero equal to zero
Question 11
5 out of 5 points
Empirical estimates of the price elasticity of demand [in Table 3.4] suggest that the demand for household consumption of alcoholic beverages is:
Selected Answer: Correct Answer:
price inelastic price inelastic
Question 12
5 out of 5 points
An income elasticity (Ey ) of 2.0 indicates that for a ____ increase in income, ____ will increase by ____.
Selected Answer: Correct Answer:
one percent; quantity demanded; two percent one percent; quantity demanded; two percent
Question 13
0 out of 5 points
When using a...

...MARGINAL PRODUCTIVITY THEORY:
A theory used to analyze the profit-maximizing quantity of inputs (that is, the services of factor of productions) purchased by a firm in the production of output. Marginal-productivity theory indicates that the demand for a factor of production is based on the marginal product of the factor. In particular, a firm is generally willing to pay a higher price for an input that is more productive and contributes more to output. The demand for an input is thus best termed a derived demand.
Marginal productivity theory is a cornerstone in the analysis of factor markets and the input side of short-run production. It provides insight into the demand for factors of production based on the notion that a profit-maximizing firm hires inputs based on a comparison between the productivity of the input and the cost of the input.
The Law of Diminishing Marginal Returns
The central principle underlying marginal-productivity theory is the law of diminishing marginal returns. This law states that as additional units of a variable input are added to a fixed input, eventually the marginal product of the variable input decreases.
This principle is an essential component of short-run production analysis, which offers insight into the positively-sloped marginalcost curve and the law of supply.
The law...

...“Apply the concepts of marginal utility theory, product differentiation, and revenue/profit maximization to some event in your personal, daily lives.” [1]
Marginal Utility Concept Application
From the three concepts at hand this is by far the easiest to exemplify. According to Sloman and Sutcliffe the concept of utility is directly related to that of satisfaction [2]. The satisfaction that one individual takes from consuming something is called utility.
Now when we consider the utility concept we must differentiate first between total utility and marginal utility.
Total utility is the total satisfaction that one individual gets from consuming all the units of one same thing during a specific timeframe. ie. We can analyze the utility of consumption of coke during one day to analyze the “optimum” number of cokes to be consumed or we could analyze the utility of each sip we take from a can of coke to analyze the best size of can to offer in the market for example. No matter which, to the analysis of this as a whole, the total utility of the consumption of coke would be in one scenario the added utilities of all the cans of coke drank during the say in the first example, or the total utility of drinking one can of coke in the second example.
Marginal utility on the other hand is the utility that one individual gets from consuming one extra unit of one same thing during a specific timeframe. ie. We can look...

...Oligopoly
From Wikipedia, the free encyclopedia
An oligopoly is a market form in which a market or industry is dominated by a small number of sellers (oligopolists). Oligopolies can result from various forms of collusion which reduce competition and lead to higher costs for consumers. [1]
With few sellers, each oligopolist is likely to be aware of the actions of the others. The decisions of one firm therefore influence and are influenced by the decisions of other firms. Strategic planning by oligopolists needs to take into account the likely responses of the other market participants.
Description[edit]
Oligopoly is a common market form where a small number of firms are in competition. As a quantitative description of oligopoly, the four-firm concentration ratio is often utilized. This measure expresses the market share of the four largest firms in an industry as a percentage. For example, as of fourth quarter 2008, Verizon, AT&T, Sprint, and T-Mobile together control 89% of the US cellular phone market.
Oligopolistic competition can give rise to a wide range of different outcomes. In some situations, the firms may employ restrictive trade practices (collusion, market sharing etc.) to raise prices and restrict production in much the same way as a monopoly. Where there is a formal agreement for such collusion, this is known as a cartel. A primary example of such a cartel is OPEC which has a profound influence on the international price of oil.
Firms...

...1. *Define scarcity and opportunity cost. What role these two concepts play in the making of business decisions?
Scarcity is a Ever-present situation in all markets whereby either less goods are available than the demand for them, or only too little money is available to their potential buyers for making the purchase. This universal phenomenon leads to the definition of economics as the "science of allocation of scarce resources."
Opportunity cost is the cost of an alternative that must be forgone in order to pursue a certain action. Put another way, the benefits you could have received by taking an alternative action.
Opportunity cost can be defined as the value of the next best alternative forgone. It can be defined as the revenue or the profit that a person/organization would have been able to earn if it had exercised the alternative decision instead of the decision that has been made.
Opportunity-cost has many practical business applications, because opportunity costs will exist as long as resource scarcity exists. The value of the next-best alternative should be considered when choosing among production possibilities, calculating the cost of capital, analyzing comparative advantages, and even choosing which product to buy or how to spend time.
2. *(a) what is Marginal Analysis? (b) Why Is Marginal Analysis Important in...