CDAE 254 - Class 20 Nov. 1

Last class: Problem set 5 6. Costs Quiz 5

Today: Result of Quiz 5 6. Costs

Next class: 7. Profit maximization and supply

Quiz 6 (Chapter 6)

Important date:Problem set 5: due today

Result of Quiz 5Result of Quiz 5

N = 55 Range = 3 – 10 Average = 7.8

6. Costs6. Costs

6.1. Basic concepts of costs

6.2. Cost minimizing input choice

6.3. Cost curves

6.4. Short-run and long-run costs

6.5. Per unit short-run cost curves

6.6. Shifts in cost curves

6.7. An example

6.8. Applications

6.3. Cost curves 6.3.1. Possible shapes of the total cost curve (function): relation between TC and q (Fig. 6.3)

(1) Constant returns to scale

(2) Decreasing returns to scale

(3) Increasing returns to scale

(4) Optimal scale: increasing returns to scale followed by decreasing returns to scale

A practice question:

If TC=50 for Q=20 and TC=90 for Q=40, what is the returns to scale of this production?

6.3. Cost curves 6.3.2. Average cost (AC) & marginal cost (MC)

(1) What is the AC and what is the MC?

AC = TC/q

MC = ΔTC/Δq

(2) AC & MC curves (functions) (Fig. 6.4) (a) Constant returns to scale

(b) Decreasing returns to scale

(c) Increasing returns to scale

(d) Optimal scale

A practice question:

If MC<AC, what is the returns to scale?

6.3. Cost curves 6.3.2. Average cost and marginal cost

(3) Optimal scale: Relationship between AC and MC

(4) Optimal scale: Lowest AC input choice

When MC < AC, AC is decreasing

When MC > AC, AC is increasing

When MC = AC, AC is at the minimum level.

6.4. Short run and long run costs 6.4.1. Very short run, short run & long run

Very short run: K and L are fixed Q is also fixed

Short run: K is fixed and L change Q can change

Long run: both K and L can change Q can change

6.4.2. Input flexibility in the short-run and long run (Fig. 6.5)

Short run: K is fixed and L can change

Long run: both K and L can change

6.4. Short run and long run costs6.4.3. Short-run total costs:

STC = vK* + wL = SFC + SVC

6.4.4. Short-run fixed, variable & total cost curves

Note that the concept “returns to scale” does not apply in the short run.

6.5. Per-unit short run cost curves 6.5.1. Short-run average cost: SAC = STC / q

6.5.2. Short-run marginal cost

SMC = ΔSTC/Δq

6.5.3. SAC and SMC curves

6.5.4. Long-run average cost & marginal cost

6.5.5. Relationship between short-run and long-run cost curves

6.5.6. An example: choosing an ink-jet printer or laser printer

Ink-jet: STC = 80 + 0.07 q

Laser: STC = 200 + 0.04 q

6.6. Shifts in cost curves

6.6.1. Change in input prices (w and v)

(1) w & v change in the same proportion

-- TC, AC and MC will change

-- Expansion path will not change

(2) w & v change in difference proportions

-- TC, AC and MC will change

-- Expansion path will change

6.6. Shifts in cost curves

6.6.2. Technology change

-- TC, AC and MC will change

-- Expansion path?

6.7. An example (continued from chapter 5) -- Production function

-- Total cost TC = vK + wL= 5K + 5L

-- Isoquant of q = 40

-- Total cost of producing 40 units of q

-- Cost-minimizing input choice for q=40

L* = 4 and K* = 4, TC = 40

-- Long-run expansion path & costs

-- Short-run total cost (STC), short-run average cost (SAC) and short-run marginal cost (SMC)

KLq 10

6.7. An example (continued from chapter 5) -- Comparison of short-run & long-run costs

6.8. Applications