CORE Econ Micro

class: center, middle, inverse, title-slide

.title[
# CORE Econ Micro
]
.subtitle[
## <div class="line-block">The firm and its customers</div>
]
.author[
### Guillermo Woo-Mora
]
.date[
### <div class="line-block">Paris Sciences et Lettres<br />
Autumn 2025</div>
]

---

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.center2[
# Intro
]

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.center[
<img src="imgs/lidl.jpeg" width="80%" style="display: block; margin: auto;" />
]

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.center[
<img src="https://rtlimages.apple.com/cmc/dieter/store/16_9/R470.png?resize=2880:1612&output-format=jpg&output-quality=85&interpolation=progressive-bicubic" width="85%" style="display: block; margin: auto;" />
]

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.center[
<img src="https://i.ytimg.com/vi/ceGZQZ8dW80/maxresdefault.jpg
" width="85%" style="display: block; margin: auto;" />
]

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.center[
<img src="imgs/figure7-1.png" width="60%" style="display: block; margin: auto;" />
]

---
.center2[
# Choosing a price
]

---
## Revenue, costs, and profit

How does a firm decide what price to charge for its product?

**total costs**: The sum of all the costs a firm incurs to produce its total output.

$$
\text{total costs} = \text{unit cost} \times \text{quantity} = C \times Q
$$

**total revenue**: the number of units sold times the price per unit.

$$
\text{total revenue} = \text{price} \times \text{quantity} = P \times Q
$$

**profit**: the difference between the revenue received from selling a product, and the costs of producing it

$$
\text{profit} = \text{total revenue} - \text{total costs} = (P \times Q) - (C \times Q) = (P-C) \times Q
$$

---
## Revenue, costs, and profit

A firm produces and sells a brand of breakfast cereal. Suppose that the unit cost is 2. `$\rightarrow \text{profit} = (P-2) \cdot Q$`

If `$P=2$`, each pound of cereal is sold for exactly what it cost to make. There would be no profit, whatever `$Q$`

---
## Revenue, costs, and profit

A firm produces and sells a brand of breakfast cereal. Suppose that the unit cost is 2. `$\rightarrow \text{profit} = (P-2) \cdot Q$`

The curve shows all the possible ways of making $10,000 profit.

---
## Revenue, costs, and profit

A firm produces and sells a brand of breakfast cereal. Suppose that the unit cost is 2. `$\rightarrow \text{profit} = (P-2) \cdot Q$`

The new curve shows all the combinations of P and Q that give $60,000 profit.

---
## Revenue, costs, and profit

A firm produces and sells a brand of breakfast cereal. Suppose that the unit cost is 2. `$\rightarrow \text{profit} = (P-2) \cdot Q$`

**isoprofit curve**: curve joinin the combinations of prices and quantities of a good that provide equal profits.

---
## Revenue, costs, and profit

A firm produces and sells a brand of breakfast cereal. Suppose that the unit cost is 2. `$\rightarrow \text{profit} = (P-2) \cdot Q$`

Three-dimensional images show how profit varies with Q and P, with each grid point representing a (Q, P) pair and the height of the surface showing the corresponding profit.

---
## Demand

The firm wants both price and quantity to be high, but setting the price too high drives customers away.

It needs information about how much consumers are willing to pay.

**demand curve**: number of units of a good that buyers would wish to buy at any given price

---
## Maximizing profit

How to choose the price? How many pounds of cereal one shold you produce?

Find a combination of P and Q on the highest possible isoprofit curve in the feasible set.

---
## Maximizing profit

How to choose the price? How many pounds of cereal one shold you produce?

Any point below the demand curve is feasible, but raising the price to the curve increases profit.

---
## Maximizing profit

How to choose the price? How many pounds of cereal one shold you produce?

Maximized profit at point E: the demand curve is tangent to the highest isoprofit curve, giving P = $4.23 and Q = 15,000 pounds.

