Pindyck and Rubinfeld Microeconomics Solutions Chapter 3

Summary microeconomics

Chapter 1: Preliminaries

Microeconomics is the branch of economics that deals with the behavior of individual economic units ranging from consumers, to firms, to workers and as well investors. Microeconomics describes and analyses the trade-offs that are faced by these different entities and investigates the role of prices as well as how they are determined.

Microeconomics analysis instruments:

• Theories: Used to explain observed phenomena in terms of a group of basic rules and assumptions.
• Models: Mathematical representations of economic theories that are used to make predictions.

Positive analysis is analysis that describes "cause and effect" relationships.

 What will happen to the price, the production and to the sales of cars if the US government imposes an importing quota on foreign cars. (no opinion)

Normative analysis is an analysis that examines questions of what ought to be.

 What is the best mix of different sized cars that should be produced to maximize profits when the tax on gasoline is imposed. (opinion)

A market is the collection of different buyers and sellers that determine the price as well as the allocation of a product or set of products through actual/potential interactions.

• On the markets for goods/products, firms and industries are considered to form the supply side whereas consumers are considered to form the demand side.

Market definition refers to the determination of which buyers and sellers are to be included within a particular market. Furthermore, it also refers to which products should be included in a particular market.

The extent of a market refers to the geographical boundaries as well as boundaries in terms of product range that are to be produced or sold within the market.

Market definition is important for the following three reasons:

• A company must define whom its actual and/or possible customers are in order to know which products and/or potential products to sell in the future.
• A company must know the product boundaries as well as geographical boundaries of its market so that it can set a price, determine budgets for advertising, and make investment decisions.
• Market definition is important for public policy decisions as it impacts various policies on future competition and prices.

Arbitrage is the practice of buying something at a low price in one location and then selling it at a much higher price in a different location.

Perfect competitive markets are markets with many buyers and sellers, thus no single buyer or seller can have a significant impact on price. In other words, in a competitive market a single price (market price) will prevail.

Noncompetitive markets are markets where many firms exist each affecting the price of a product.

Chapter 2: The basics of supply and demand

Supply curves show the relationship between the quantity of a good that producers are willing to sell at a certain price. The relationship can be expressed in the following format: Qs = Cs(p)

• Upward sloping, therefore the higher the price, the more the firms are able to and willing to produce and sell.

Change in price and other variables: impact on supply curve:

• A change in price, and therefore Qs i.e. quantity supplied, is represented by a movement along the supply curve.
• A change in any other supply determining variable, such as lower material costs, result in a shift of the supply curve itself.

Importance of supply and demand analysis:

• Supply and demand analysis enables us to understand and predict the effects of changing market conditions.
• It allows us to analyze the effects of economic policy.
• It allows us to carry out an equilibrium analysis, i.e. to find out when the supply and demand are in balance, and to find out how exogenous changes in the economic conditions affect the equilibrium.

Supply-demand model assumptions

• At any given price, a given quantity will be produced as well as sold.
• A market must be at least roughly competitive.

A shift in the supply curve will induce a price drop which will cause an increase in quantity produces and an increase in sales (due to the price drop).

A shift in the demand curve will increase price, which will cause an increase in quantity produced.

Price elasticity of demand and supply

• The price elasticity of demand: use Qd
• The price elasticity of supply: use Qs
• Price elasticity shows the percent change that will occur in supply (or demand) in response to a percentage increase in price.

Price elasticity of supply is usually positive:

• As price increases, the suppliers have an incentive to increase output

Price elasticity of demand is usually negative:

• As price increases, quantity demanded decreases.

Infinitely elastic demand means that consumers will buy as much as they can at one particular price.

Completely inelastic demand means that consumers will buy a fixed quantity, regardless of the price.

 In the presence of close substitutes: a price increase causes consumers to buy more of the substitute instead, hence demand is highly price elastic (Epd > 1).  In the absence of close substitutes: a price increase would not result in consumers buying different goods, hence demand will be price inelastic (Epd < 1)

Price elasticity of demand changes as we move along a curve.

