chapter the costs of production 13. what does a firm do? firm’s objective – firms seek to...
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Chapter
The Costs of Production
13
What Does a Firm Do?
• Firm’s Objective– Firms seek to maximize profits
• Profits = Total Revenues minus Total Costs• Choose output (Q*) such that
– Max {TR(Q*) –TC{Q*}
• Total revenue– Revenue received from sale of its output
• Total cost– Market value of the inputs a firm uses in
production2
2-3
• Total revenue = P*Q– Revenue received from sale of its output
– Market price for the good– Perfect Comp -> P-taker
– Firm’s output decision does not affect market/equilibrium price (too small)– Price received = market equilib
price; does not change with firm’s output
– What is then is the firm’s output level that maximizes profits?
2-4
• Total cost– Market value of the inputs a firm uses in
production– Cost = price(input 1)*Q(input 1) + … +
price(input n)* Q(input n)– C(Q) = Qi
2-5
K. Translog (Transcendental Logarithmic) Cost Function
2nd order (arbitrary) approximation to a cost function with 3 inputs (K,L<M)
The three factor Translog production function is: ln(q) = ln(A) + aL*ln(L) + aK*ln(K) + aM*ln(M) + bLL*ln(L)*ln(L) +
bKK*ln(K)*ln(K) + bMM*ln(M)*ln(M)+ bLK*ln(L)*ln(K) + bLM*ln(L)*ln(M) + bKM*ln(K)*ln(M) = f(L,K,M). (*) where L = labour, K = capital, M = materials and supplies, and q = product.
Which can be simplified to a linear cost function (when there are no interaction or higher order terms)
ln(q) = ln(A) + aL*ln(L) + aK*ln(K) + aM*ln(M) + = f(L,K,M).
Why Are Costs Important to a Firm?
• Primary economic objective of a firm– Maximize profits
• Total revenues depend on customer demand• Tot Rev(Q) = Price x Qty Demanded
– Price-taker (competitive world)» Initially assume: firm is a Price-taker (competitive world)» Competitors numerous and perfect substitutes» Demand for the firm’s product is perfectly elastic» Price can not be affected/chosen by 1 firm
• Costs {can controlled by p-taking firm}– Depend on amount supplied (Q*) by the firm– prices of and amounts used of inputs
6
2-7
• Choose Q* such that profits are maximized• Max {TR(Q*) –TC{Q*}
• First order condition δΠ/δQ = 0• P = δTC{Q}/δQ = 0 or price = marginal cost
• Choose Q* where market price is just equal to the increase in total costs (marginal/incremental/additional) costs of producing 1 more unit of output
2-8
PC Market: Profits Max’ed at Q* where P = MCIn long-run, no economic profit -> produce at Min ATC(Q*)
Price does not change
Marginal Costs
Profits Max’ed
• Atomicity – There is a large number of small producers and consumers on a given market,
• each so small that its actions have no significant impact on others. – Firms are price takers, meaning that the market sets the price that they must choose.
• Homogeneity – Goods and services are perfect substitutes; that is, there is no product differentiation. (All firms sell an
identical product) • Perfect and complete information
– All firms and consumers know the prices set by all firms• Equal access
– All firms have access to production technologies, and resources are perfectly mobile. • Free entry
– Any firm may enter or exit the market as it wishes (no barriers to entry). • Individual buyers and sellers act independently
– The market is such that there is no scope for groups of buyers and/or sellers to come together to change the market price (collusion and cartels are not possible under this market structure)
• Behavioral assumptions of perfect competition are that:– Consumers aim to maximize utility/well-being– Producers aim to maximize profits.
9
Basic Assumptions
What are Costs?
• Costs as opportunity costs– Explicit costs
• Input costs that require an outlay of money by the firm
• Reflect value of input used by other producers/markets – price willing to pay
– Implicit costs• Input costs that do not require an outlay of
money by the firm• Opportunity costs of time; alternative investment
10
What are Implicit Costs?
• The cost of capital as an opportunity cost– Implicit cost of investment in firm
• Interest income not earned– Invested in business
• Not shown as cost by an accountant– But is an opportunity cost to an economist; the
foregone investment/return– Key difference between economists/accountants and
treatment of what costs are and how they affect economic versus accounting profits
11
What are Implicit Costs?
