1st Stage: firm's profit maximization problem:
Choose: < output >
In order to maximize: < profits >
2nd Stage: firm's cost minimization problem:
Choose: < inputs >
In order to minimize: < cost >
Subject to: < producing the optimal output >
Firms’ products are perfect substitutes
Firms are “price-takers”, no one firm can affect the market price
Market entry and exit are free†
† Remember this — it turns out to be the most important feature that distinguishes different types of industries!
Recall that profit is: $$\pi=\underbrace{pq}_{revenues}-\underbrace{(wl+rk)}_{costs}$$
We’ll first take a closer look at costs today
Next class we’ll put costs together with revenues to find optimal \(q^*\) that maximizes \(\pi\) (the first stage problem)
This leads to the difference between:
A really difficult concept to think about!
Supply is actually Demand in disguise!
An (opportunity) cost to buy (scarce) inputs for production because other people demand those same inputs to consume or produce other valuable things!
Because resources are scarce, and have rivalrous uses, how do we know we are using resources efficiently??
In functioning markets, the market price measures the opportunity cost of using a resource for an alternative use
Firms not only pay for direct use of a resource, but also indirectly compensate society for “pulling the resource out” of alternate uses in the economy!
Examples:
Opportunity cost is a forward-looking concept
Choices made in the past with non-recoverable costs are called sunk costs
Sunk costs should not enter into future decisions
Many people have difficulty letting go of unchangeable past decisions: sunk cost fallacy
Licensing fees, long-term lease contracts
Specific capital (with no alternative use): uniforms, menus, signs
Research & Development spending
Advertising spending
“Accounting point of view”: are you taking in more cash than you are spending?
“Economic point of view”: is your product you making the best social use of your resources
Implications for society: are consumers best off with you using scarce resources (with alternative uses!) to produce your current product?
Remember: this is an economics course, not a business course!
Ludwig von Mises
1881—1973
“The direction of all economic affairs is in the market society a task of the entrepreneurs. Theirs is the control of production. They are at the helm and steer the ship. A superficial observer would believe that they are supreme. But they are not. They are bound to obey unconditionally the captain's orders. The captain is the consumer. Neither the entrepreneurs nor the farmers nor the capitalists determine what has to be produced. The consumers do that. If a businessman does not strictly obey the orders of the public as they are conveyed to him by the structure of market prices, he suffers losses, he goes bankrupt, and is thus removed from his eminent position at the helm. Other men who did better in satisfying the demand of the consumers replace him.”
“The consumers patronize those shops in which they can buy what they want at the cheapest price. Their buying and their abstention from buying decides who should own and run the plants and the land. They make poor people rich and rich people poor. They determine precisely what should be produced, in what quality, and in what quantities,” (p.270).
von Mises, Ludwig, 1949, Human Action
$$C(q)=f+VC(q)$$
$$C(q)=f+VC(q)$$
1. Fixed costs, \(f\) are costs that do not vary with output
$$C(q)=f+VC(q)$$
1. Fixed costs, \(f\) are costs that do not vary with output
2. Variable costs, \(VC(q)\) are costs that vary with output (notice the variable in them!)
† Assuming that (i) firms are always choosing input combinations that minimize total cost and (ii) input prices are constant. See more in today’s appendix.
Example: Airlines
Fixed costs: the aircraft, regulatory approval
Variable costs: providing one more flight
Example: Car Factory
Fixed costs: the factory, machines in the factory
Variable costs: producing one more car
Example: Starbucks
Fixed costs: the retail space, espresso machines
Variable costs: selling one more cup of coffee
Diff. between fixed vs. sunk costs?
Sunk costs are a type of fixed cost that are not avoidable or recoverable
Many fixed costs can be avoided or changed in the long run
Common fixed, but not sunk, costs:
When deciding to stay in business, fixed costs matter, sunk costs do not!
Example: Suppose your firm has the following total cost function:
$$C(q)=q^2+q+10$$
Write a function for the fixed costs, \(f\).