 Epd is measured at a particular point on the demand curve, and even though ∆Q/∆P might be constant, the ratio P/Q would change as we move along the curve, which is what causes the change in Epd as we move along the curve.

Income elasticity of demand refers to the percentage change in quantity demanded resulting from a percentage increase in income.

• Eid = I/Q x ∆Q/∆I

Ep= P/Q x ∆Q/∆P

Cross price elasticity of demand refers to the percentage change in quantity demanded for a good that results from a one-percent price increase in another good.

• Elasticity of demand of good A with respect to price of good B:

Pb/Qa x ∆Qa/∆Pb

• It is positive when the goods are substitutes (a rise in price of good 1 will make good 2 cheaper relative to good 1 so customers will demand more of good 2).
• It is negative when goods are complements (the two goods tend to be used together).

Arc elasticity of demand is price elasticity of demand, but it is over a range of prices rather than a particular point on the demand curve.

• Ep = P./Q. x ∆Q/∆P  Where, P. is the average of the initial and final prices in the range and Q. is the average of the corresponding quantity.

Difference between short-run and long-run elasticities

• Short-run: allowing only a year or less to pass by before measuring changes in quantity demanded of supplied.
• Long-run: allowing enough time for consumers/producers to fully adjust to the price change before measuring the changes in quantity demanded or supplied.

Elastic demand refers to the increase in demand for a certain good that results from a price change.

• The change in quantity demanded is bigger than the change in price, ∆Qd > ∆P, which results in EpD having a magnitude greater than 1, i.e. the demand is elastic.

Inelastic demand refers to the decrease in demand for a certain good that results from a price change.

• The change in quantity demanded is smaller than the change in price, ∆Qd < ∆P, which results in EpD having a magnitude less than 1 i.e. the demand is inelastic.

Short-run demand

• Demand, e.g. for coffee, is less price elastic because habits change gradually
• Demand for durable goods is more price elastic

Long-run demand

• Demand, e.g. for coffee, is more price elastic because consumers have had enough time to change their habits
• Demand for durable goods is less price elastic

Short-run supply

• Supply is less price elastic because firms face capacity constraints
• Supply of durable goods is more price elastic (because goods can be recycled as part of supply if price increases)

Marginal rate of substitution refers to the maximum amount of a good that a consumer is willing to give up in order to obtain one additional unit of another good.

• MRS = - ∆A (vertical axis) / ∆B (horizontal axis)
• ∆A is negative, so the negative sign in from of the equation ensures that MRS is positive.

Bads are goods for which having less is preferred to having more. Examples include air pollution, where less of it is preferred to more.

Utility is a number that represents the level of satisfaction/happiness that a consumer gets from a certain market basket.

Utility function is a formula that assigns a level of utility to individual market baskets. It is a way of ranking different baskets.

• Ordinal utility functions rank different market baskets from most to least preferred, but the magnitude does not say much because we do not know by how much one casket is preferred over another.
• Cardinal utility functions tell by how much one market basket is preferred to another, but it is ignored because we cannot make such measurements.

Budget constraints are the second element of consumer theory. They refer to constraints that consumers face due to having a limited income.

A budget line is a line that indicates all combinations of goods for which the total amount of money spent is equal to income.

Effect of changing income on the budget line:

• Slope remains the same
• I increases: budget line moves outward
• I decreases: budget line moves inward

Effect of price changes on the budget line:

• Price of one good (on y axis) decreases, budget line rotates outward
• Price of one good (on y axis) increases, budget line rotates inward.

Goods are chosen to maximize satisfaction given the limited budget that is available.

The necessary conditions to maximize a basket:

• The basket must be located on the budget line (more specifically, it must be located on the highest indifference curve that touches the budget line, i.e. that it is tangent to it).
• The basket must give consumers the most preferred combination of goods.

When is satisfaction maximized?

When:

• Marginal Rate of Substitution = Ratio of the prices In other words:
• Marginal benefit = marginal cost

Where marginal benefit is the benefit associated with consuming one additional unit of the good and marginal cost is the cost of the additional unit of the good.

The satisfaction maximizing equation indicates:

• It tells the value of each consumer's MRS
• It does not inform us of the quantity of goods that a consumer buys: This depends on individual preferences, so quantity purchased by two customers can differ even though their MRS is the same.