---
## Maximizing profit

The profit maximization problem is also a **constrained choice problem**⁠

---

.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity. 
]

---

.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

- For instance: calculate profit at each point on the demand curve. Plotted in the lower panel.
]

.pull-right[
<img src="imgs/figure7-4b-a.png" width="100%" style="display: block; margin: auto;" />
]

---

.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

- For instance: calculate profit at each point on the demand curve. Plotted in the lower panel.

- When Q = 2,160, P = $6.63. Profit is $2,160 × 4.63 = $10,000. Since the quantity is low, so is the profit.
]

.pull-right[
<img src="imgs/figure7-4b-b.png" width="100%" style="display: block; margin: auto;" />
]

---

.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

- For instance: calculate profit at each point on the demand curve. Plotted in the lower panel.

- As quantity increases, profit rises until...
]

.pull-right[
<img src="imgs/figure7-4b-c.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

- For instance: calculate profit at each point on the demand curve. Plotted in the lower panel.

- As quantity increases, profit rises until **profit reaches a maximum of $33,450 at E, where Q = 15,000 and P = 4.23.**

]

.pull-right[
<img src="imgs/figure7-4b-d.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

- For instance: calculate profit at each point on the demand curve. Plotted in the lower panel.

- Beyond E, the profit falls. More cereal is sold, but there is less profit on each unit. Profit is zero when the price is equal to the unit cost, $2.

]

.pull-right[
<img src="imgs/figure7-4b-e.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

- For instance: calculate profit at each point on the demand curve. Plotted in the lower panel.

- To sell a very high quantity, the price has to be lower than the unit cost, so profit is negative.

]

.pull-right[
<img src="imgs/figure7-4b-f.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

- For instance: calculate profit at each point on the demand curve. Plotted in the lower panel.

- The lower panel shows that profit is maximized at E. As indicated on the isoprofit curves, this is the tangency point we found before.

]

.pull-right[
<img src="imgs/figure7-4b-g.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Maximizing profit

Firm managers likely don’t think about the decision this way; the price is probably set through trial and error, guided by experience and market research.

But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity.

`$\rightarrow$` **The purpose of our economic analysis is not to model the manager’s thought process, but to understand the outcome, and how it depends on the firm’s cost and consumer demand.**

]

.pull-right[
<img src="imgs/figure7-4b-g.png" width="100%" style="display: block; margin: auto;" />
]

---
.center2[
# Economies of scale and the cost advantages of large-scale production
]

---
## Economies of scale in production

A firm’s costs depend on its production scale and technology, and larger firms may be more profitable due to technological or cost advantages.

Production function (technology): `$Y = f(X) = X^{\alpha}$`.
--
 Inputs increase in a given proportion: `$\lambda > 0$`

$$ \Rightarrow f(\lambda X) = (\lambda X)^{\alpha} = \lambda^{\alpha} X^{\alpha} = \lambda^{\alpha} f(X) $$

| Production | Technology | Homogeneity |
| -----------------------------------------|
| Increases more than proportionally | **Increasing returns to scale** | `$f(\lambda X) > \lambda f(X) \quad \forall \alpha > 1$` |
| Increases proportionally | **Constant returns to scale** | `$f(\lambda X) = \lambda f(X) \quad \alpha = 1$` |
| Increases less than proportionally | **Decreasing returns to scale** | `$f(\lambda X) < \lambda f(X) \quad \forall \alpha < 1$` |

.pull-left[
**Economies of Scale: Examples**

- **Cost advantages**: Large firms can purchase inputs on more favourable terms.
- **Demand advantages**: Network effects (value of output rises with number of users e.g. software application)
]

.pull-right[
**Diseconomies of Scale: Examples**

- Additional layers of bureaucracy due to too many employees.
]

---
.center2[
# Production and costs
]

---
## Production and costs

Costs per unit of output may vary with the level of production. How does this affect the firm’s price and quantity decision?

