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Understanding Production Costs and Marginal Analysis

Learn about total product, marginal product, diminishing returns, short-run production, fixed and variable inputs, costs, and marginal cost analysis in microeconomics. Explore cost curves, average costs, and the relationship between production levels and total costs.

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Understanding Production Costs and Marginal Analysis

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  1. Chapter 6 Supply: Cost Side of Market

  2. Recall: TP Curve - Total Product

  3. Slope of TP curve: MP - Marginal Product • The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input.

  4. Marginal Product of Labor Curve

  5. Key Points of TP • TP first increases then max out and starts to decrease • TP increases at a slower pace • TP is maximized when MP=0 • MP is decreasing but positive when TP is increasing • MP is decreasing and negative when TP is decreasing • MP = 0 when TP is maximized

  6. Diminishing Returns to an Input (diminishing marginal product) • diminishing returns to an input: an increase in the quantity of an input leads to a decline in the marginal product of that input, holding the levels of all other inputs fixed • Other things held constant, as more of a variable input is used in production, its marginal productivity will decline after a certain point.

  7. Total Product, Marginal Product, and the Fixed Input

  8. Short-Run Production: some inputs are fixed • Total Product: Q = f (L, K, N, E) • Total Product of Labor: Q = f (L) (K, N, E fixed) • Marginal Product of Labor: MPL= dQ / dL • Average Product of labor: APL=Q/L

  9. Short-Run Production:Q, AP, MP, and shift in Q

  10. K=1

  11. Homework 3 • Use a table to show TP, MP, AP of labor when K=2 • Use tables to show TP, MP, AP of capital when L=1, L=2, respectively • Draw the TP curves of labor when K=1, K=2, respectively • Draw the TP curves of capital when L=1, L=2, respectively • Bonus: what can you conclude from the tables and graphs?

  12. Production: one input • TP = Q = f(L,K,N,E) • When K,N,E fixed: SR • TP(L) = f (L) • AP(L) = TP(L) / L • MP(L) = dTP(L) /dL • MP is the slope of TP • TP maximized when MP = 0

  13. Short-Run Production (one input) Summary • L=0 leads to Q=0 • when MP is increasing, Q is increasing at an increasing rate • when MP is decreasing, Q may still increase but at a decreasing rate • When MP=0, Q stop increasing and start decreasing (Q is maximized). • AP reaches its maximum when AP=MP

  14. Q MP>AP AP MP<AP AP MP<0 TP F MP=0 TP Max TP Ⅱ Ⅲ Ⅰ MP=AP AP Max E AP L 0 A B MP

  15. Questions to Consider • Why will MP decline before AP declines? • Why will AP decline before TP declines? • Why will MP intersect AP at AP’s maximum?

  16. From Production to Cost • Production: transferring inputs into outputs • Inputs: resources, production factors, - L, K, N, E • Variable inputs: • level of usage change with level of production • An input whose quantity can be altered in the short run • Fixed inputs: • level of usage does not change with level of production (in the Short-Run) • An input whose quantity cannot be altered in the short run • Long-run: all inputs are variable (no fixed inputs)

  17. Costs: expenses on inputs • The total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output. • TC=TFC + TVC

  18. SR Costs: TFC and TVC • TFC: • total amount paid for fixed inputs. • The sum of all payments made to a firm’s fixed inputs • not vary with output in the SR • TVC: • total amount paid to variable inputs • The sum of all payments made to the firms variable inputs • increases when output increases

  19. SR Costs: Marginal Cost • The cost of producing one additional unit of output • MC=dTC/dQ • In SR, dTC = dTVC, therefore SMC = dTVC/dQ

  20. Increasing Marginal Cost • Increasing Marginal Cost: as more of a product is produced, the additional cost of producing one more unit of output is increasing.

  21. Table 6.2, P.173 Employees per day Bottles per day Fixed cost ($/day) Variable cost ($/day) Total cost ($/day) Marginal cost ($/bottle) Fixed, Variable, and Total Costs 0 0 40 0 40 1 80 40 12 52 2 200 40 24 64 3 260 40 36 76 4 300 40 48 88 5 330 40 60 100 6 350 40 72 112 7 362 40 84 124 0.15 0.10 0.20 0.30 0.40 0.60 1.00

  22. Total Cost Curve • The total cost curve shows the relationship between production level (quantity of output produced) and the total cost of the production. • It becomes steeper as more output is produced due to diminishing returns to inputs, or due to increasing marginal cost.