• The cost of your labor as an opportunity cost– Implicit cost of your labor (owner)
• Wages not earned/paid by someone else– Do you pay yourself a wage if you own the business?
• If not, then not shown as cost by an accountant– But is an opportunity cost to an economist; the
foregone salary – Another example key difference between how costs
are recognized by economists/accountants
12
What are Costs?
• Economic profit– Total revenue minus total cost
• Including both explicit and implicit costs
• Accounting profit– Total revenue minus total explicit cost
13
Figure
Economists versus accountants
1
14
Economists include all opportunity costs when analyzing a firm, whereas accountants measure only explicit costs. Therefore, economic profit is smaller than accounting profit
Production and Costs
• Production function– Relationship between
• Quantity of inputs used to make a good• And the quantity of output of that good
– Gets flatter as production rises • Diminishing marginal returns to inputs (e.g., K, L)
• Marginal product– Increase (change) in output arising from an
additional unit of input (ΔQ/ΔL)
15
Table
A production function and total cost: Caroline’s cookie factory
1
16
Number of workers
Output(quantity of cookies produced per hour)
Marginal product of labor
Cost of factory
Cost of workers
Total cost of inputs(cost of factory + cost of workers)
0123456
05090
120140150155
$30303030303030
$0102030405060
$30405060708090
50403020105
Figure
TotalCost
50
40
30
20
10
80
70
60
$90
Quantityof Output(cookies
per hour)
100
80
60
40
20
160
140
120
Caroline’s production function and total-cost curve
2
17
(a) Production function
The production function in panel (a) shows the relationship between the number of workers hired and the quantity of output produced. Here the number of workers hired (on the horizontal axis) is from the first column in Table 1, and the quantity of output produced (on the vertical axis) is from the second column. The production function gets flatter as the number of workers increases, which reflects diminishing marginal product. The total-cost curve in panel (b) shows the relationship between the quantity of output produced and total cost of production. Here the quantity of output produced (on the horizontal axis) is from the second column in Table 1, and the total cost (on the vertical axis) is from the sixth column. The total-cost curve gets steeper as the quantity of output increases because of diminishing marginal product.
(b) Total-cost curve
Number of Workers Hired
0 1 2 3 4 5 6
Productionfunction Total-cost curve
Quantityof Output
(cookies per hour)
0 20 40 60 80 100 120 140 160
Figure
The Various Measures of Cost
• Fixed costs (short-run)– Do not vary with the quantity of output
produced• Variable costs (short and long-run)
– Vary with the quantity of output produced• Average fixed cost (AFC)
– Fixed cost divided by the quantity of output• Average variable cost (AVC)
– Variable cost divided by the quantity of output 19
Table
The various measures of cost: Conrad’s coffee shop
2
20
Quantityof coffee
(cups per hour)TotalCost
FixedCost
VariableCost
AverageFixedCost
AverageVariable
Cost
AverageTotalCost
MarginalCost
0123456789
10
$3.003.303.804.505.406.507.809.30
11.0012.9015.00
$3.003.003.003.003.003.003.003.003.003.003.00
$0.000.300.801.502.403.504.806.308.009.90
12.00
-$3.001.501.000.750.600.500.430.380.330.30
-$0.300.400.500.600.700.800.901.001.101.20
-$3.301.901.501.351.301.301.331.381.431.50
$0.300.500.700.901.101.301.501.701.902.10
Figure
Total Cost
5.004.003.002.001.00
8.007.006.00
9.0010.0011.0012.0013.0014.00
$15.00
Conrad’s total-cost curve
3
21
Here the quantity of output produced (on the horizontal axis) is from the first column in Table 2, and the total cost (on the vertical axis) is from the second column. As in Figure 2, the total-cost curve gets steeper as the quantity of output increases because of diminishing marginal product.
