i$)$ derive the Total Cost Function, TC$($q$),(4$ points$)$

ii$)$ draw the isoquant for the given level of output, $(2$ points$)$

iii$)$ draw the isocost associated with the minimum Total Cost of producing the

given amount of output, $(2$ points$)$

iv$)$ identify the cost minimizing amount of Labor and Capital $($L$*$ and K$*),(2$

points$)$

v$)$ determine whether the production function exhibits increasing, constant, or

decreasing returns to scale $(2$ points$),$ and

v$)$ label your graph carefully and accurately. $(2$ points$)$

Production Function: q $=$ L$1/2$K$1/2$

$$ Input prices: w $=16,$ r $=4$

$$ q $=8$

TC$($q$)=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Draw your graph in this space:

Increasing, Constant or Decreasing Returns to scale? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$