Problem #1
a. Using the simulation in the spreadsheet would yields Q=584 b. [pic]

Problem #2
a. Using solver to solve the embedded model in the Excel sheet or by trying different values for h the optimum value will be obtained as “h=4” b. Marginal Revenue = Marginal Benefit
[pic]
c. Optimal profit from Problem #1 = 331
Current optimal profit = 371
The difference is due to the effect of Sheen’s effort on the demand. This relation is not surprising. Players in the different stages of a supply chain can increase demand for their product through efforts in advertisement, product development etc.

Problem #3
a. Armentrout’s optimal stocking quantity is 516.
b. Armentrout’s cost of overstocking ($0.80) is significantly higher than his cost of understocking ($1.00 - $0.80 = $0.20). So his optimal value would be less than mean. It is important to note how the division of profit between channel members affects the sales. Since Sheen is getting most of the profit the margin of retailer is reduced so he reduces his inventory level which leads to decline of fill rate in channel. [pic]

c. As in the integrated channel Sheen’s profit initially increases with h and later decreases. At low levels of h, the marginal benefit from additional effort is significant because demand increases significantly with each additional unit of effort. At high h the growth in demand as a function of h is slower – in other words, the marginal benefit from additional effort is lower and is less than the marginal cost. So Sheen’s profit is maximized at an intermediate value h = 2.25. The optimal h in this differentiated channel is lower than the integrated channel because Sheen’s marginal benefit is lower (a part of benefit goes to Armentrout). So she puts less effort in the paper since she has less profit per paper. d. When we lower the transfer price Armentrout’s benefit would increase...

...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...

...3.05 MarginalCost Analysis
Name:______________________________________________
Step One: Launch the data generator to get started (located in the last page of the lesson, or use the numbers given below:
Quantity
Price (in whole dollars)
Total Revenue
Marginal Revenue
Total CostMarginalCost
Profit (or loss)
0
42
0
35
1
41
41
68
2
40
80
94
3
39
117
107
4
38
152
114
5
37
185
129
6
36
216
180
7
35
245
235
8
34
272
296
Step Two: Determine a product market (a specific good or service) appropriate to the prices listed. This will be the title of your graph and data table. You will be creating a graph on Step Four.
Step Three: Calculate the marginal revenue, marginalcost, and profit for each quantity level. Fill in the data table. Use the Case Study presentation at the bottom of the lesson page in 3.05 for step by step instructions on how to calculate your figures. This case will also help you construct your Step Four.
o Total Revenue = Quantity x Price
o Total Cost = Fixed Cost + Variable Cost
o Profit or Loss = Total Revenue – Total Cost
o ―Marginal means additional
o Marginal Revenue is computed by finding the difference of the previous two quantities...

...Marginal Revenue and MarginalCost
An understanding of marginal revenue and marginalcost is economically crucial to owning and operating a successful business. Marginal revenue is the amount of change in total revenue by selling one additional product. So if a company sells four extra unit of product and brings extra total revenue of 500 dollars than the marginal revenue for this month would be 125 dollars. This is found by taking the change in total revenue, 500 dollars, and dividing it by the change in quantity, 4 units of product. This gives you the marginal revenue which can help a company understand what each unit is worth and how much they will be making for each extra unit.
Marginalcost is how much it cost the company to produce one more product. A company calculates the marginalcost by taking the change in total cost and dividing it by the change in quantity. If it cost a company 400 dollars to produce eight units and it cost a company 425 dollars to produce nine units than the marginalcost for making product nine is 25 dollars.
Finding a profit and understanding when you are earning a profit is crucial because this defines how much your company with gross every...

...calculate average and marginalcost to make production decisions.” Reference: Gregory Mankiw’s Principles of Microeconomics, 2nd edition, Chapter 13. Long-Run versus Short-Run In order to understand average cost and marginalcost, it is first necessary to understand the distinction between the “long run” and the “short run.” Short run: a period of time during which one or more of a firm’s inputs cannot be changed. Long run: a period of time during which all inputs can be changed. For example, consider the case of Bob’s Bakery. Bob’s uses two inputs to make loaves of bread: labor (bakers) and capital (ovens). (This is obviously a simplification, because the bakery uses other inputs such as flour and floor space. But we will pretend there are just two inputs to make the example easier to understand.) Bakers can be hired or fired on very short notice. But new ovens take 3 months to install. Thus, the short run for Bob’s Bakery is any period less than 3 months, while the long run is any period longer than 3 months. The concepts of long run and short run are closely related to the concepts of fixed inputs and variable inputs. Fixed input: an input whose quantity remains constant during the time period in question. Variable input: an input whose quantity can be altered during the time period in question. In the case of Bob’s Bakery, ovens are a fixed input during any period less...