**cost function**: The relationship between a firm’s total costs and its quantity of output. The cost function `$C(Q)$` tells you the total cost of producing `$Q$` units of output (including the opportunity cost of capital).

---
## Production and costs

Beautiful Cars: small firm producinga differentiated product (specialty cars).

`$$C(Q) = F + cQ$$`

- `$F$`: fixed costs
- `$c$`: the cost per car

---
.pull-left[
## Production and costs

Suppose:
- `$F = 80,000$` per day
- `$c = 14,400$` per car

The top panel shows the cost function, `$C(Q)$`. It shows the total cost for each level of output, `$Q$`.
]

.pull-right[
<img src="imgs/figure7-7a.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Production and costs

Suppose:
- `$F = 80,000$` per day
- `$c = 14,400$` per car

The top panel shows the cost function, `$C(Q)$`. It shows the total cost for each level of output, `$Q$`.

- The firm incurs in `$F$` irrespective of output. When `$Q = 0$`, the only costs are the fixed costs: `$C(0) = 80,000.$`
]

.pull-right[
<img src="imgs/figure7-7b.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Production and costs

Suppose:
- `$F = 80,000$` per day
- `$c = 14,400$` per car

The top panel shows the cost function, `$C(Q)$`. It shows the total cost for each level of output, `$Q$`.

- As `$Q$` increases, the firm needs to employ more production workers and purchase more raw materials

- At point A, 10 cars are produced at a cost of 224,000.
]

.pull-right[
<img src="imgs/figure7-7c.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Production and costs

Suppose:
- `$F = 80,000$` per day
- `$c = 14,400$` per car

The top panel shows the cost function, `$C(Q)$`. It shows the total cost for each level of output, `$Q$`.

- The **average cost** of a car is the total cost divided by the number of cars:

`$$AC = \frac{C(Q)}{Q} = \frac{F + cQ}{Q} = c + \frac{F}{Q}$$`

- As output rises above A, AC falls.

- At point B, the total cost is 512,000, and AC is 17,067.

- At point D, AC is lower still: 16,000.
]

.pull-right[
<img src="imgs/figure7-7d.png" width="100%" style="display: block; margin: auto;" />
]

---
.pull-left[
## Production and costs

Suppose:
- `$F = 80,000$` per day
- `$c = 14,400$` per car

The top panel shows the cost function, `$C(Q)$`. It shows the total cost for each level of output, `$Q$`.

- The **average cost** of a car is the total cost divided by the number of cars:

`$$AC = \frac{C(Q)}{Q} = \frac{F + cQ}{Q} = c + \frac{F}{Q}$$`

- We can calculate the AC at every value of `$Q$` to draw the **average cost function** in the lower panel.

]

.pull-right[
<img src="imgs/figure7-7e.png" width="100%" style="display: block; margin: auto;" />
]

---
## Production and costs

**marginal cost** (MC): the additional cost of producing one more unit of output, which corresponds to the slope of the cost function.

`$$MC = \frac{\Delta C}{\Delta Q}$$`

---
.center2[
# Demand, elasticity, and revenue
]

---
### Demand

**willingness to pay (WTP)**: An indicator of how much a person values a good, measured by the maximum amount they would pay to acquire a unit of the good.

A consumer buys a car if the price is less than or equal to her WTP; the demand curve shows how many consumers (the quantity) are willing to buy at each possible price.

The demand curve shows the trade-off between price and quantity: firms want both high prices and high sales, but raising the price reduces demand.

---
## The elasticity of demand

How much demand falls when price rises depends on the slope of the demand curve. A steep curve means demand doesn’t drop much when price increases.

**price elasticity of demand**⁠ is a measure of the responsiveness of consumers to a price change

$$
\varepsilon = - \frac{\% \text{ change in Q}}{\% \text{ change in P}}
$$

---
## The elasticity of demand

How much demand falls when price rises depends on the slope of the demand curve. A steep curve means demand doesn’t drop much when price increases.

