Theory of the Firm

• 1) How a firm makes cost-minimizing production decisions.

• 2) 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

• Short Run versus Long Run:– SR: one input is fixed.

– Typically: K is fixed in the short run so can only Q by L.

– LR: both inputs variable.

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 6.1 and Figure 6.1

• Average product of labor:– APL = TP/L = Q/L– Output per unit of labor

To Note About Figure 6.1

• 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.

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 6.2.

Labor Productivity and Standard of Living

• Labor productivity: – APL for an entire industry or for the economy

as a whole. – One linkage between micro and macro. – Determines real standard of living for a

country.

• Background: Aggregate value of all produced = payments all factors of production, including labor. Consumers receive these factor payments in form of wages, etc. – So, consumers in aggregate can rate of

consumption in LR only by total amount they produce.

– How increase? • By increasing stock of K• By technological improvements.

• International Trends (Table 6.3)

Long Run

• Long Run: both K and L variable• See Table 6.4: shows different

output levels associated with different amounts of K and L.

• Isoquant (‘iso’ means same): curve that shows all possible combinations of inputs that yields the same output (shows flexibility in production).

• Isoquant: shows how K and L can be substituted to produce same output level.– Shows input flexibility.– See Figure 6.4.

Continue with LR

• 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• Diminishing MRTS.

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 6.5.

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.

Exercise• L Q MPL APL

• 0 0 - -• -----------------------------------• 1 150 • -----------------------------------• 2 200• -------------------------------------• 3 200• --------------------------------------• 4 760• --------------------------------------• 5 150• --------------------------------------• 6 150• ---------------------------------------

Two Special Cases of Production Functions

• MRTS is a constant (I.e., isoquant is a straight line)– Perfect substitutes

• MRTS = 0:– Fixed proportion production

function– Only “corner” points relevant.

• See Figures 6.6 and 6.7.

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 6.9

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 AB, BC, and CD.

• B) Are there increasing, decreasing or constant returns to scale between A and B? B and C? C and D?