CDAE 254 - Class 19 Oct. 31

Last class:Result of the midterm exam5. Production

Today:5. Production6. CostsQuiz 6 (Sections 5.1 – 5.7)

Next class: 6. Costs

Important date:Problem set 5 due Tuesday, Nov. 7

Problem set 5-- Due at the beginning of class on Thursday, Nov. 2

-- Please use graph paper to draw graphs

-- Please staple all pages together before you turn them in

-- Scores on problem sets that do not meet the above requirements will be discounted.

Problems 5.1., 5.2., 5.4., 5.6. and 5.8.

5. Productions

5.1. Production decisions 5.2. Production functions 5.3. Marginal physical productivity 5.4. Isoquant and isoquant map 5.5. Return to scale 5.6. Input substitution 5.7. Changes in technology

5.8. An example 5.9. Applications

5.7. Changes in technology5.7.1. A graphical analysis

(1) The curve labeled by q0 = 100

represents the isoquant of the old technology:

100 units of the output can be produced by different combinations of L and K.e.g., Point B: L= 20 and K= 20 Point E: L= 10 and K= 40 Point F: L= 30 and K= 14

5.7. Changes in technology5.7.1. A graphical analysis

(2) The curve labeled by q0* = 100

represents the isoquant of the new technology:

100 units of the output can be produced by different combinations of L and K.e.g., Point A: L= 15 and K= 14 Point C: L= 20 and K= 9

Point D: L= 10 and K= 20

5.7. Changes in technology5.7.1. A graphical analysis

(3) Comparison of the two technologies in producing 100 units of the output:

From B to A: From B to D: From B to C:From E to D:

From F to A:

5.7. Changes in technology5.7.2. Technical progress vs. input substitution

(1) Input substitution (move along q0 = 100)

e.g., from Point B to Point E:L reduced from ( ) to ( ) K increased from ( ) to ( )

APL increased from ( ) to ( )

APK reduced from ( ) to ( )

5.7. Changes in technology5.7.2. Technical progress vs. input substitution

(2) Technical progress (move from q0 = 100

to q0* = 100)

e.g., from Point B to Point D:L reduced from ( ) to ( ) K has no change

APL increased from ( ) to ( )

APK has no change

5.8. An example5.8.1. Production function:

where q = hamburgers per hour L = number of workers K = the number of grills

5.8.2. What is the returns to scale of this function? When L = 1 and K = 1, q = when L = 2 and K = 2, q = when L = 3 and K = 3, q =

LKq 10

5.8. An example5.8.4. How to construct (graph) an isoquant?

-- For example q = 40

-- Simplify this function:

4010 LKq

4010 LK

4LK

16LK

5.8. An example5.8.4. How to construct (graph) an isoquant?

-- Calculate K for each value of L (Table 5.3):

when L=1, K= ( ) when L=2, K= ( ) …… when L=10, K= ( )

-- Draw the isoquant of q=40

16LK LK 16

5.8. An example5.8.5. Technical progress -- A new production function: -- Construct the new isoquant of q=40

when L=1, K= ( ) when L=2, K= ( ) when L=3, K= ( ) …… -- Draw the new isoquant of q=40

LKq 20

LK2040 LK4

5.9. Applications

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

6.1. Basic concepts of costs6.1.1. Opportunity cost, accounting cost, and economic

cost: -- Opportunity cost: the cost of a good or

service as measured by the alternative uses of the resources that are foregone by producing the good or service.

e.g., one acre of land, 10 hours of labor and $20 of capital can be used to produce

800 lb. of hay OR 60 bu. of soybeans.What is the opportunity cost of producing 60 units of soybeans?

6.1. Basic concepts of costs6.1.1. Opportunity cost, accounting cost, and economic

cost:

-- Accounting cost: the cost of a good or service as measured by what was paid for it (i.e., out-of-pocket expenses, historical costs of machines and depreciation related to them, and other bookkeeping entries).

e.g., accounting cost of producing 60 bu. of soybeans:

6.1. Basic concepts of costs6.1.1. Opportunity cost, accounting cost, and economic

cost:

-- Economic cost: the payment required to keep a resource in its present use, or the amount that the resource would be

worth in its next best alternative use.e.g., Mr. Smith is making 60k a year

with IBM -- the next best offer in this region is also 60K.

6.1. Basic concepts of costs6.1.2. Labor costs, capital costs, and

entrepreneurial costs:

Labor costs = w L

Capital costs = v K

Entrepreneurial cost e.g., Phil has a flexible job with a wage rate of $10 per hour. He also

has his own roofing business and has just completed a project: Revenue: $3000 Materials: $1100

Hired labor: $500 His labor: 50 hrs Accounting profit = Economic profit = Entrepreneurial cost =

6.1. Basic concepts of costs6.1.3. Two simplifying assumptions:

(1) All the inputs are aggregated into labor and capital inputs (L and K)

(2) The inputs are hired in perfectly competitive markets

6.1. Basic concepts of costs6.1.4. Costs and profits Total economic costs = TC = wL + vK

Total revenues = TR = Pq = P f (L, K)

Total economic profits

= = TR – TC

= Pq – wL – vK

= P f(L, K) – wL – vK

where q = f (L, K) is the production function

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? 6.2.3. A firm’s expansion path.

Class exercise (Tuesday, Oct. 26) If the cost is TC = 4L + 5K and the rate of technical

substitution (RTS) is equal to 2, what will be the directions of change in L and K to minimize the cost?

6.3. Cost curves 6.3.1. Possible shapes of the total cost curve (1) Constant returns to scale (2) Decreasing returns to scale (3) Increasing returns to scale (4) Optimal scale

6.3. Cost curves 6.3.2. Average cost (AC) and marginal cost (MC) (1) What is the AC and what is the MC? (2) AC and MC curves (a) Constant returns to scale (b) Decreasing returns to scale (c) Increasing returns to scale (d) Optimal scale (3) Optimal scale: Relationship between AC and MC (4) Optimal scale: Lowest AC input choice