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Author Topic: can anybody solve these  (Read 4317 times)

slayerdave

  • Guest
can anybody solve these
« on: October 18, 2009, 06:49 PM »
                                                                                                

1.  a) Complete the following table and identify the stages and phases of production:  

K(capital)        L(labour)   TP(total product)   MPL(marginal product)   APL(marginal product)
5                    0                0      
5                    1              20      
5                    2              45      
5                    3              75      
5                    4            110      
5                    5            130      
5                    6            140      
5                    7            140      
5                    8            135      

b) A fishing company conducted a series of experiment to determine the amount of fish that could be caught.   The results are:
                                  
Fishermen            Fish (lbs.)
1                          1
2                          4
3                        24
4                        48
5                        70
6                        90
7                        98
8                      104
9                        104
10                      102
11                        99

       a) Calculate the total, marginal and average product.                                                                                      
  
      c) Suppose the price for a lb. of fish is $10 and wage rate is $60, how many fishermen should
          be employed to be optimal?                                                                                      
                                                                                  

2.  Chemco uses 25 workers and 50 machines to produce its product. The MPL of the last worker is 73 units of output/day; the MPM of the last machine is 240 units of output/day. The daily paid for each worker is EC$30 and the rental of each machine is EC$100/day.


a)   What is the MP per dollar spent on a worker?                                                      

     b)  What is the MP per dollar spent on machine?                                                        

     c)  Is Chemco utilizing workers and machines in the cost?minimizing manner?                                                                                                                                      

3. Compare and contrast the stages and phases of production with the aid of a diagram                

4. The production function for Open Bottle is Q = 25L0.25 K0.75
 
    a) What is the marginal product of labour?                                                                    
    
    b) What is the average product of labour?                                                                      
    
    c) What is the marginal product of capital?                                                                    

    d) What is the average product of capital?                                                                    
    e) Calculate the MRTS; given that price of labour is $50 and price of capital is $90.  


5.  Dirt Diggers (DD) is a firm that excavates roadside ditches for laying drainpipes. It s output follows the production function Q = 10L ? 0.1L2; where L denotes labour hours and Q the length of the ditch in metres. The firm hires labour at a wage of $12 per hour. Hint: MRPL = MRCL

      a) DD has received an offer to excavate 250 metres for a price of $500. Should DD accept the
          offer?                                                                                                                        

      b) What offer would be profitable?                                                                          
          

6. a)  The Open Chemical Ltd obtained the following estimate of the firm?s
         Production (Leontief production function):    Q = F(K, L) = min {10.4K, 11L}
         How much output is produced when 22 units of labour and 19 units of capital are
         employed?                                                                                                                                                                                          
  
  
 b)  Prove the following (K = capital and L = labour):

(i)  ?K/?L = MPL/MPK;                                                                                                                                                                  

      


6b (continued)

          (ii)  The sum of the exponents of labour and capital in a Cobb?Douglas production function
                measures the returns to scale; and                                                                                                                                                    

         (iii) The exponents a and b of a production function Q = ALaKb are estimates of the output
               elasticities of labour and capital respectively.                                                    

7. UWIDEC production function is lnQ = 4.73 + 0.29lnK + 0.68lnL
  
    a)  Convert the production function into its normal form.                                                                                                                              

    b)  What is the firm?s output elasticity and returns to scale?  Explain.                                                                                                      

8. Ear Us (producer of hi?tech hearing aid) production function is Q = K0.5L0.5. The company over the years uses input rates of 60 and 120 for capital and labour respectively. The price of capital is $50 and labour is $25 per telephone.

      a)  Is there efficiency in production? Why?                                                                                                                                          
      
      b)  If $100,000 is allocated to production, what is the maximum output?                                                                                                

9.  A new footwear manufacturing company commenced business in St. Vincent and its
       production function is Q = 85KL2. Given that the price of labour is EC$20 and the MRTS
       is K = 1.5L

a)  What is the price of capital?                                                                                                                                                                  
    
     b)  If the desired output is 2,500 units, how many units of capital and labour will be used?
                                                                                                                                            
« Last Edit: October 27, 2009, 08:47 PM by slayerdave »
 

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makubex87

  • Guest
Re: can anybody solve these
« Reply #1 on: October 26, 2009, 10:12 PM »
I'm willing to help  but I can't understand the tables, maybe because of the layout.

Can you please fix the layout,so that I can help you?


 

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