**cost function** - relates cost to output level for future prediction

- VC = bQ
- linear function, implies constant marginal cost

- VC = bQ + gQ2
- quadratic function, implies linear marginal cost

- VC = bQ + gQ2 + dQ3
- cubic function, implies quadratic (U-shaped) marginal cost

**Cobb-Douglas cost/production function** - when production in form Q = AKaLb

- C(Q) = wL(Q) + rK(Q)
- use production function and MRTS to find L and K functions in terms of Q

- MRTS = w/r = MPL / MPK
- w/r = (AbKaLb-1) / (AaKa-1Lb) = (bK) / (aL)
- waL = rbK
- L = (rb)K / (wa)
- K = (wa)L / (rb)
- substitute these back into the production function to find both L and K in terms of Q
- no need to use lagrangian method

- substitute L and K functions back into the initial cost function to get final outcome
- note that in short-run, either K or L will be fixed
- leaves the production function in terms of just K or L and makes it easy to solve
- in finding total cost, don't forget to calculate the fixed cost as well