Theory of the Firm Theory of the Firm: How a firm makes cost-minimizing production decisions; how its costs vary with output. Chapter 6: Production: How to combine inputs to produce output Chapter 7: Costs of Production Chapter 8: Firm’s profit- maximizing decision in a competitive industry

Chapter 6: Production Production technology: how firms combine inputs to get output. Inputs: also called factors of production Production Function: math expression that shows how inputs combined to produce output. Q = F (K, L) –Q = output –K = capital –L = labor

Production Function Production function: Q, K, and L measured over certain time period, so all three are flows. Production function represents: –1) specific fixed state of technology –2) efficient production Isoquant (‘iso’ means same): curve that shows all possible combinations of inputs that yields the same output (shows flexibility in production). See Table 6.1; Figure 6.1

Short Run vs Long Run Isoquant: shows how K and L can be substituted to produce same output level. Short Run (SR): capital is fixed in the short run. So can only  Q by  L. Decision-making: marginal benefit versus marginal cost.

Production Terminology Product: same as output Total product of labor = TP L As  L   Q, first by a lot, then less so, then Q will  Marginal product of labor: –MP L =  TP/  L =  Q/  L –additional output from adding one unit of L –See Table 6.2 and Figure 6.2 Average product of labor: – AP L = TP/L = Q/L –Output per unit of labor

To Note About Figure 6.2 Can derive (b) from (a). AP L at a specific amount of L: slope of line from origin to that specific point on TP L MP L for specific amount of L: slope of line tangent to TP L at that point. Note specific points in (a) and (b). MP L hits AP L: –1) at the max point on AP L –2) from above.

Law of Diminishing Returns Given existing technology, with K fixed, as keep adding one additional worker: at some point, the  to TP from the one unit  L will start to fall. I.e., MP L curve slopes upward for awhile, then slopes downward, eventually dropping below zero. Assumes each unit of L is identical (constant quality). Consider technological improvement: See Figure 6.3.

Long Run: Production w/Two Variable Inputs Can relate shape of isoquant to the Law of Diminishing Marginal Returns. Marginal Rate of Technical Substitution (MRTS): –(1) Shape of isoquant. –(2) Shows amount by which K can be reduced when one extra unit of L is added, so that Q remains constant. –(3) MRTS  as move down curve

More on Isoquant Isoquant curve: shows how production function permits trade-offs between K and L for fixed Q. MRTS = -  K/  L  fixed Q Isoquants are convex. Much of this comparable to indifference curve analysis. See Figure 6.7.

Derive Alternative Expression for MRTS As move down an isoquant, Q stays fixed but both K and L . As  L: additional Q from that extra L = MP L *  L As  K: reduction in Q from  K = MP K * -  K. These two sum to zero. MP L *  L + MP K * -  K = 0. MP L /MP K = -  K/  L = MRTS. MRTS = ratio of marginal products.

Exercise L Q MP L AP L

Two Special Cases of Production Functions MRTS is a constant (I.e., a straight line) – Perfect substitutes MRTS = 0: –Fixed proportion production function –Only “corner” points relevant. See Figures 6.8 and 6.9.

Returns to Scale (RTS) Long run concept: by how much does Q  when inputs  in proportion? Or: if double inputs, by how much does Q change? 1) Increasing RTS: if double inputs  more than double Q –Production advantage to large firm. 2) Constant RTS: if double inputs  double Q. 3) Decreasing RTS: if double inputs  less than double Q. See Figure 6.11.

Exercise Input Output L K Combo A B C D A) Calculate %  in each of K, L, and Q in moving from A  B, B  C, and C  D. B) Are there increasing, decreasing or constant returns to scale between A and B? B and C? C and D?