A corner solution arises when a customer's marginal rate of substitution does not equal the price ratio for all levels of consumption. The customer, therefore, maximizes their satisfaction by only buying one of the numerous goods available for purchase.

The revealed preferences approach

• The revealed preferences approach checks whether individual choices are consistent with the consumer theory assumptions.

Marginal utility measures the additional satisfaction that is obtained from consuming one additional unit of a particular good.

Marginal utility that yields less and less satisfaction as more and more of a good is consumed is referred to as diminishing marginal utility.

The equal marginal principle states that utility is maximized when a consumer's marginal utility per dollar of expenditure across all goods is equalized.

• MRS= MUa/Mub
• We also know that utility is maximized when: MRS = Pa/Pb  We can conclude that MUa/MUb=Pa/Pb, equivalently, MUa/Pa=MUb/Pb

Chapter 4: Individual and market demand

A price-consumption curve is a curve that traces all utility maximizing combinations of two goods as the price of one of the goods changes.

An individual demand curve is a curve that relates the quantity of a good that a single consumer will buy to its price.

• Individual demand can be derived using the price-consumption.

The properties of an individual demand curve are:

• The level of utility that can be attained changes along the curve.
• At every point on the curve the consumer maximizes their utility (because at every point on the curve, MRS= the reatio of the prices of the goods' condition is satisfied).

An income-consumption curve traces all combinations of goods that maximize utility as the income of a consumer changes. As income changes, demand curve shifts to the left or the right.

Normal goods are goods that consumers want to buy more of as their income increases.

Inferior goods are goods that consumers want to buy less of as their income increases.

Engel curves are curves that relate the quantity of a good consumed to income.

• Upward sloping Engle curve applied to normal goods.

The effects of a price decrease:

• Consumers buy more of the good that has become cheaper, and less of the good that is now relatively more expensive.
• Consumers enjoy greater real purchasing power due to one of the goods becoming cheaper.

A situation where a change in consumption of a good results from a change in its price, while utility remains constant, is referred to as the substitution effect.

A situation where relative prices are constant, and a change in consumption of a good is a result of an increase in purchasing power is referred to as the income effect.

 When added together they make up the total effect.

The market demand curve represents the relationship between the quantity of a good that all customers in a market will buy related to its price.

 The market demand curve can be derived by adding up the individual curves of all of the customers in the market

Demand curve's reaction when more consumers enter the market

• The market demand curve shifts further to the right as more customers enter the market  Factors that influence the consumer demand will also affect market demand.

The building blocks of market demand

An isoelastic demand curve is a demand curve that has a price elasticity that is constant.

Consumer surplus is a measure of how much better off individuals are in the market. It is the difference between how much consumers are willing to pay for a good and how much they actually pay.

Network externalities are situations in which a consumer's demand depends on the purchases of others. These externalities can be negative, if the externality leads to a decrease in demand in response to growth in purchases by others, or positive, in the case of an increase in demand in response to a growth in purchases by others.

Situations where the quantity of a good demanded by a consumer increases because others possess that good is referred to as the bandwagon effect -> the bandwagon effect is a positive network externality.

A situation where the quantity of a good demanded by a consumer decreases because others possess that good is referred to as the snob effect.

• A situation in which a consumer would prefer to own exclusive or unique goods, rather than goods similar to those owned by others  The snob effect is a negative network externality.

Consumer Preferences

Budget Constraints

Consumer Choice

Individual Demand

Market Demand

Productivity growth sources:

• Stock of capital: the total amount of capital available for production.
• Technological change: technological development allows factors of production to be used efficiently.

An isoquant is a curve that shows all possible combinations of inputs that would yield the same output.

An isoquant map is a graph that combines numerous isoquants that can then be used to describe production functions.

When and why do firms use isoquants?

• Firms can use isoquants when making production decisions as they show how much flexibility firms have.
• Isoquants allow managers to choose the ideal input combinations that would minimize costs and maximize profits.

The marginal rate of technical substitution is the amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant. It is also equal to the ratio of the marginal products of the inputs involved.

