CDAE Class 19 Oct. 31 Last class: Result of the midterm exam 5. Production Today: 5. Production 6. Costs Quiz 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 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 technology A graphical analysis (1) The curve labeled by q 0 = 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 technology A graphical analysis (2) The curve labeled by q 0 * = 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 technology 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 technology Technical progress vs. input substitution (1) Input substitution (move along q 0 = 100) e.g., from Point B to Point E: L reduced from ( ) to ( ) K increased from ( ) to ( ) AP L increased from ( ) to ( ) AP K reduced from ( ) to ( )

5.7. Changes in technology Technical progress vs. input substitution (2) Technical progress (move from q 0 = 100 to q 0 * = 100) e.g., from Point B to Point D: L reduced from ( ) to ( ) K has no change AP L increased from ( ) to ( ) AP K has no change

5.8. An example Production function: where q = hamburgers per hour L = number of workers K = the number of grills 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 =

5.8. An example How to construct (graph) an isoquant? -- For example q = Simplify this function:

5.8. An example 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

5.8. An example 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

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 costs 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 costs 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 costs 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 costs 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: $3000Materials: $1100 Hired labor: $500 His labor: 50 hrs Accounting profit =Economic profit = Entrepreneurial cost =

6.1. Basic concepts of costs 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 costs 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 A graphical analysis (Fig. 6.1) What is the condition for the best point? 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 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 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