  23. Total Cost Curve for George and Martha’s Farm

  24. Total Cost and Marginal Cost Curves for Ben’s Boots

  25. Average Cost • Average total cost, often referred to simply as average cost, is total cost divided by quantity of output produced. • Average fixed costis the fixed cost per unit of output (total fixed cost divided by quantity of output produced). • Average variable costis the variable cost per unit of output (total variable cost divided by quantity of output produced).

  26. SR Costs: Average Costs • Average Fixed Cost: AFC=TFC/Q • Average Variable Cost: AVC=TVC/Q • Average Total Cost: ATC=TC/Q=(TFC+TVC)/Q =TFC/Q+TVC/Q=AFC+AVC

  27. Example:Total Costs and Average Costs

  28. Total Costs and Marginal Cost

  29. Q, TC, TVC, ATC, AVA, MC

  30. Q, TC, TVC, ATC, AVA, MC

  31. Homework 4 • Based on the info given in the previous slide, draw the following curves: • ATC • AVC • AFC • MC • Describe the relationships between MC and ATC, AVC, respectively

  32. Average Total Cost Curve for Ben’s Boots The average total cost curve at Ben’s Boots is U-shaped. At low levels of output, average total cost falls because the “spreading effect” of falling average fixed cost dominates the “diminishing returns effect” of rising average variable cost. At higher levels of output, the opposite is true and average total cost rises.

  33. Four curves together: Marginal Cost and Average Cost Curves

  34. The Relationship Between the Average Total Cost and the Marginal Cost

  35. Table 6.4, P.176 Average Variable Cost and Average Total Cost Average total cost ($/unit of output) Average variable cost ($/unit of output) Variable cost ($/day) Total cost ($/day) Marginal cost ($/bottle) Employees per day Bottles per day 0 0 0 40 1 80 12 0.150 52 0.650 2 200 24 0.120 64 0.320 3 260 36 0.138 76 0.292 4 300 48 0.160 88 0.293 5 330 60 0.182 100 0.303 6 350 72 0.206 112 0.320 7 362 84 0.232 124 0.343 0.15 0.10 0.20 0.30 0.40 0.60 1.00

  36. Upward-sloping MC corresponds to diminishing returns MC ATC AVC 80 200 260 300 362 MC = AVC & ATC at their minimum points 330 350 The Marginal, Average Variable, and Average Total Cost Curves 0.65 0.60 0.55 0.50 0.45 0.40 Cost ($/bottle) 0.35 0.30 0.25 0.20 0.15 0.10 0.05 Output (bottles/day)

  37. More Realistic Cost Curves Marginal cost curves do not always slope upward. The benefits of specialization of labor can lead to increasing returns at first represented by a downward-sloping marginal cost curve. Once there are enough workers to permit specialization, however, diminishing returns set in.

  38. Short-Run Costs: Summary • at Q=0, VC=0, but FC>0 • when MC is declining, ATC and AVC both decline at an increasing rate • when MC starts increasing, ATC and AVC may both be decreasing but at a decreasing rate • MC intersects AVC and ATC at their minimum, respectively

  39. Questions to Consider • Why will MC increase before AVC increases? • Why will MC increase before ATC increases? • Why will AVC increase before ATC increases? • Why will MC intersect AVC and ATC at their minimum, respectively?

  40. Short-Run versus Long-Run Costs In the short-run: fixed cost is completely outside the control of a firm. In the long-run: all inputs are variable • Fixed cost in SR may also be varied in LR • In the long run a firm’s fixed cost becomes variable

  41. The Long-Run Average Total Cost Curve • The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost for each level of output.

  42. Short-Run and Long-Run Average Total Cost Curves

  43. Economies and Diseconomies of Scale • There are economies of scale when long-run average total cost declines as output increases. • There are diseconomies of scale when long-run average total cost increases as output increases. • There are constant returns to scale when long-run average total cost is constant as output increases.

  44. Relations BetweenSR Costs and SR Production • Q=f (L, K), and TC=TVC+TFC=wL + rK • AVC=TVC/Q=wL/AP*L=w/AP • SMC=dTVC/dQ=d(wL)/dQ =w(dL/dQ) =w/MP

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