题目

 Explain the meaning of a shadow price and calculate the shadow price of qualified researcher time. 

考点:Chapter4Limitingfactoranalysis

Shadow price 

The shadow price is the extra contribution or profit that may be earned if one more unit of a binding resource or limiting factor becomes available. 

It can be used to inform managers of the maximum price that should be paid for more of a scarce resource over and above the basic rate. The shadow price of a constraint that is not binding at the optimal solution is zero. 

Calculation of shadow prices 

At the optimal solution, A = 32.94 and B = 57.10  

Contribution = $54,507 

Qualified researchers 

(32.94 × 20) + (57.10 × 12) = 1,344 = availability 

The constraint is binding. If one more hour of labour was available, the new optimal product mix would be at the intersection of the lines: 

             20a + 12b = 1,345 (1)  

                8a + 15b = 1,120 (2)

 (2) × 2.5 

               20a + 37.5b = 2,800 (3) 

(3) – (1) 

              25.5b = 1,455        

                      b = 57.06 

Substitute into (1)  

                20a + 684.72 = 1,345  

                                      a = 33.01 

Contribution = (580 × 33.01) + (620 × 57.06) = $54,523 

The shadow price of one hour of qualified researcher's time is the extra contribution generated which is $16. 

多做几道

 A public health clinic is the subject of a scheme to measure its efficiency and effectiveness. Among a number of factors, the 'quality of care provided' has been included as an aspect of the clinic's service to be measured. Three features of 'quality of care provided' have been listed. 

(1) Clinic's adherence to appointment times 

(2) Patients' ability to contact the clinic and make appointments without difficulty 

(3) The provision of a comprehensive patient health monitoring programme 

Required

 (i) Suggest a set of quantitative measures which can be used to identify the effective level of achievement of each of the features listed.

(ii) Indicate how these measures could be combined into a single 'quality of care' measure. 

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18

【论述题】

The absence of the profit measure in non profit seeking organisations causes problems for the measurement of their efficiency and effectiveness. 

Required 

(i) Explain why the absence of the profit measure should be a cause of the problems referred to.

(ii) Explain how these problems extend to activities within business entities which have a profit motive. Support your answer with examples. 

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24

【论述题】

Compare and contrast the use of residual income and return on investment in divisionalperformance measurement, stating the advantages and disadvantages of each. 

 Division Y of Chardonnay currently has capital employed of $100,000 and earns an annual profit after depreciation of $18,000. The divisional manager is considering an investment of $10,000 in an asset which will have a ten-year life with no residual value and will earn a constant annual profit after depreciation of $1,600. The cost of capital is 15%. 

Calculate the following and comment on the results. 

(i) The return on divisional investment before and after the new investment 

(ii) The divisional residual income before and after the new investment 

 Explain the potential benefits of operating a transfer pricing system within a divisionalised company. 

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