• MRTS of labor for capital, in other words, is the amount by which capital can be reduced when one additional unit of labor is used, so that output remains constant.
• MRTS = - ∆K/∆L = MPL / MPK

MRTS= - ∆A / ∆B

• MRTS is diminishing, i.e. it falls as we move down along an isoquant.
• This is because productivity of inputs is limited. Adding more of input A, in place of input B will result in a decrease in the productivity of A because production requires a balanced mix of both inputs.

A fixed-proportions production function describes situations where the method of production is limited just like in the case of car production.

Chapter 7: The Cost of Production

Accounting costs include actual expenses together with depreciation charges for capital equipment.

Economic costs are the costs that a firm faces for utilizing economic resources in production, and it includes opportunity costs.

 Opportunity costs are costs associated with opportunities that have been forgone due to a firm's resources not being put to their best alternative use.

Sunk costs are costs that have been incurred and cannot be recovered.

Prospective sunk costs are considered to be an investment.

• A firm contemplating whether to buy a specialized piece of equipment faces prospective sunk costs, i.e. they face an investment and should analyze whether this investment would be economical (would it generate large revenues?). if the specialized equipment is bought, then it would become a sunk cost as the equipment would not be used for anything other than what it was made to be used for (its opportunity cost would be zero).

Total costs = Fixed costs + Variable costs

• Where:

Fixed costs refers to any costs that do not vary with output level and can be eliminated only by shutting down the production process.

Variable costs refers to costs that vary with output level.

 Fixed costs impact future decisions.  Sunk costs do not impact future decisions.

Amortization is a policy of treating a one-time expenditure as an annual cost that can be spread out over time.

• Sunk costs can be treated as fixed costs by amortizing them and the expenditure over a number of years.

Marginal costs are increase in costs due to the production of one additional unit of output.

• Marginal Cost = ∆Variable cost / ∆Quantity

Average costs refer to a firm's total costs divided by its level of output. Average (total) costs constitute of average fixed costs and average variable costs.

• Average costs = Total Cost / Quantity

The determinants of short run costs

• The rate at which variable and total costs increase in the short-run depends on
  • The production processes
  • The extent to which diminishing marginal returns to variable costs is involved

Economies of scale refers to a situation in which output can be doubled for less than double the cost (input proportions vary).

 When workers specialize in activities that they are most productive in.

Diseconomies of scale refers to a situation where the doubling of output requires more than double the cost.

 The advantage of buying in bulk may disappear once certain quantities are reached because at some point supplies of essential inputs will be limited and hence their costs will rise. So, when doubling output, the costs would be more than double.

Measuring economies of scale

• Economies of scale are measured in terms of a cost-output elasticity, Ec:

Ec = ∆C/C x ∆Q/Q

• Equivalently: Ec = MC/AC

Chapter 8: Profit maximization and competitive supply

The perfect competition model relies on the following assumptions:

• Price taking A firm is a price taker if it has no influence over the market price. Hence, it takes the price as it is given.  This is the case when a market is made up of several small firms, each of which satisfies a small proportion of the total market demand. Therefore, their decisions do not impact the market price.
• Product homogeneity Products in a market are homogeneous if they are perfectly substitutable. In other words, these products are identical, or nearly identical, to each other.
• Free entry (or exit) is a condition that states that firms wanting to enter or exit a market/an industry can do so without incurring any special cost.

A market is highly competitive when the firms within the market face demand curves that are highly elastic (with rather easy entry and exit)

 Remember: competitive behavior does not necessarily indicate that the market is highly competitive. Analysis of the firms and their strategic interactions would be necessary.

Some managers deviate from profit maximization behavior:

• To satisfy shareholders
• To maximize short-run profits at the expense of long-run profit in order to earn a bonus or a promotion.
• Because it requires technical and marketing information which is costly to acquire.  Firms with such managers are not likely to survive in competitive industries

Firms that do survive in competitive industries make long-run profit maximization their priority (otherwise they can be replaced by shareholders or board of directors, or a new management could take over the entire firm).

A cooperative organization is an association of businesses or people that is jointly owned and operated by members for mutual benefit.

