I am begging you for hep for an exam please

Could somebody give me the workings out and answers to the following tutorial as i am useless and cant do it and have the exam in 2 days and am finding this subject hard. i have tried solving tem so many times buti cant do it, it is completely wrong ad my lecurer wont help me please bordies help me i can learn it if i have the solutions and wok from there, i am reallyfinding this stuck and if i fail this i will have to repeat my hole year which i cannot afford so wil end up quittig please please help [/B]
1 Profit Max.

A firm produces one type of electronic component and prices are stable at €50 each, i.e. P = MR = €50. The engineering dept. estimates that the relevant TC is:

TC = €78,000 + €18Q + €0.002Q2


a) Calculate the p max O/P
b) Calculate the max p



2. Profit Max.

21st Century Insurance offers mail-order car insurance in Ireland. It is a low-cost provider of insurance in this mkt. and they charge the same insurance premium, €750, to all clients in a particular risk category. Mgt. believe they cannot alter this single premium fee due to competitive reasons. TC for the company is:

TC = €2,500,000 + €500Q + €0.005Q2


a) Calculate the p max O/P
b) Calculate the max p
c) Calculate the return-on-sales


3. Revenue Max.

Desktop Publishing Software Inc. develops and markets software packages for business computers. Although sales have grown rapidly during recent years, mgt fear that the recent increase in the number of competitors in the industry may severly retard future growth opportunities. It believes the time has come to ‘either get big or get out’. The following monthly demand and cost info. has been provided by the accounting and marketing depts.

P = €1,000 - €Q TC = €50,000 + €100Q

a) Calculate monthly Q, P and p at the SR revenue max. O/P
b) Calculate monthly Q, P and p at the ST p max. O/P
c) When would SR revenue max. lead to LR p max.?



4. Average Cost Min.
Giant Screen TV Ltd. is a Waterford based importer and distributor of 1.5 metre flat-screen TV’s. The following revenue and cost information is available:

TR = €1,800Q - €0.006Q2 TC = €12,100,000 + €800Q + €0.004Q2


a) Calculate O/P, MC, AC, P, and p at the AC min. O/P level
b) Calculate the values in a) at the p max. O/P
c) Compare and discuss the answers to a) and b)


5 Constrained Optmisation – Substitution

A firm manufactures two products, X and Y. It seeks to max. its total profit function given by the following equation


p = 80X – 2X2 – XY – 3Y2 + 100Y


a) Calculate the quantities of products X and Y that should be produced to max p
b) calculate the max. p
c) If the firm now faces the constraint that the combined O/P of products X and Y must be 12, i.e. X + Y = 12, recalculate the values in a) a and b) above



6 Constrained Optmisation – Lagrangian Multiplier

Use the Lagrangian Multiplier method to solve the problem in 5 c) above


7 Constrained Optmisation – Substitution

The Warren & Smith Company manufacture commercial zippers of 2 kinds, kind X and kind Y. Its production dept. estimates that the AC function for the firm is:

AC = X2 + 2Y2 – 2XY – 2X – 6Y + 20

a) What level of O/P of both zippers X and Y will minimise the firm’s AC?
b) What is the AC in a) above
c) If the firm expects that the combined otal number of units of zippers X and Y will be 6, how many units of zipper X and zipper Y must the firm produce to min. its AC
d) What is the firm’s AC in c) above

8 Constrained Optmisation – Lagrangian Multiplier
Solve the problems posed in Q 7 above using the Lagrangian Multiplier method
Brohas, a local games manufacturer, produces and sells two types of games, type X and type Y. The profit function for the firm is:

p = €75X - €4X2 + €2XY - € Y2 + 48Y

Because of a severe lack of availability of trained machine operators, Brohas can produce a maximum of 45 games per hour. Bearing this constraint in mind:

a) Use the Lagrangian Multiplier method to calculate the firm’s profit maximising output for both types of game (to the nearest whole number) per hour and the maximum hourly profit they can make.

b) What would it mean to the firm’s profit if they could produce 51 games per hour?

c) What is the cost to Brohas, in terms of hourly profit, of not being able to obtain the optimal numbers of trained machine operators?






Question 2


a) Using a suitable economic diagram, explain the unique relationship between various relevant costs at the Average Cost minimising output. b) Burning-Rubber manufactures a high-performance tyre called Sport 100. Management have estimated the following: Fixed development costs for the current year will be €600,000, Marginal costs for manufacture and distribution are €63 per tyre. In addition, based on recent sales the following Price relationship exists:
P = €130 - €0.000125Q

Required:

A) Calculate Output, Price and Total Revenue at the Revenue Maximising output.
Calculate Output, Price and Total Revenue at the Profit Maximising output.

