multivariate economic analysis

[fishnumber2]

Assume that production of a particular good depends upon the inputs Capital and Labor according to the following function: Q=2K^0.5*L^0.5

a. Suppose that K=1. Is Q and increasing or decreasing function of L? Is Q a concave or convex function of L? Explain.
b. Supposed that L=1. Is Q an increasing or decreasing function of K? Is Q a concave or convex function of K?
c. Now let both K and L vary. Derive the contour set for Q=1. Illustrate this contour set by placing L on the x-axis and K on the y-axis. Under these circumstances, is K an increasing function or decreasing function of L? Is K a convex or concave function of L?

...I know I'm supposed to take the partial derivatives but the K=1 is throwing me off. Any assistance would be appreciated.

 

[Deleted member 4993]

Assume that production of a particular good depends upon the inputs Capital and Labor according to the following function: Q=2K^0.5*L^0.5

What are Q, K and L?

a. Suppose that K=1. Is Q and increasing or decreasing function of L? Is Q a concave or convex function of L? Explain. If K=1 then Q = 2 * L[sup:2n064nph]1/2[/sup:2n064nph]... can you plot it? - see it first then take derivative
b. Supposed that L=1. Is Q an increasing or decreasing function of K? Is Q a concave or convex function of K?similar to above
c. Now let both K and L vary. Derive the contour set for Q=1. Illustrate this contour set by placing L on the x-axis and K on the y-axis. Under these circumstances, is K an increasing function or decreasing function of L? Is K a convex or concave function of L? Now time for partial derivative has come - but solve the above two first - and we'll talk further.

Do you know what is meant by contour plots?

...I know I'm supposed to take the partial derivatives but the K=1 is throwing me off. Any assistance would be appreciated.