1. CDAE 254 - Class 21 Nov 7 Last class: Result of Quiz 6 6. Costs Today: Problem set 5 questions 6. Costs Next class: 6. Costs 7. Profit maximization and supply Quiz 7 (Sections 6.1 – 6.6)

2. CDAE 254 - Class 21 Nov 7 Important dates: Problem set 5 due today Problem set 6 due Thursday, Nov. 16 (6.1., 6.4., 6.6., 6.9., and 6.10 from the textbook) Final exam: 3:30 – 6:30pm, Friday, Dec. 15

3. 6. 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

4. 6.2. Cost-minimizing input choice 6.2.1. A graphical analysis (Fig. 6.1) 6.2.2. What is the condition for the best point? Slope of the cost line = slope of the isoquant -w/v = -RTS w/v = RTS What will happen if the two are not equal? e.g., if w/v = 0.5 and RTS = 0.8, the producer will increase X and decrease Y to minimize cost. Note that this is similar to the analysis of utility maximization in Chapter 3.

5. Class exercise (Thursday, Nov. 2) If the cost is TC = 4L + 5K and the rate of technical substitution (RTS) is equal to 1.2, what will be the directions of change in L and K to minimize the cost? Why?

6. 6.2. Cost-minimizing input choice 6.2.3. A firm’s expansion path (Fig. 6.2) -- A curve of all the cost-minimizing inputs choices (points) for different levels of output -- It can be a curve or a straight line

7. 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

8. 6.3. Cost curves 6.3.2. Average cost (AC) and marginal cost (MC) (1) What is the AC and what is the MC? AC = TC/q MC = ΔTC/Δq (2) AC and MC curves (functions) (Fig. 6.4) (a) Constant returns to scale (b) Decreasing returns to scale (c) Increasing returns to scale (d) Optimal scale

9. 6.3. Cost curves 6.3.2. Average cost (AC) and marginal cost (MC) (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.

10. 6.4. Short run and long run costs 6.4.1. Distinction between short run and long run Very short run: Short run: Long run: 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 6.4.3. Short-run total costs: STC = vK* + wL = SFC + SVC

11. 6.4. Short run and long run costs 6.4.4. Short-run fixed, variable & total costcurves Note that the concept “returns to scale” does not apply in the short run.

12. 6.5. Per-unit short run cost curves 6.5.1. Short-run average cost SAC = STC / q 6.5.2. Short-run marginal costSMC = ΔSTC/Δq 6.5.3. SAC and SMC curves 6.5.4. Long-run average cost and 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