Write down the cost minimization problem of the firm

2.2

Find the optimal L* and K* as a function of q. For this production function, you can use tangency condition

or the Lagrangian method. Show your work

2.3. Find the total cost function (or curve).

2.4. Find the marginal cost and the average cost in the long run.

2.5. Suppose K is fixed at K=1, find the marginal cost in the short run.