Trade and PPF

Absolute and comparative advantage

Party A has an absolute advantage over Party B in the production of a good if, for a given amount of resources, A can produce a greater number of that good than B.

Party A has a comparative advantage over Party B in the production of a good if A’s opportunity cost of producing that good is lower than B’s opportunity cost.

For example, two parties spend some fixed time making two goods:

The opportunity costs of both goods for both parties is represented in the following table:

Trade is determined by the comparative advantage, not the absolute advantage. Trade allows parties to specialize in producing the good in which they have the lower opportunity cost and increase the total output.

PPF

A production possibility frontier (PPF) graphs the output that an individual can produce with a particular set of resources.

It draws the set of possible output choices when these resources are used efficiently.
Production efficiency is achieved when it’s not possible to produce more of one good without producing less of some other goods.
Points inside the PPF are inefficient and points outside are infeasible.

The shape of an agent’s PPF is determined by its level of resources and technology. If there’s an increase in the resources or improvement in technology to produce both goods, the PPF will shift outwards from the origin in both axes. A rotation is when a shock boosts the production of one good. If the agent doesn’t trade, the PPF also describes the agent’s consumption choices.

The slope of the tangent of the PPF at any point measures the opportunity cost of producing an extra unit of a good in terms of the other. Notice that when the PPF should be concave, i.e., the opportunity cost of some goods is increasing in its level of output. This is because some resources are more suited for the production of other goods.

In our example, the PPF of both parties and their joint PPF is as follows:

Production and Costs

Using the available technology, a firm converts inputs - usually more than one of labor, machines (often called capital), and natural resources (typically called land) - into output sold in the marketplace.

The short-run and long-run

The short run is the period during which at least one of the factors of production is fixed, i.e., the level of input used cannot be changed regardless of the output produced. In the long run, all factors of production are variable. Note that the difference is not in the set time of production, but in how long it takes for all of a firm’s inputs to become variable.

Production

A production function shows the relationship between the quantity of inputs used and the (maximum) produced amount of output, given the state of technology.

Enter an expression for output $q(L)$:

Marginal product

The marginal product (MP) of some input refers to how output responds when there is a change in the number of that specific input used. This is a short-run concept.

If the MP becomes progressively smaller as we increase the use of that input, this is called diminishing marginal product; If the MP becomes larger, this is called increasing marginal product.

Diminishing MP is thought to be very common.

Returns to scale

Returns to scale refer to how the number of outputs changes when there is a proportional change in the quantity of all inputs. If the output increases by the same proportional change, there are constant returns to scale. If the output increases by more (less) than the proportional increase in all inputs, there are increasing (decreasing) returns to scale. Returns to scale is a long-run concept.

Short-run costs

To use the inputs of production and transform them into outputs, a firm will have to incur some costs, which may include:

wages paid to workers,
cost of leasing, or
purchasing factories and machines.

A cost function is an equation $TC=f(q)$ that links the quantity of outputs with its associated production cost.

When the output is $0$, the total cost is strictly positive.
The total cost curve rises as output increases, $MP>0$.
The total cost curve rises at an increasing rate, $MP'<0$.

Enter an expression for $TC = f(q)$:

Fixed and variable costs

Fixed costs (FC) are costs that do not vary with the quantity of output produced.

Variable costs (VC) are those costs that vary with or depend on the quantity of output produced.

Marginal cost

The marginal cost (MC) is the increase in total cost that arises from an extra unit of production.

Due to diminishing MP, a typical MC curve will eventually increase with increasing output.

Average costs

Average fixed cost (AFC) is a fixed cost per unit of output:

Note that it is always downward-sloping.

Average variable cost (AVC) is the variable cost per unit of output:

Because AVC is affected by diminishing MP, the AVC curve will eventually be upward-sloping over output.

Average total cost (ATC) is the total cost per unit of output:

The decline in AFC usually dominates at low input levels, but at higher ones, AVC will dominate. This makes the ATC curve a U-shape.

