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A certain firm in the beverage industry is faced with the following Cobb-Douglas production function of...

A certain firm in the beverage industry is faced with the following Cobb-Douglas production function of Q left parenthesis L comma K right parenthesis equals 4 L to the power of 0.3 end exponent space K to the power of 0.5 end exponent

a) What is A P subscript L and APK? [6 marks]

b) What is the level of M P subscript L space end subscript and M P subscript K when K = 40 and L = 40 [12 marks]

c) According to the Cobb- Douglas function , calculate the MRTS when K =35 and L = 25 [6 marks]

d) Increase capital with 75% and labour with 75% and see what will happened to output level.

Solutions

Expert Solution

The production function is given as .

(a) The average products of inputs would be as or or , and or or .

(b) The marginal product of labor would be as or or or , and for the given values, we have or or .

The marginal product of capital would be as or or or , and for the given values, we have or or .

(c) The marginal rate of technical substitution would be as or or or , and for the given values, we have or or .

This basically means that for an increase in marginal unit of labor, the capital must decrease by 0.84 units in order to produce same as before, at wehre L=25 and K=35.

(d) Increasing capital and labor by 75%, we have the new production level as or or or , ie , meaning that the output is increased by 56.47%.

As can be seen, since the production technology is decreasing returns to scale, the increase in output (56.47%) is less than the increase in both inputs (75%).

Rahul Sunny answered 1 year ago

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