Assignment Task :

 

QUESTION ONE
Pagane Ltd produces two joint products X &Y in the ratio of 2:1.After the split off point the products can be sold for industrial use or taken to mixing plant for blending and refining. The following information is given for a specific week:                      
Joint process costs (which are allocated on volume) are 85% fixed and 15%variable, whereas the mixing plants costs are 30% fixed and 70% variable. There are only 50 hours available in the mixing plant (usually 30hrs are taken up to processing of product X &Y equally and 20 hrs are used for other work that generates a contribution of Sh 2500 per hour)

It has been suggested that it might be possible to change the mix of the joint process to 3:2 for X & Y respectively at a cost of Sh8 for each additional litre of Y produced by the process.
 
1.
The demand curve for y is Qy = 10,000 - 25P.
i. How many units could be sold for sh100?
ii. At what price would good y sales fall to zero?
iii. What is the total revenue (TR) equation for y in terms of output, Q? What is the marginal revenue equation in terms of Q?
iv. What is the point-price elasticity of demand when P = sh200? What is total revenue at this price? What is marginal revenue at this price? Explain your result.
v. Suppose that the price of y fell to P =sh 150, What would be the new point-price elasticity of demand? What is total revenue at this price? What is marginal revenue at this price? Explain your result.
vi. Suppose that the price of y rose to P =sh 250 ,What would be the new point-price elasticity of demand? What is total revenue at this price? What is marginal revenue at this price? Explain your result.
vii. Suppose that the supply of y is given by the equation Qs = -5,000 + 50P.What is the relationship between quantity supplied and quantity demanded at a price of sh300? In this market, what is the equilibrium price and what is the quantity 
 
2.
The Cobb–Douglas production function is widely used in economic and empirical analysis because it possesses several useful mathematical properties. The general form of the Cobb–Douglas production function is given as Q = AKaLb where A is a positive constant and 0 < a < 1, 0 < b < The law of diminishing marginal product states that as units of a variable input are added to a fixed input, output will increase at a decreasing rate.
i. Suppose that capital (K) is the fixed input and that labor (L) is the variable input. Demonstrate the law of diminishing marginal product using the Cobb–Douglas production function. 
ii. Assuming that capital is the constant factor of production, what is the proportional change in output resulting from a proportional change in labor input 
3. The average product of labor is given by the equation APL = 600 + 200L-L2 
i. What is the equation for the total product of labor (TPL) 
ii. What is the equation for the marginal product of labor (MPL) 
iii. At what level of labor usage is APL = MPL 

 

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  • Posted on : January 20th, 2018

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