Profit is the difference between the total revenues and total costs of a firm

• Π = R – C  Where revenue is R = PxQ

Marginal revenue refers to the change in revenue that results from output increasing by one unit.

• MR = ∆R / ∆Q

Profit maximization

• Profit is maximized when MC(q) = MR = P, alternatively we can say that profit is maximized when MR – MC = 0
• If the firm is perfectly competitive, to maximize its profits it should ensure that P = MR = MC i.e., the price it charges should be equal to the firm's marginal costs.

The three conditions of long-run competitive equilibrium:

• All firms in the industry are maximizing their profits.
• All firms are earning zero economic profit, so there is no incentive to enter or exit the industry.
• The price of a good is such that the quantity supplied is equal to the quantity demanded.

Economic rent is a term used for the amount that a firm is willing to pay for an input minus the minimum amount necessary to buy it.

 In competitive markets this is often positive, both in the short-run as well as the long-run, even though profit is zero.

The long run producer surplus of a firm in a competitive market consists of the economic rent from all its scarce inputs.

The three different cost industries:

• Constant-cost industry: long-run supply curve is horizontal at P = (minimum) LAC
• Increasing-cost industry: long-run supply curve is upward sloping. (Higher prices are needed to cover the increasing cost).
• Decreasing-cost industry: long-run supply curve is downward sloping.

Responses to output tax:

An output tax:

• Raises a firm's marginal cost
• Raises a firm's average variable cost curve o F a single firm is taxed: as long as it can still earn a positive/zero economic profit, it

                                will choose output level at which MC + t = P            

   If a firm's cost are too high, it will exit the industry o If every firm in the industry is taxed: marginal costs will increase due to the tax, firms

                                will reduce their output at the current market price            

   This will reduce the total output supplied by the industry and firms will raise their prices.

Long-run elasticity of supply for constant-cost and increasing-cost industries:

• Constant-cost industry o Long-run supply curve is horizontal so the long-run Es is infinitely large
• Increasing-cost industry o Long-run Es is large (positive) but finite

Chapter 10: Market power: Monopoly and Monopsony

A monopoly is a market where there is only one seller and numerous buyers.

A monopsony is a market where there are numerous sellers but only one buyer.

Market power refers to the ability of a seller or a buyer to affect the overall price of a good.

Marginal revenue (MR) is the change in revenue due to an increase in output by one unit.

• First, find the revenue which is : Revenue = Price x Quantity
• Then, differentiate in terms of Q if dealing with a demand function to find the marginal revenue: MR = ∆R/∆Q
• If you have only numbers, the MR is the difference between the initial and the subsequent revenue.

Practical rule of thumb for pricing and why it is used:

• A firm's profit function is : π = Revenues (Q) – Costs (Q)
• The profit maximizing quantity is found by using derivatives: ∆π/∆Q = ∆R/∆Q - ∆C/∆Q = 0
• Equivalently: ∆π/∆Q = MR – MC = 0
• Finally, solve for Q

Managers use a rule of thumb for pricing as it can be applied in practice much more easily due to it requiring a lot less information

 P = MC / (1 + (1/Ed)) o Where Ed is the elasticity of demand for the firm

Output decisions depend on MC and the demand curve, there is no supply curve in a monopolistic market.

• A shift in demand can lead to: o Change in price, no change in quantity o Change in quantity, no change in price o Change in both price and quantity

Effect of tax on a monopolist

• MR= MC + tax
• The marginal cost curve shifts upwards by an amount t and intersects marginal revenue at a different point

                                o This causes a decrease in Q and an increase in P (this increase can be by more than t)            

Output decision: for a firm with multiple plants

• Divide the total output between the plants so that marginal cost of each plant is equal to each other
• Since profit is maximized when MR=MC and marginal cost must be equal for all plants, profits will be maximized when MR=MC of each plant

Pindyck and Rubinfeld Microeconomics Solutions Chapter 3

Source: https://www.studeersnel.nl/nl/document/universiteit-van-amsterdam/microeconomics/summary-microeconomics-pindyck-rs-and-rubinfeld-dl-summary-of-the-book-chapter-1-7/123227

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