Theory of the Firm

1. 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

2. 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

3. 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

4. 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.

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

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

7. 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., MPL 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.

8. 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

9. 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.

10. 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 = MPL * L • As K: reduction in Q from K = MPK * -K. • These two sum to zero. • MPL*L + MPK * -K = 0. • MPL/MPK = -K/L = MRTS. • MRTS = ratio of marginal products.

11. Exercise • L Q MPL APL • 0 0 - - • ----------------------------------- • 1 150 • ----------------------------------- • 2 200 • ------------------------------------- • 3 200 • -------------------------------------- • 4 760 • -------------------------------------- • 5 150 • -------------------------------------- • 6 150 • ---------------------------------------

12. 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.

13. 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.

14. Exercise • Input Output L K • Combo • A 100 20 40 • B 250 40 80 • C 600 90 180 • D 810 126 252 • 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?