The MC curve intersects the AVC curves at the minimum of AVC.

Long-run costs

Long-run marginal cost

In the long run, all inputs can be varied to increase one unit of output produced. Hence, for the same level of output, long-run marginal cost will be less than or equal to short-run marginal cost.

Long-run average cost

For the same reason, the long-run average cost can be no greater than the short-run average cost. The long-run average cost curve will be the lower envelope of all of the short-run average cost curves.

If long-run average costs are decreasing with output, this is called economies of scale. If long-run average costs are increasing with output, this is known as diseconomies of scale.

Equilibrium and welfare

Enter an expression for demand curve:

Enter an expression for supply curve:

Equilibrium

A market is in equilibrium if, at some market price, the quantity $Q_d$ demanded by consumers equals the quantity $Q_s$ supplied by firms. The price at which this occurs is called the market-clearing price (or equilibrium price), denoted $P^*$.

Welfare

We can measure the observed changes in the benefits consumers and firms gain in the markets using welfare analysis.

Consumer surplus

Consumer surplus (CS) is the welfare consumers receive from buying units of goods or services in the market. It is given by the consumer’s willingness to pay, minus the price paid, for each unit bought. We can find an individual’s CS by calculating the area between the demand curve and the price line.

Producer surplus

Producer surplus (PS) is the welfare producers (usually firms) receive from selling units of a good or service in the market. It is given by the price the producer receives, minus the cost of production, for each unit of the good or service bought. We can find a firm’s PS by calculating the area between the price line and the firm’s supply curve.

Total surplus

The total surplus (TS) is the sum of consumer and producer surplus in the market equilibrium. TS is the area between the demand and supply curves, up to the market equilibrium, quantity $Q^*$.

Elasticity

We are interested in measuring how a change in one variable affects another. One issue with measuring quantitative changes is that different markets use different units of measurement. A way we deal with this is to look at proportional changes.

Measuring elasticity

Elasticity $\varepsilon$ measures how responsive one variable $y$ changes in another variable $x$; We can calculate it by deciding the percentage change in $y$ by the percentage change in $x$:

$$\varepsilon=\frac{\%\Delta y}{\%\Delta x}$$

where $\%\Delta x=\frac{\Delta x}{x}$. The larger the absolute value of $\varepsilon$, the more responsive $y$ is to changes in $x$; Conversely, the smaller the absolute value of $\varepsilon$, the less responsive $y$ is to changes in $x$.

Point method

If we are interested in elasticity at a particular point and $y(x)$ is differentiable at that point, we can use the point method.

$$\varepsilon = \frac{\Delta y / {y}}{\Delta x / {x}}= \frac{\Delta y}{\Delta x} \cdot \frac x y= \frac{dy}{dx} \cdot \frac x y$$

Midpoint (or arc) method

If we are interested in elasticity when moving from one point to another, we use the midpoint method.

$$\varepsilon = \frac{\Delta y / {y^m}}{\Delta x / {x^m}}= \frac{\Delta y}{\Delta x} \cdot \frac{x^m}{y^m}$$

where $x^m=\frac{x_1+x_2}2$ and $y^m=\frac{y_1+y_2}2$.

Applications

The elasticity of demand ($\varepsilon_d$) measures how sensitive the quantity $Q_d$ demanded of a good change in its price $P$.

Enter an equation for $P$ and $Q_{d}$:

Enter a value for $P$ or $Q_{d}$:

The elasticity of supply ($\varepsilon_s$) measures how sensitive the quantity $Q_s$ supplied of a good change in its price $P$.

Enter an equation for $P$ and $Q_{s}$:

Enter a value for $P$ or $Q_{s}$:

The cross-price elasticity examines the relationship between the quantity demanded of one good and the price of another related good. Specifically, it measures how sensitive the quantity $Q_A$ demanded of a good A changes in the price $P_B$ of another good B.