Write a function for the variable costs, \(VC(q)\).
\(q\) | \(f\) | \(VC(q)\) | \(C(q)\) |
---|---|---|---|
\(0\) | \(10\) | \(0\) | \(10\) |
\(1\) | \(10\) | \(2\) | \(12\) |
\(2\) | \(10\) | \(6\) | \(16\) |
\(3\) | \(10\) | \(12\) | \(22\) |
\(4\) | \(10\) | \(20\) | \(30\) |
\(5\) | \(10\) | \(30\) | \(40\) |
\(6\) | \(10\) | \(42\) | \(52\) |
\(7\) | \(10\) | \(56\) | \(66\) |
\(8\) | \(10\) | \(72\) | \(82\) |
\(9\) | \(10\) | \(90\) | \(100\) |
\(10\) | \(10\) | \(110\) | \(120\) |
$$AFC(q)=\frac{f}{q}$$
$$AFC(q)=\frac{f}{q}$$
$$AVC(q)=\frac{VC(q)}{q}$$
$$AFC(q)=\frac{f}{q}$$
$$AVC(q)=\frac{VC(q)}{q}$$
$$AC(q)=\frac{C(q)}{q}$$
$$MC(q) = \frac{\Delta C(q)}{\Delta q}$$
Calculus: first derivative of the cost function
Marginal cost is the primary cost that matters in making decisions
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
If marginal \(>\) average, then average \(\uparrow\)
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
If marginal \(>\) average, then average \(\uparrow\)
When marginal \(=\) average, average is maximized/minimized
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
If marginal \(>\) average, then average \(\uparrow\)
When marginal \(=\) average, average is maximized/minimized
Example: Suppose a firm’s cost structure can be described by: $$\begin{align*} C(q)&=15q^2+8q+45\\ MC(q)&=30q+8\\ \end{align*}$$
Write expressions for the firm’s fixed costs, variable costs, average fixed costs, average variable costs, and average (total) costs.
Find the minimum average (total) cost.
Find the minimum average variable cost.
Long run: firm can change all factors of production & vary scale of production
Long run average cost, LRAC(q): cost per unit of output when the firm can change both \(l\) and \(k\) to make more \(q\)
Long run marginal cost, LRMC(q): change in long run total cost as the firm produce an additional unit of \(q\) (by changing both \(l\) and/or \(k\))
Long run: firm can choose \(k\) (factories, locations, etc)
Separate short run average cost (SRAC) curves for each amount of \(k\) potentially chosen
Long run: firm can choose \(k\) (factories, locations, etc)
Separate short run average cost (SRAC) curves for each amount of \(k\) potentially chosen
Long run average cost (LRAC) curve “envelopes” the lowest (optimal) regions of all the SRAC curves!
“Subject to producing the optimal amount of output, choose l and k to minimize cost”
Further important properties about costs based on scale economies of production: change in average costs when output is increased (scaled)
Economies of scale: average costs fall with more output
Diseconomies of scale: average costs rise with more output
Constant economies of scale: average costs don’t change with more output
Note economies of scale \(\neq\) returns to scale!
Returns to Scale (last class): a technological relationship between inputs & output
Economies of Scale (this class): an economic relationship between output and average costs
Minimum Efficient Scale: \(q\) with the lowest \(AC(q)\)
Economies of Scale: \(\uparrow q\), \(\downarrow AC(q)\)
Minimum Efficient Scale: \(q\) with the lowest \(AC(q)\)
Economies of Scale: \(\uparrow q\), \(\downarrow AC(q)\)
Diseconomies of Scale: \(\uparrow q\), \(\uparrow AC(q)\)
Example: A firm's long run cost structure is as follows:
$$\begin{align*} LRC(q)&= 32000q-250q^2+q^3\\ LRMC(q)&=32000-500q+3q^2\\ \end{align*}$$
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1st Stage: firm's profit maximization problem:
Choose: < output >
In order to maximize: < profits >
2nd Stage: firm's cost minimization problem:
Choose: < inputs >
In order to minimize: < cost >
Subject to: < producing the optimal output >
Firms’ products are perfect substitutes
Firms are “price-takers”, no one firm can affect the market price
Market entry and exit are free†
† Remember this — it turns out to be the most important feature that distinguishes different types of industries!
