Lecture1-CostFunction 上海交大产业组织实务课件.pdf

Estimation of Cost Function Empirical IO: Lecture 1 Chun-Yu Ho, SJTU Introduction • Start from economies of scale and look into an example of electricity power – Christensen Greene (1976, JPE) • Extend the cost function to multi-product setting and examine economies of scope – Cohn, Rhine Santos (1989, RESTAT) • Another test of economies of scope: Subaddtivity – Evans and Heckman (1984, AER) Cost Function • Definition 1: Conditional factor demand is the inputs choices (e.g. labor, L; capital K) – Minimize the cost given factor prices (e.g. wage, w; rent, r) and output level, y • Definition 2: Cost function is the minimal cost at the factor prices (w, r) and output level, y – Cost function = conditional factor demand*factor prices Cost Function – Cobb-Douglas α β • Minimize C = rK + wL subject to Q K L – Minimize cost by choosing (L, K) given factor prices are (w, r) and the output level is Q • Step 1: Use the constraint to substitute out 1 α − one choice variable (in this case L) L QβK β 1 α − – Re-write the cost function as C rK +wQ βK β Cost Function – Cobb-Douglas • Step 2: Choose the optimal level of K to minimize cost 1 α ∂C α − −1 r − wQ βK β 0 ∂K β • The optimal choices of K and L are