**price elasticity of demand**⁠ is a measure of the responsiveness of consumers to a price change

Price changes by `$\Delta P$`, change demand by `$\Delta Q$`.

$$
\varepsilon = - \frac{\% \text{ change in Q}}{\% \text{ change in P}} \iff \varepsilon = - \frac{100 \Delta Q}{Q} / \frac{100 \Delta P}{P}
$$

$$
\varepsilon = - \frac{\text{proportional change in Q}}{\text{proportional change in P}} \iff
\varepsilon = - \frac{\Delta Q}{Q} / \frac{\Delta P}{P}
$$

$$
\iff
\varepsilon = - \frac{P}{Q} \cdot \frac{\Delta Q}{\Delta P}
$$
--

Since `$\frac{\Delta P}{\Delta Q}$` is the demand curve's slope:

`$$\iff \varepsilon = - \frac{P}{Q} \cdot \frac{1}{D_{slope}}$$`

---

---

|        | Point K | Point L | 
|--------|---------|---------|---------------|
| `$Q$`  | 18      | 19      |
| `$P$`  | 32,800  | 32,400  |

---

|        | Point K | Point L | change        |
|--------|---------|---------|---------------|
| `$Q$`  | 18      | 19      | `$\Delta Q = 1$` |
| `$P$`  | 32,800  | 32,400  | `$\Delta P = -400$`    |

---

|        | Point K | Point L | change        | % change                                   |
|--------|---------|---------|---------------|---------------------------------------------|
| `$Q$`  | 18      | 19      | `$\Delta Q = 1$`        | `$\frac{100 \times \Delta Q}{18} = 5.56\%$` |
| `$P$`  | 32,800  | 32,400  | `$\Delta P = -400$`    | `$\frac{100 \times \Delta P}{32{,}800} = -1.22\%$` |

---

.pull-left[
|        | Point K | Point L | change        | % change                                   |
|--------|---------|---------|---------------|---------------------------------------------|
| `$Q$`  | 18      | 19      | `$\Delta Q = 1$`        | `$\frac{100 \times \Delta Q}{18} = 5.56\%$` |
| `$P$`  | 32,800  | 32,400  | `$\Delta P = -400$`    | `$\frac{100 \times \Delta P}{32{,}800} = -1.22\%$` |
]

.pull-right[
.center[
`$$\varepsilon = - \frac{100 \Delta Q}{Q} / \frac{100 \Delta P}{P} \; \Rightarrow \varepsilon  = - \frac{5.56}{-1.22} = 4.56$$`
]
]

---

.pull-left[
.center[
`$$\varepsilon = - \frac{P}{Q} \cdot \frac{1}{D_{slope}}$$`
]
]

.pull-right[
|              | A     | B     | C     |
|--------------|-------|-------|-------|
| `$Q$`        | 20    | 40    | 70    |
| `$P$`          | 32,000 | 24,000 | 12,000 |
| slope of demand    | -400  | -400  | -400  
| `$\varepsilon$` |  |  |  |
]

---

.pull-left[
.center[
`$$\varepsilon = - \frac{P}{Q} \cdot \frac{1}{D_{slope}}$$`
]
]

.pull-right[
|              | A     | B     | C     |
|--------------|-------|-------|-------|
| `$Q$`        | 20    | 40    | 70    |
| `$P$`          | 32,000 | 24,000 | 12,000 |
| slope of demand    | -400  | -400  | -400  |
| `$\varepsilon$` | 4.00 | 1.50 | 0.43 |
]

---

.pull-left[

- **Elastic demand** if `$\varepsilon > 1$`

- **Unitary elastic demand** if `$\varepsilon = 1$`

- **Inelastic demand** if `$\varepsilon < 1$`

]

---

.pull-left[

- **Elastic demand** if `$\varepsilon > 1$`

- **Unitary elastic demand** if `$\varepsilon = 1$`

- **Inelastic demand** if `$\varepsilon < 1$`

**Note how within a same demand curve we have the three types of elasticity**

]