Recall that profit is: $$\pi=\underbrace{pq}_{revenues}-\underbrace{(wl+rk)}_{costs}$$
We’ll first take a closer look at costs today
Next class we’ll put costs together with revenues to find optimal \(q^*\) that maximizes \(\pi\) (the first stage problem)
This leads to the difference between:
A really difficult concept to think about!
Supply is actually Demand in disguise!
An (opportunity) cost to buy (scarce) inputs for production because other people demand those same inputs to consume or produce other valuable things!
Because resources are scarce, and have rivalrous uses, how do we know we are using resources efficiently??
In functioning markets, the market price measures the opportunity cost of using a resource for an alternative use
Firms not only pay for direct use of a resource, but also indirectly compensate society for “pulling the resource out” of alternate uses in the economy!
Examples:
Opportunity cost is a forward-looking concept
Choices made in the past with non-recoverable costs are called sunk costs
Sunk costs should not enter into future decisions
Many people have difficulty letting go of unchangeable past decisions: sunk cost fallacy
Licensing fees, long-term lease contracts
Specific capital (with no alternative use): uniforms, menus, signs
Research & Development spending
Advertising spending
“Accounting point of view”: are you taking in more cash than you are spending?
“Economic point of view”: is your product you making the best social use of your resources
Implications for society: are consumers best off with you using scarce resources (with alternative uses!) to produce your current product?
Remember: this is an economics course, not a business course!
Ludwig von Mises
1881—1973
“The direction of all economic affairs is in the market society a task of the entrepreneurs. Theirs is the control of production. They are at the helm and steer the ship. A superficial observer would believe that they are supreme. But they are not. They are bound to obey unconditionally the captain's orders. The captain is the consumer. Neither the entrepreneurs nor the farmers nor the capitalists determine what has to be produced. The consumers do that. If a businessman does not strictly obey the orders of the public as they are conveyed to him by the structure of market prices, he suffers losses, he goes bankrupt, and is thus removed from his eminent position at the helm. Other men who did better in satisfying the demand of the consumers replace him.”
“The consumers patronize those shops in which they can buy what they want at the cheapest price. Their buying and their abstention from buying decides who should own and run the plants and the land. They make poor people rich and rich people poor. They determine precisely what should be produced, in what quality, and in what quantities,” (p.270).
von Mises, Ludwig, 1949, Human Action
$$C(q)=f+VC(q)$$
$$C(q)=f+VC(q)$$
1. Fixed costs, \(f\) are costs that do not vary with output
$$C(q)=f+VC(q)$$
1. Fixed costs, \(f\) are costs that do not vary with output
2. Variable costs, \(VC(q)\) are costs that vary with output (notice the variable in them!)
† Assuming that (i) firms are always choosing input combinations that minimize total cost and (ii) input prices are constant. See more in today’s appendix.
Example: Airlines
Fixed costs: the aircraft, regulatory approval
Variable costs: providing one more flight
Example: Car Factory
Fixed costs: the factory, machines in the factory
Variable costs: producing one more car
Example: Starbucks
Fixed costs: the retail space, espresso machines
Variable costs: selling one more cup of coffee
Diff. between fixed vs. sunk costs?
Sunk costs are a type of fixed cost that are not avoidable or recoverable
Many fixed costs can be avoided or changed in the long run
Common fixed, but not sunk, costs:
When deciding to stay in business, fixed costs matter, sunk costs do not!
Example: Suppose your firm has the following total cost function:
$$C(q)=q^2+q+10$$
Write a function for the fixed costs, \(f\).
