Question

# The production function for the Roundtree Laser Company is: Q=(10L^.5)(K^.3)(M^.3) where: Q: number of lasers produced...

The production function for the Roundtree Laser Company is: Q=(10L^.5)(K^.3)(M^.3)

where: Q: number of lasers produced per week L: amount of labor used per week K: the amount of capital used per week M: quantity of raw materials used per week

a) Does the production function exhibit decreasing returns to scale?

b) Does the production function exhibit diminishing marginal returns?

(a) No, for this cobb-douglas production function to exhibit decreasing returns to scale, the sum of the power coefficients of L,K and M should be less than 1. But here it is 0.5+0.3+0.3=1.1 which is greater than 1. This production function exhibits increasing returns to scale.

(b) Yes this production Function exhibits diminishing marginal returns. To check this we double differentiate the production function w.r.t to L,K and M.

Since all are negative, so we have diminishing marginal returns.

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