---
## The elasticity of demand

- **Inverse demand function**: `$P=f(Q)$`
--

- **Direct demand function**: `$Q=g(P)$`

`$g$` is the inverse function of `$f$`: `$g(P)=f^{-1}(P)$`
 
--
Remember:

`$$\varepsilon = - \frac{P}{Q} \cdot \frac{dQ}{dP}$$`

Note: `$\frac{dP}{dQ}= 1 / \frac{dQ}{dP} \iff \frac{dQ}{dP} = 1 / \frac{dP}{dQ}$`

`$$\Rightarrow \; \varepsilon = - \frac{P}{Q} / \frac{dP}{dQ} = \frac{f(Q)}{Q} \cdot \frac{1}{f'(Q)}$$`

You can calculate the elasticity for every demand function. [Try the two examples in the book](https://books.core-econ.org/the-economy/microeconomics/07-firm-and-customers-05-demand-elasticity-revenue.html#two-ways-of-writing-the-elasticity)

---
## Elasticity and revenue

The firm’s price elasticity of demand will depend on how much competition it faces from other firms.

In panel A, limited competition makes demand steep and inelastic at point E (elasticity = 0.4).

In panel B, greater competition makes demand flatter and elastic at E (elasticity = 2).

---
## Elasticity and revenue

The firm’s price elasticity of demand will depend on how much competition it faces from other firms.

If the firm operates at point E, where `$P = 20$` and `$Q = 5$`, its revenue is equal to the area of the rectangle under the curve: `$revenue = P × Q = 100$`, in both cases.

---
## Elasticity and revenue

The firm’s price elasticity of demand will depend on how much competition it faces from other firms.

If output increases to `$Q = 6$`, the firm gains revenue on the extra unit in both cases.

---
## Elasticity and revenue

The firm’s price elasticity of demand will depend on how much competition it faces from other firms.

But lowering the price reduces revenue on the original five units. With inelastic demand (Panel A), raising output by one unit requires a bigger price cut than with elastic demand (Panel B).

---
## Elasticity and revenue

The firm’s price elasticity of demand will depend on how much competition it faces from other firms.

If demand is inelastic, the loss outweighs the gain: revenue falls. If demand is elastic, the gain is bigger than the loss and revenue rises.

---
## Elasticity and revenue

The change in revenue when output is increased by one unit is called the **marginal revenue⁠** (MR).

- `$\varepsilon > 1 \Rightarrow MR > 0$`: the firm can increase revenue by raising output because prices fall only a little.

- `$\varepsilon < 1 \Rightarrow MR < 0$`: the firm can increase revenue by decreasing output because prices rise a lot.

---
## Elasticity and revenue

The change in revenue when output is increased by one unit is called the **marginal revenue⁠** (MR).

- A firm’s revenue is given by price `$\times$` quantity (`$R=PQ$`)
- The inverse demand function, `$P=f(Q)$`, tells us the maximum price, `$P$`, at which `$Q$` cars can be sold

`$$\Rightarrow R=f(Q) \cdot Q$$`

`$$\Rightarrow MR= \frac{dR}{dQ} = f(Q) + f'(Q)  \cdot Q$$`
--

Recall

$$\varepsilon = - \frac{f(Q)}{Q} \cdot \frac{1}{f'(Q)} \iff Q \cdot f'(Q) = - \frac{f(Q)}{\varepsilon} $$

`$$\Rightarrow MR= f(Q) - \frac{f(Q)}{\varepsilon} = f(Q) (1 - \frac{1}{\varepsilon})= P (1 - \frac{1}{\varepsilon})$$`

- `$\varepsilon > 1 \Rightarrow MR > 0$`: the firm can increase revenue by raising output because prices fall only a little.

- `$\varepsilon < 1 \Rightarrow MR < 0$`: the firm can increase revenue by decreasing output because prices rise a lot.

