For the production function q= k^0.25 l^0.25
1. Find total cost function C(w,r;q). Show that it is homogeneous of degree one in input prices and explain the intuition behind this property.
2. Find the profit function?(w,r,p). Show that it is homogeneous of degree one in all prices and explain the intuition behind this property.
3. Find the input demand functions k(w,r,p) and l(w,r,p).
4. Decompose the substitution and output effects of a change in w on labour demand.