A firm produces a product with labor and capital as inputs. The production function is described byQ=2LK . Letw=1andr=1 be the prices of labor and...

A firm produces a product with labor and capital as inputs. The production function is described by Q=2LK

. Let w=1 and r=1

 be the prices of labor and capital, respectively.

1. Find the equation for the long-run total cost curve as a function of quantity Q
2. Solve the short-run cost-minimization problem when capital is fixed at a quantity of 5 units (i.e.,K=5). Derive the equation for the firms short-run total cost curve as a function of quantity Q and graph it together with the long-run total cost curve.
3. (optional). How would the short-run and long-run total cost curves look like if we increase/decrease w and r? Comment.