Kool (producer of hi–tech fans) production function is Q = KL0.5. The company over the years...
Kool (producer of hi–tech fans) production function is Q = KL0.5. The company over the years uses input rates of 80 and 20 for capital and labour respectively. The price of capital is $100 and labour is $25 per fan.
a) Is there efficiency in production? Why?
b) If $25,000 is allocated to production, what is the maximum output?
Homework Answers
a) Output is Q = KL^0.5
Also w = 25 and r = 100
From production function MRTS = MPL / MPK or 0.5K/L
Wage rental ratio is 25/100 = 0.25.
At K = 80 and L = 20, MRTS = 0.5*80/20 = 2
Since MRTS > wage rental ratio, the firm is not efficient when it uses K = 80 and L = 20
b) First use the fact that MRTS = 0.5K/L and wage rental ratio is 0.25.
At the optimum choice MRTS = w/r or 0.5K/L = 0.25. This gives L = 2K.
Now the budget constraint is 25000 = wL + rK or 25000 = 25L + 100K
Use L = 2K to get 25000 = 25*2K + 100K.
This gives K = 25000/150 = 166.67 units and L = 333.33 units
Maximum production Q = 3043 units.
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