3 Production and Competition

• last lecture was consumer taking care of needs / consumer behavior
  • demand given
• this lecture is suppliers and how they take actions and decisions
  • supply (price) given / perfect competition analysis
• related to: Competition

3 Steps

• revenue expectations
  • demand
  • competition → lower prices
• cost constraints
  • technology → different combinations of inputs produce same output
  • efficiency → choosing least cost to produce same output
  • input cost → revenue must be higher than production cost → profit
• output choices
  • what to do with profits?

Production Technology

• production function
  • shows highest output possible (not efficiently)
  • maps the equilibrium prices of inputs and outputs
  • $Q=F(K,L)$ output = F( capital , labor )
    • Marginal Changes in Labor and Capital interesting

Short Term Production

• short term != short term → depends on business
• Production with one variable input
  • certain inputs cannot be adjusted fast e.g. expert machinery
  • Law of Diminishing Marginal Returns

Long Term Production

• all production inputs can be adjusted → multi-variable
• Production with two variable input
  • different combinations of capital and labor can yield same output → Substitution
  • Isoquant → all combinations of input which yield the same output
  • Marginal Rate of Technical Sustitution
    • MRTS → Diminishing Marginal Returns for each Isoquant
    • how much can capital substitute labor and vice versa
  • special case: inputs are perfect substitutes
    • Isoquants are linear → any combination of capital and labor feasible
  • special case: inputs cannot be substituted
    • Isoquants are L shaped → precise mapping of capital and labor

Returns to Scale

• scaling inputs and outputs equally → both 2x
• how much is the output going to change → 1x? 1.5x? 2x? 3x? 10x?
  • 2x → constant returns to scale
  • <2x → decreasing returns to scale

  • 2x → increasing returns to scale

• if returns to scale is
  • increasing then a monopoly is beneficial for society
  • decreasing then a split into many small companies is beneficial for society
• $F(L,K)=A\ast L^{\alpha }\ast K^{\beta }$
• scaling by factor $\lambda >1$ : $F(\lambda L,\lambda K)={\lambda }^{\alpha +\beta }\ast F(L,K)$
  • Cobb-Douglas production function

Production Costs

• cost function
  • cost minimization for given
  • linear (simple models) or convex ($x^2$)
• $C=w\ast L+r\ast K$
  • Cost = wages * labor + rent rate * capital
• economic cost != accounting cost
  • economic cost → cost of utilizing resources in production
  • Opportunity Cost very relevant
  • Past Sunk Cost irrelevant → not human-like behavior
• fixed costs vs variable costs
  • marginal costs → how much one more unit in output will cost
  • average costs → amount produced / total cost

Short Term

• capital and output level is fixed
  • calculating labor level which satisfies the desired output level
• no substitution whatsoever
• marginal cost vs marginal product of labor

Long Term

• capital can be adjusted too
  • capital / labor combination can be chosen at will
• Isocost → all combinations of capital and labor
  • constant function $-\frac{w}{r}$
• Isocost function and Isoquant function have to intersect
  • lowest cost until Isocost is tangent to Isoquant curve
  • $-\frac{w}{r}=MRTS=+\frac{M{P}_L}{M{P}_K}$
  • $\frac{M{P}_L}{w}=\frac{M{P}_K}{r}$
• change in Input Cost (wage $w$ or rent rate $r$)
  • tangent line changes slope and therefore intersection point
  • e.g. wages rise → hire less workers → substitute with more capital

Expansion

• short term → only labor can be increased (faster but higher Isocost)
• long term → scaling labor and capital equally (least Isocost → more efficient)
• for different quantities drawing different cost functions
  • envelope of functions are linear if returns to scale constant
• choosing output amount → calculating best cost function → calculating best capital / labor combination

Maximum Profit

• choosing optimal output amount
• Marginal Revenue = Marginal Costs
  • function is always concave
• what if maximum profit is negative?
  • shut the company down → 0$ profit > negative profit
  • long term: $p\ge AC(q)$ … price needs to be larger than average cost of quantity
  • short term: $p\ge AVC(q)$ … price needs to be larger than average variable cost of quantity

Market Supply

Short Term

• just summing up all individual supply functions