I need help with F&G ONLY. I don't need help with A-E so if you post any answers other than F&G, ill be downvoting it.

Suppose that a firm's production function is given by Q=(K1/3+L1/3), here is a given parameter. (a) Find the marginal product of capital and labor. (b) Find the average product of capital and labor. (c) Does this production function have increasing, constant or decreasing returns to scale? Show how the returns to scale result depends on the parameter . (d) Find the marginal rate of technical substitution (RTS) (e) Use your result in (d) to find the elasticity of substitution. For the next two questions, suppose =3. (f) Assume that capital is fixed in the short run, we know that K=K. Set up the cost minimization problem of the firm and solve for the conditional demand for L. Find the short run cost function. (g) Assume that the firm can choose both, capital and labor. Set up the cost minimization problem of the firm and solve for the conditional demand for K and L. Find the cost function