Chapter 6 Supply: Cost Side of Market

Recall: TP Curve - Total Product

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.

Marginal Product of Labor Curve

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

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.

Total Product, Marginal Product, and the Fixed Input

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: MP L = dQ / dL Average Product of labor: AP L =Q/L

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

K=1 LTP=QMPAP

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?

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

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

Q L 0 TP AP MP E AB Ⅰ Ⅱ Ⅲ F MP>AP AP  MP<AP AP  MP<0 TP  MP=AP AP Max MP=0 TP Max

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?

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)

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

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

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

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.

Fixed, Variable, and Total Costs Employees per day Bottles per day Fixed cost ($/day) Variable cost ($/day) Total cost ($/day) Marginal cost ($/bottle) Table 6.2, P.173

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.

Total Cost Curve for George and Martha’s Farm

Total Cost and Marginal Cost Curves for Ben’s Boots

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

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

Example: Total Costs and Average Costs

Total Costs and Marginal Cost

Q, TC, TVC, ATC, AVA, MC QTFCTVCTCATCAVCMC

QTFCTVCTCATCAVCMC Q, TC, TVC, ATC, AVA, MC

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

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.

Four curves together: Marginal Cost and Average Cost Curves

The Relationship Between the Average Total Cost and the Marginal Cost

Average Variable Cost and Average Total Cost Employees per day Bottles per day Variable cost ($/day) Average variable cost ($/unit of output) Total cost ($/day) Average total cost ($/unit of output) Marginal cost ($/bottle) Table 6.4, P.176

Upward-sloping MC corresponds to diminishing returns MC = AVC & ATC at their minimum points MC Cost ($/bottle) 0.05 Output (bottles/day) ATC AVC The Marginal, Average Variable, and Average Total Cost Curves

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.

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

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?

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

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.

Short-Run and Long-Run Average Total Cost Curves

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.

Relations Between SR 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