Answer to Question #221300 in Microeconomics for nithu

Question

The water Economist has estimated short run water responsiveness function for rice farming under major irrigation condition in the Dry Zone of Sri Lanka as follows;

Y = 21W +30.3W2 – 3W3, Where Y = Output (paddy kg /Acre) , W = irrigation Water (Cubic Meter – m3)

a) Determine three stages of this short run production process and graphically show the result.

b) Determine rational production stage and what is the maximum and minimum output level of this rational stage.

c) Determine the range of water level which is representing the low of diminishing marginal returns.

Answer 1

a.

There are three stages of production in the short run period. These stages are;

i. Increasing returns stage

ii. Dcreasing returns stage

III. Negative returns stage

b.

The rational production stage is stage two which is decreasing returns stage. This is because all resources used in the process of production are effectively and optimally utilized. This is the only stage where the production can take place is stage 2, where both marginal and average products are declining, but they are positive. 

To find the maximum and minimu output in the rational stage we differentiate the short run production with respect to W

y = 21w + 30.3w²-3w³

The results after differentiation will be;

mp=21+ 0.6w -9w²

The result is the MP

we then set MP=0

0=21+ 0.6w -9w²

solving for w we get

w1=0.33 and w2=-7.06

minimum product will be ; 21(0.33)+ 30.3(0.33²) - 3(0.33³)

Minimum output = 10 units

maximum output will be; 21(-7.06)+ 30.3(-7.06²) - 3(-7.06³)

=2417 units

c.

The range representing the law of diminishing returns is 10 units to 2417 units