Enter an equation for $P_{B}$ and $Q_{A}$:

Enter a value for $P_{B}$ or $Q_{A}$:

Income elasticity $\eta$ measures how sensitive the quantity demanded of a good $Q$ changes in income $Y$.

Enter an equation for $Y$ and $Q$:

Enter a value for $Y$ or $Q$:

Monopoly

A market with one seller is a monopoly, and that seller is a monopolist. The market power of a monopolist allows it to charge higher prices in order to increase its profits and have implications on welfare.

Characteristics of a monopoly

Monopolies have the following characteristics:

One seller and many buyers. There is a single producer of all output in the market.
Price maker. Because the monopolist is the only firm in the market, it has the market power to determine the price in the market - that is, it is a price maker.
Barriers to entry. Firms that might like to enter the market are prevented from doing so by barriers to entry.

Single-price monopolist

Marginal revenue

Enter an equation for demand curve:

Marginal revenue is the firm's additional revenue from selling odemandne extra unit of a good.

Profit maximization

Enter a formula for total cost:

Profit is defined as $\pi=TR-TC$.

Assuming that profit is concave down, we take the first derivative and set it to zero to maximize profit.

$$\frac{d\pi}{dQ}=\frac{dTR}{dQ}-\frac{dTC}{dQ}=MR-MC=0$$

Rearranging gives us the profit-maximizing condition.

$$MR=MC$$

The maximum profit can be written as the area of a rectangle. $$ \pi^m = P^m \cdot Q^m - ATC^m \cdot Q^m = (P^m - ATC^m) \cdot Q^m $$

Welfare under the single-price monopolist

The market equilibrium (competitive quantity) is $Q=Q^*$ such that $MB=MC$. The monopoly quantity is $Q=Q^m$ such that $MR=MC$. Note that as $MB>MR$ for all units $Q>0$, the monopolist sells less than the competitive market quantity, i.e., $Q^m>Q^*$.

Consumer and producer surplus

The consumer surplus is given by the area below the demand curve and above the price line (given by monopoly quantity) for all units traded.

The producer surplus is given by the area below the price line and above the supply curve (given by monopoly quantity) for all units traded.

The monopolist’s producer surplus is larger than that of a competitive market.

Total revenue and deadweight loss

The total surplus is given by $TS = CS + PS = \int_0^{Q^m} P_d - P_s \,dQ$. Because $Q^m > Q^*$, the total surplus under a monopoly is smaller than that in a competitive market. The gains from trade for units between $Q^m$ and $Q^*$ are not realized; We refer to the lost welfare as deadweight loss (DWL).

Oligopoly

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Introduction

An oligopoly is a market that contains a small number of firms. Because there are only a handful of key producers in the market, the decisions of each firm have ramifications for not only itself but also for each of its competitors. Given the impact oligopolists have on one another, a firm’s strategic choice will typically depend on what other firms are doing. This strategic interaction between firms is a key feature of oligopoly, not present in perfect competition, monopoly, or monopolistic competition.

Characteristic of an oligopoly

Oligopolies have the following characteristics:

Few sellers and many buyers. Output in the market is produced by a handful of firms.
Price maker. Because there are only a small number of firms in the market, each firm retains the power to set its own prices.
Barriers to entry. Entry into the market is difficult as there are high barriers to entry.
Potential product differentiation. Products may be differentiated or not depending on the market.

Simultaneous move games

Often firms will need to make strategic decisions without knowledge of what other firms in the market have decided to do. In such circumstances, firms make decisions as though their choices were made simultaneously. In such cases, it will be appropriate to analyze the strategic interaction of those firms as a simultaneous move game.

Price war

In some cases, the game faced by the firms in an oligopoly might resemble a prisoner’s dilemma.

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Taxes and subsidies

We will restrict our analysis to taxes and subsidies on consumption and production, but it is important to be aware that other types of taxes and subsidies also exist.

Taxes

Enter an expression for demand curve:

Enter an expression for supply curve:

A tax is a compulsory payment made to the government. We consider per-unit taxes which is a fixed amount for each unit; as opposed to ad valorum tax, where the amount of the tax is a fixed percentage.