Quantity of Output(cups of coffee per hour)
0 1 2 3 4 5 6 7 8 9 10
Total-cost curve
The Various Measures of Cost
• Average total cost (ATC)– Total cost divided by the quantity of output– Average total cost = Total cost / Quantity ATC = TC / Q
• Marginal cost (MC)– Increase in total cost
• Arising from an extra unit of production– Marginal cost = Change in total cost / Change
in quantity MC = ΔTC / ΔQ
22
The Various Measures of Cost
• Average total cost = Total Costs(Q) ÷Q– Cost of a typical unit of output
• Average Fixed Costs = Total Fixed Costs ÷ Q• Average Variable Costs = Total Var Costs ÷ Q• Marginal cost = ΔTC(Q+1 – Q)/ΔQ
– Increase in total cost from producing an additional unit of output
23
EXHIBIT 5.1Daily Costs of Manufacturing Pine Lumber
5-24
EXHIBIT 5.2The Marginal Cost of Manufacturing Pine
Lumber
5-25
EXHIBIT 5.1Daily Costs of Manufacturing Pine Lumber
5-26
EXHIBIT 5.3The Cost Curves
5-27
The Various Measures of Cost
• Cost curves and their shapes• U-shaped average total cost: ATC = AVC + AFC
– AFC – always declines as output rises– AVC – typically rises as output increases
• Diminishing marginal product
• At the minimum of ATC or AVC– The bottom (lowest point) of the U-shaped
curve– MC = min(ATC) and MC = min(AVC)
28
The Various Measures of Cost
• Cost curves and their shapes• Efficient scale
– Quantity of output that minimizes average total cost
• Relationship between MC and ATC – When MC < ATC: average total cost is falling– When MC > ATC: average total cost is rising– The marginal-cost curve crosses the average-
total-cost curve at its minimum
29
Figure
Cost curves for a typical firm
5
30
Costs
1.00
0.50
2.00
1.50
2.50
$3.00
Many firms experience increasing marginal product before diminishing marginal product. As a result, they have cost curves shaped like those in this figure. Notice that marginal cost and average variable cost fall for a while before starting to rise.
Quantity of Output
0 2 4 6 8 10 12 14
MC
ATC
AVC
AFC
Figure
FIGURE 9.2 Short-Run Supply Curve of a Perfectly Competitive Firm
At prices below average variable cost, it pays a firm to shut down rather than continue operating.Thus, the short-run supply curve of a competitive firm is the part of its marginal cost curve that lies above its average variable cost curve.
Costs in Short Run and in Long Run
• Many decisions– Some inputs are fixed (unalterable)in the
short run– All inputs are variable in the long run,
• Firms – greater flexibility in the long-run– Long-run cost curves
• Differ from short-run cost curves• Much flatter than short-run cost curves
– Short-run cost curves• Lie on or above the long-run cost curves
32
Figure
Average total cost in the short and long runs
6
33
AverageTotalCost
Because fixed costs are variable in the long run, the average-total-cost curve in the short run differs from the average-total-cost curve in the long run.
Quantity of Cars per Day0
ATC in shortrun with
small factory
ATC in shortrun with
medium factory
ATC in shortrun with
large factory
ATC in long run
10,000
$12,000
1,000 1,200
Economiesof scale
Diseconomiesof scaleConstant returns to scale
Figure
Costs in Short Run and in Long Run
• Economies of scale– Long-run average total cost falls as the
quantity of output increases– Increasing specialization
• Constant returns to scale– Long-run average total cost stays the same as
the quantity of output changes
35
Costs in Short Run and in Long Run
• Diseconomies of scale– Long-run average total cost rises as the
quantity of output increases– Increasing coordination problems
36
Table
The many types of cost: A summary
3
37
Term Definition MathematicalDescription
Explicit costs
Implicit costs
Fixed costs
Variable costs
Total cost
Average fixed cost
Average variable cost
Average total cost
Marginal cost
Costs that require an outlay of money by the firm
Costs that do not require an outlay of money by the firm
Costs that do not vary with the quantity of output produced
Costs that vary with the quantity of output produced
The market value of all the inputs that a firm uses in production
Fixed cost divided by the quantity of output
Variable cost divided by the quantity of output
Total cost divided by the quantity of output
The increase in total cost that arises from an extra unit of production
FC
VC
TC = FC + VC
AFC = FC / Q
AVC = VC / Q
ATC = TC / Q
MC = ΔTC / ΔQ
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