---
.center2[
# Setting price and quantity to maximize profit
]

---
## Setting price and quantity to maximize profit

A firm chooses its price `$P$` and quantity `$Q$` based on its demand curve and production costs.

The demand curve defines the feasible combinations of `$P$` and `$Q$`.

To find the profit-maximizing point, we draw the isoprofit curves and locate the tangency point.

$$
\Pi(P,Q) = P \cdot Q - C(Q)
$$

`$$\Pi(P,Q) = Q (P - \frac{C(Q)}{Q}) = Q (P - AC)$$`

**Example**

`$C(Q)= F + cQ$`, with `$c = 14,400$` and `$F = 80,000$`

`$$\Rightarrow \frac{C(Q)}{Q} = \frac{F}{Q} + c$$`

`$$\Rightarrow  \Pi(P,Q) = Q (P - \frac{F}{Q} - c) = Q (P - c) - F = Q(P-14,400) - 80,000$$`

---

`$$\Pi(P,Q) = Q(P-14,400) - 80,000$$` 
--

If the price is equal to the marginal cost of a car and the firm makes a loss equal to its fixed cost.

---

`$$\Pi(P,Q) = Q(P-14,400) - 80,000$$`

If `$P = AC$`, the firm’s economic profit is zero. So the AC curve is also the zero-profit curve: it shows all the combinations of P and Q that give zero economic profit.

---
### How we derive the isoprofit curves?

For a general profit function: `$\Pi(P,Q) =  P \cdot Q - C(Q)$`

If we set a given level of profit `$\Pi_0 \Rightarrow \quad \Pi_0 =  P \cdot Q - C(Q)$`

We can rearrange P such that

`$$P = \frac{\Pi_0 + C(Q)}{Q}$$`

`$$\Pi_0 = 0 \Rightarrow \quad P = \frac{0 + C(Q)}{Q} = \frac{C(Q)}{Q} = AC$$` 
--

**Slope of an isoprofit curve** at any point:

$$
\frac{dP}{dQ}
= -\,\frac{Q C'(Q) - \big(C(Q) + \Pi_0\big)}{Q^2}
$$

And since `$C(Q) + \Pi_0 = PQ$`, we have:

$$
\frac{dP}{dQ}
= \frac{C'(Q) - P}{Q}
= \frac{\text{MC} - P}{Q}
$$

---

`$$\Pi(P,Q) = Q(P-14,400) - 80,000$$`

The Isoprofit 3 downward-sloping curve shows the combinations of P and Q giving higher levels of profit. Profit is $150,000 at points G and H.

---

`$$\Pi(P,Q) = Q(P-14,400) - 80,000$$`

Profit `$= Q(P − AC)$`: At point G, producing 11 cars yields a price of 35,309 and an average cost of 21,673, giving 13,636 profit per car and total profit of 150,000.

---

`$$\Pi(P,Q) = Q(P-14,400) - 80,000$$`

Higher profit occurs on curves nearer the top-right of the diagram. Points H and K involve the same quantity and average cost, but K earns more because its price is higher.

---
### Profit maximization: MRT = MRS

- The isoprofit curve is the indifference curve, with its slope showing the **MRS** between selling more and charging more.

- The demand curve is the feasible frontier, with its slope showing the **MRT** between lower prices and higher sales.

---
### Profit maximization: MRT = MRS

.pull-left[
**Slope of isoprofit curve**

`$$MRS = -\frac{(P - c)}{Q}$$`
]

.pull-right[
**Slope of demand curve**

`$$MRT = -\frac{P}{\varepsilon Q}$$`
]

`$$MRS = MRT$$`

$$
\iff \frac{P - c}{Q} = \frac{P}{\varepsilon Q}
$$

$$
\iff \frac{P - c}{P} = \frac{1}{\varepsilon}
$$

- `$\text{Profit margin} = P – MC$`

- `$\text{Price markup} = (P – MC)/P$`

`$\rightarrow$` price markup is equal to the inverse of the demand elasticity