Economics question; HELP! Pt. 1?

Question

I was hoping someone could show me a walk-through of this problem:

A Genealogical firm called "Greats" produces output using only one input. It's production function is: f(x)= *square root* x

A. Does the firm have: increasing, constant, or decreasing returns of scale?

B. How many units of output does it take to produce 10 units of output? ____ If the output costs "w" per unit, what does it cost to produce 10 units of output? ___

C. How many units of input does it take to produce "y" units of output? ____ if the input costs "w" per unit, what does it cost to produce "y" units of output? ____

D. If the input costs "w" per unit, what is the average cost of producing "y" units? AC(w,y) = _________

Answer 1

A.  If you look at the graph, the function increases, but at an increasingly slower rate.  This means that as the number of inputs increases proportionally, the output does not increase as fast.  Therefore, it has decreasing returns to scale.  (If you want the calculus sol'n to this, email me)

B. solve the equation

10=rt(x)

10^2=rt(x)^2

x=100

for the cost, multiply the cost by the number of input required

c=w*100

C. solve the equation again

y=rt(x)

y^2=rt(x)^2

y^2=x

again, multiply by the cost

y^2*w

D. take the cost from the last part

y^2*w

now divide by the number of units produced

y^2*w/y=y*w