C) Compare and discuss your answers to parts (A) and (B). Do your answers compare in the way you would have expected?

Question 3


a) Determine if each of the following statements are True or False and justify your answer.

i) Given a downward sloping demand curve and increasing marginal costs, profit maximising firms will always sell less output at lower prices than revenue maximising firms.

ii) Total profits is the difference between total revenue and total costs and will always be positive at the profit maximising output.

iii) Marginal cost must be less than average cost at the average cost minimising output.

iv) The demand curve will be downward sloping if marginal revenue is less than price

v) Marginal profit equals zero at the profit maximising level of output

b) Using a suitable example, define each of the following:
i) Two-part pricing
ii) Peak-load pricing
iii) International Price Discrimination/Dumping
c) Calculate the Optimal Mark-Up On Price for a firm that has a Point Price elasticity of – 1.25.

Question 4


a) Describe what is meant by Price Discrimination, and explain the rationale behind a firm using such a process. In your answer give relevant practical examples.
b) Holidays 4 All Ltd, provides holiday accommodation for both family and senior citizen customers. Yearly demand and marginal revenue relations for overnight accommodation is as outlined below.

Family

Senior Citizen
Pf = €40 - €0.0004Qf
Psc = €30 - €0.00025Qsc


Fixed costs are not applicable and the average variable cost of providing a night’s accommodation is constant at €20.

i) Assuming they can price discriminate between family and senior citizen customers, calculate the optimal price, output for each customer segment, and total profit.
ii) Calculate the point price elasticity for each customer class and comment on whether your results are consistent with your recommendation on price in part (i) Question 1

Gimlet Ltd manufactures and sells foam insulation applicators. The production manager has determined that the following Price and Total Cost (TC) functions apply for the firm:

P = €3,000 - €0.5Q TC = €100,000 + € 1,500Q + 0.1Q2

a) Assuming the objective of the firm is to minimise Average Costs (AC), calculate the following at the AC min. output level:

i) Output
ii) MC
iii) AC, and
iv) Profit

b) Without doing any further calculations, describe how you would expect AC and Profit to compare under Profit Max conditions versus AC Min conditions

c) Define what is meant by Managerial Economics and explain how Managerial Economics tools and techniques can be used to help managers in the decision making process.
d) How is the popular notion of business/accounting profit different from the concept of economic profit?
e) Using an appropriate example, explain what is meant by Innovation Profit Theory.

Question 2

Cleanair manufactures and sells two types of industrial air filters, type X and type Y. The profit function for the firm is:

Tp = €70X - €4X2 + €2XY - € Y2 + 50Y

Because of a severe lack of availability of filter paper, a component part of their filters, Cleanair can only produce a maximum of 20 filters per hour. Bearing this constraint in mind:

a) Use the Substitution Method to calculate:

i) The firm’s profit maximising output of both type X and type Y filters (to the nearest whole number), and ii) The maximum profit they can make.
b) What is the cost to Cleanair of not being able to obtain the optimal amount of filter paper?
c) Explain what the Lagrangian multiplier is. In your answer describe how, if a constraint exists, the Lagrangian Multiplier enables one to determine the effect on the objective function if the constraint is relaxed.
Question 3

a) The Shoe Company, a producer of one particular type of walking shoe, operates as an integrated unit and has the following Demand and Cost info.

P = €100 – 0.001Q TC = €312,500 + 25Q + 0.0015Q2


Assuming the company’s objective is to maximising profit, calculate their

i) Output
ii) Selling Price, and
iii) Max. Profit

b) Now assume The Shoe Company was reorganised into two semi-autonomous divisions, manufacturing (which makes the shoes) and distribution (which packages and sells the shoes), with the Demand and Cost information as outlined below. In addition, also assume that a competitive market exists externally, such that the company is able to buy in an unlimited quantity of the shoes at a market price of €35 per pair.

TCm = €250,000 + 20Q + 0.001Q2 TCd = €62,500 + 5Q + 0.0005Q2

Calculate the company’s:

A) Transfer Price (5 marks)
Optimal Output(s) (2 x 5 marks)
C) Selling Price, and (5 marks)
D) Profit. (5 marks)


c) A local shop sells a product that has a Price elasticity of Demand of – 1.2, calculate:

i) The shop’s Optimal Markup on Price, and
ii) The Shop’s Optimal Markup on Cost