Write a function for the variable costs, \(VC(q)\).
\(q\) | \(f\) | \(VC(q)\) | \(C(q)\) |
---|---|---|---|
\(0\) | \(10\) | \(0\) | \(10\) |
\(1\) | \(10\) | \(2\) | \(12\) |
\(2\) | \(10\) | \(6\) | \(16\) |
\(3\) | \(10\) | \(12\) | \(22\) |
\(4\) | \(10\) | \(20\) | \(30\) |
\(5\) | \(10\) | \(30\) | \(40\) |
\(6\) | \(10\) | \(42\) | \(52\) |
\(7\) | \(10\) | \(56\) | \(66\) |
\(8\) | \(10\) | \(72\) | \(82\) |
\(9\) | \(10\) | \(90\) | \(100\) |
\(10\) | \(10\) | \(110\) | \(120\) |
$$AFC(q)=\frac{f}{q}$$
$$AFC(q)=\frac{f}{q}$$
$$AVC(q)=\frac{VC(q)}{q}$$
$$AFC(q)=\frac{f}{q}$$
$$AVC(q)=\frac{VC(q)}{q}$$
$$AC(q)=\frac{C(q)}{q}$$
$$MC(q) = \frac{\Delta C(q)}{\Delta q}$$
Calculus: first derivative of the cost function
Marginal cost is the primary cost that matters in making decisions
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
If marginal \(>\) average, then average \(\uparrow\)
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
If marginal \(>\) average, then average \(\uparrow\)
When marginal \(=\) average, average is maximized/minimized
Mathematical relationship between a marginal & an average value
If marginal \(<\) average, then average \(\downarrow\)
If marginal \(>\) average, then average \(\uparrow\)
When marginal \(=\) average, average is maximized/minimized
Example: Suppose a firm’s cost structure can be described by: $$\begin{align*} C(q)&=15q^2+8q+45\\ MC(q)&=30q+8\\ \end{align*}$$
Write expressions for the firm’s fixed costs, variable costs, average fixed costs, average variable costs, and average (total) costs.
Find the minimum average (total) cost.
Find the minimum average variable cost.
Long run: firm can change all factors of production & vary scale of production
Long run average cost, LRAC(q): cost per unit of output when the firm can change both \(l\) and \(k\) to make more \(q\)
Long run marginal cost, LRMC(q): change in long run total cost as the firm produce an additional unit of \(q\) (by changing both \(l\) and/or \(k\))
Long run: firm can choose \(k\) (factories, locations, etc)
Separate short run average cost (SRAC) curves for each amount of \(k\) potentially chosen
Long run: firm can choose \(k\) (factories, locations, etc)
Separate short run average cost (SRAC) curves for each amount of \(k\) potentially chosen
Long run average cost (LRAC) curve “envelopes” the lowest (optimal) regions of all the SRAC curves!
“Subject to producing the optimal amount of output, choose l and k to minimize cost”
Further important properties about costs based on scale economies of production: change in average costs when output is increased (scaled)
Economies of scale: average costs fall with more output
Diseconomies of scale: average costs rise with more output
Constant economies of scale: average costs don’t change with more output
Note economies of scale \(\neq\) returns to scale!
Returns to Scale (last class): a technological relationship between inputs & output
Economies of Scale (this class): an economic relationship between output and average costs
Minimum Efficient Scale: \(q\) with the lowest \(AC(q)\)
Economies of Scale: \(\uparrow q\), \(\downarrow AC(q)\)
Minimum Efficient Scale: \(q\) with the lowest \(AC(q)\)
Economies of Scale: \(\uparrow q\), \(\downarrow AC(q)\)
Diseconomies of Scale: \(\uparrow q\), \(\uparrow AC(q)\)
Example: A firm's long run cost structure is as follows:
$$\begin{align*} LRC(q)&= 32000q-250q^2+q^3\\ LRMC(q)&=32000-500q+3q^2\\ \end{align*}$$