Tax on comsumption

Enter a tax on consumption $t_c$:

Suppose that for every unit purchased, consumers must pay a tax of $t$ to the government in addition to the price to the producer. If the demand curve without tax is $Q=Q(P)$, then the demand curve with tax is $Q=Q(P+t)$. Graphically, the demand curve shifts downwards by $t$ after taxing.

Tax on production

Enter a tax on production $t_p$:

Suppose that for every unit sold, producers must pay a tax of $t$ to the government in addition to the price to the producer. If the supply curve without tax is $Q=Q(P)$, then the supply curve with tax is $Q=Q(P-t)$. Graphically, the supply curve shifts upwards by $t$ after taxing.

Effect of tax on welfare

Both consumer surplus and producer surplus will decrease as a result of the tax, for two reasons: first, fewer units are traded in the market; second, on each unit, consumers pay a higher price and producers receive a lower price relative to a market without a tax.

The government now receives some surplus in the form of tax revenue. The government revenue $GR$ is the product of the per-unit tax $t$ and the quantity traded under taxes $Q^t$.

The deadweight loss (DWL) is the loss in total surplus due to the tax. It is the area between the demand and supply curves from the quantity traded under taxes $Q^t$ to the quantity traded without taxes $Q^*$.

The more elastic the demand or supply curves, the greater the effect of the tax on the quantity traded in the market, which will result in a greater DWL.

Incidences of tax

The legal incidence of the tax refers to who is legally responsible for paying the tax. By contrast, the economic incidence of the tax refers to who, as a matter of fact, actually bears the burden of the tax. As a general rule, the legal incidence of the tax doesn’t necessarily bear all the economic incidence of the tax. The economic incidence of the tax is determined solely by the relative elasticities of the demand and supply curves.

Externalities

Introduction

Competitive markets are usually Pareto efficient in the long run. In contrast, the situations where the market outcome is not efficient are called market failures. One type of market failure is externalities.

External costs and benefits

Enter an expression for demand curve:

Enter an expression for supply curve:

An externality is a cost or benefit that accrues to a person who is not directly involved in an economic activity or transaction. These costs or benefits are also known as “external costs” or “external benefits”.

A positive externality occurs when the economic activity results in external benefits for a third party. A negative externality occurs when the economic activity results in external costs for a third party.

Positive externalities

Enter an expression for $MEB$:

Consumers derive benefits from consuming goods. However, in the presence of a positive externality, the consumption or production of the good also has external benefits for a third party. Hence, the benefit to society as a whole must include both the consumer’s benefit and the external benefit.

The marginal benefit to society of an additional unit of the good is known as the marginal social benefit (MSB). It is made up of the marginal private benefit (MPB) enjoyed by the consumer and the marginal external benefit (MEB) that accrues to a third party.

Negative externalities

Enter an expression for $MEC$:

Similarly, producers incur costs from producing goods. However, in the presence of a negative externality, the consumption or production of the good also has external costs for a third party. Hence, the cost to society as a whole must include both the producer’s cost and the external cost.

The marginal cost to society of an additional unit of the good is known as the marginal social cost (MSC). It is made up of the marginal private cost (MPC) incurred by the producer and the marginal external cost (MEC) that accrues to a third party.

The problem with externalities

Externalities are a source of market failure because they represent external costs or benefits not accounted for by the market. Because consumers only account for their private benefits and producers only account for their private costs, the market equilibrium is determined by the private demand and supply curves. $$ MPB=MPC $$

However, from the perspective of society as a whole, any external costs and benefits associated with the consumption or production of the good should also be taken into account. Hence the socially optimal equilibrium is determined by the marginal social benefit and cost curves. $$ MSB=MSC $$

The DWL indicates the surplus forgone in the market equilibrium relative to the efficient outcome. It is the area between the marginal social benefit and cost curves, from the market quantity to the socially optimal quantity.