...decisions is when to buy new machines or equipment or upgrade the machines or equipment that the business already has. Using analysis of the needs of the business and how the new equipment will help the business to function and the cost of the product will determine what the managers of the business decides.
Marginalcosts are change in total costs divided by change in output. Marginal revenue is the change in total revenue divided by change in output. Increase in fixed costs means that when the fixed costs cannot be changed it is the short run and when the fixed costs change it is the long run.
The second questions that I chose to answer was the following: A managerial decision I recently had to make which required a complete review of the economic considerations involved whether to transition into a digital format with our portable x-ray machines by performing transformation upgrades to both existing analog units or to trade them in and use their value to offset the total price incurred by the purchase of new units.
Value Considerations
Current Value of analog systems:
Flat value: $12,000 ea
Intrinsic value:
Exams (units)/day: 8.5
Average revenue/unit: $65.00
$553/day X 365 = $201845/year
Cost Consideration #1:
The cost to upgrade (2) GE AMX 4 Plus Portable X-ray Units is $88,000 each. The upgrade...

...Investigation Draft II Asif Sarker
12/25/12
Asif’s Backscratchers Inc.
Problem: Asif runs a big modern day company that is like any other. The company sells quantities of products that are plastic backscratchers. The company right now is failing severely because there are much more products being made then being sold and we need a way to find out how to find the number of production level that will maximize a company’s profit.
We are given that the Total money the company spends is 840 + 10.26x - 0.0541x2 + 0.0007x3
And the Profit we are making from this amount of quantities are 30.5 – 0.001x + 10.004x2
So what do we know so far? What kind of math can be used? The answer is derivatives. Usually you learn about derivatives in pre calc when you first learn about finding slopes of tangent lines right? Your teacher goes to tell you that derivatives are the regularly seen as a method finding the slope of a point for a function. But more importantly Derivatives runs our society. If you are thinking “oh the big companies and the rich white people run our society”, then you are right. These people know their calculus and use it to become rich.
Derivatives are pretty simple for polynomials. To find the derivative of a polynomial you use the power rule. There are many other rules that can be used for other types of functions.
The proof for the power rules:
Historically the power rule was derived from Cavalieri’s...

...ABSORPTION
AND
MARGINAL COSTING
Outline: 1. Learning Objectives 2. Differences between absorption and variable costing 3. Impact on profit under each costing technique 1. Learning objectives a. Explaining the differences between absorption costing and marginal costing b. Explaining the impact on stock valuation & profit under each costing system c. Explaining the impact on under each costing system d. Preparing multi-period absorption andmarginal costing profit statements 2. Explaining the differences between absorption costing and Marginal costing 298) Flow of Costs under Full Absorption & Marginal Costing PERIOD COST Selling and administrative expenses FULL ABSORPTION COSTING PRODUCT COSTS Fixed manufacturin g overhead Variable manufacturing overhead Direct materials and direct labour
Work in process inventory
Expenses for the period
Cost of goods sold
Closing inventories
PERIOD COST Selling and administrative
MARGINAL COSTING PRODUCT COSTS Fixed manufacturin Variable manufacturing Direct materials and
1
expenses
g overhead
overhead
direct labour
Work in process inventory
Expenses for the period
Cost of goods sold
Closing inventories
Absorption Costing = full costing - DM + DL + Marginal + fixed manufacturing OH product...

...the average variable cost is
a. at the same level of output as the minimum average total cost
b. at a smaller level of output than the minimum average total cost
c. at a larger level of output than the minimum average total cost
d. at the same level of output as the average fixed costs
e. same as minimum marginalcost
2. The multiplant monopolist maximises profits when
a.Marginalcost equals marginal revenue
b. When marginalcost in each plant are equal
c. When average cost in each plant is equal
d. When marginal revenue in each plant is zero
e. When he produces only in the low cost plant
3. If the market price is exactly equal to average cost,
a. the firm shuts down as there is no profit
b. the firm shuts down as the variable costs cannot be covered
c. Continues to operate in the short run
d. The firm shuts down as it cannot cover its fixed
e. The firm shuts down if the price is lower than average variable cost
4. Which of the following would shift a firms short run average cost upward
a. An advance in technology
b. An increase in wages
c. An increase in demand for the product
d. Reduction in excise taxes
e. Reduction in interest costs
5. Which of the...

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