Lecture notes
Microeconomics 2 Lecture Notes 21/22
- Module
- Microeconomics 2
- Institution
- The University Of York (UOY)
Microeconomics 2 Lecture Notes 21/22
[Show more]
Seller
Follow
Content preview
1. Partial equilibrium1) Introduction
There are two ways in which economists have studied market economies
• General equilibrium (Leon Walras) – whole economy
• Partial equilibrium (Alfred Marshall) – single good
We will study the partial equilibrium framework because it is much simpler than any general
equilibrium model. However, it isn’t as realistic because important interdependencies are ignored. In
contrast to the general equilibrium model, we have no trade between consumers, no trade between
firms, and significant restrictions on preferences.
Partial equilibrium General equilibrium
Developed by Alfred Marshall Leon Walras
Considers One good vs “everything else” Whole economy
Underlying assumptions Markets for different goods Markets for different goods
are independent are interdependent
Equilibrium Prices based on prices of other Prices of goods are
goods being constant determined simultaneously
Pros Tractable, welfare analysis and More realistic
comparative statics feasible
Cons Some interactions ignored More difficult
2) Consumers
The general assumption for consumers is that they are rational:
• Maximise their own “utility” – self-interested
• Understand all aspects of the market – know all the prices, and supply and demand decisions
of the other consumers and producers
• Unlimited computational power – whatever their preferences are, they can always work out
their optimal choice, as well as the optimal supply and demand decisions of the other
producers and consumers in the market.
The partial equilibrium model focuses on a single consumption good as a “negligible” part of the
whole economy. All other goods are bundled together and treated as one good.
That the market for the consumption good is “negligible” implies that there are negligible wealth
effects. This means that a change in income doesn’t affect the demand for our consumption good. It
also implies that there is price independence which means that a change in the price of our good
doesn’t affect the prices in the other markets. We can use the quasi-linear utility model to represent
these preferences in a way that respects these properties.
Quasi-linear utility model
We consider a consumer in a market with 2 goods: x is a consumption good with price p, m is
everything else, or “money”, with a price normalised to 1 (numeraire). The consumer has an
exogenously given income I.
A consumer is said to have quasi-linear preferences if she has a utility function of the form U(x, m) =
u(x) + m where u is increasing and concave (for example, u(x) = log(x), u(x) = √x).
,Individual demand in quasi-linear model
Consumer i maximises utility when U(x, m) = u(x) + m subject to the budget constraint px + m = I
where (px + m) is the expenditure of the consumer, and I is the given income of the consumer. By
rearranging the budget constraint, we get m = -px + I, which we can substitute into the utility
function above to get U(x, m) = u(x) -px + I.
Now we have an unconstrained problem which we want to maximise: max[x] u(x) – px + I, by solving
the first-order condition: u’(x) = p. The first order condition is independent of m (the amount of
money the consumer has) which means that m doesn’t affect the consumer’s choice of x. The
demand of this consumer is a function x*(p) such that u’(x*(p)) = p for all p.
If u(x) = log(x) then u’(x) = 1/x so the first-order condition would be 1/x = p so x*(p) = 1/p.
No wealth effects in the quasi-linear model
The black lines on the model above are the budget lines and the blue lines are the indifference
curves. As m increases, the budget lines move up but the tendency point (x*) remains at the same
level. Demand remains the same independent of the amount of money; this is the visual
representation of the absence of wealth effect.
Fundamental law of demand
How does demand react to price changes? Recall the demand function x*(p) solves u’(x*(p)) = p, and
suppose the price increases (p^ > p), so that u’(x*(p)) < p^ which is the new first-order condition (p is
replaced with p^ and it is now an inequality as p^ > p). Now we have to think about how to increase
the left side of the inequality to make both sides equal. We know that u is concave so u’(x) decreases
in x (over time). Therefore, x*(p^) < x*(p). This is the fundamental law of demand.
Aggregate demand
,Now suppose we have many, n, individuals in the market with demands x*1(p), x*2(p), …m x*n(p).
The aggregate demand is the sum of the individual demands: D(p) = x*1(p) + … + x*n(p) = Σni=1 xi(p). If
the preferences of the individuals are identical so x*i(p) = x*(p), then D(p) = nx*(p).
Inverse demand
If the demand is strictly decreasing, we can invert it. The demand curve is written as quantity q =
D(p) demanded at price p. The inverse demand function would then be price p = PD(q) such that
consumers demand q. Graphically, this corresponds to mirroring the demand curve along the 45
degree line. This will be useful later on when we discuss firm behaviour, specifically profit functions
which are functions of q.
The left hand panel shows the aggregate demand and the right shows the inverse demand. The
inverse demand is found by mirroring the aggregate demand in the 45 degree line. Note that the
aggregate demand is not linear and the line continues along the x axis once quantity reaches 0. This
is because quantity cannot be less than 0. Therefore, we must make sure that this kink in the curve is
reflected in the inverse demand graph.
Inverse demand and marginal utility
For simplicity, suppose there are n identical consumers. Recall that for each p, the demand function
of each consumer solves u’(x*(p)) = p. We want to express that equation in terms of quantity. For
given q, we have x*(p) = q/n, and p = PD(q) (inverse demand), so we can write u’(q/n) = PD(q) for all q.
For a given aggregate demand q, the inverse demand measures the corresponding consumers’
marginal utility.
3) Firms
Profit maximisation and cost functions
We assume that:
• Firms convert money into the consumption good (they buy inputs to produce the
consumption good)
• The cost of producing an amount q of the good is given by a cost function C(q)
• Firms are negligible in size compared to the market (they are price takers)
, • Firms maximise profits
Cost functions
The total cost of production is the sum of the fixed and variable costs: C(q) = c(q) + F, where F is the
fixed costs, for example, set-up costs or buying machinery, and c(q) are the costs that vary without
output, for example, labour.
The marginal cost is the cost of an additional (infinitesimal) unit of output; it is the slope of the cost
curve at a given output level: MC(q) = C’(q). The average cost is defined as the cost per unit; for q > 0,
the firm’s average total cost function is AC(q) = C(q)/q (total cost divided by total output).
Convexity of costs
The general assumption of the cost function is that it is increasing and convex, C’(q) > 0, C’’(q) > 0.
This convexity reflects the law of diminishing returns from production: using production processes
more intensively makes it over-proportionally less efficient. These assumptions imply:
• Profit maximisation problem has a unique solution
• Marginal cost is increasing
• Average cost curve has an inverse u-shape
• Marginal cost curve and average cost intersects at its minimum.
Why does the marginal cost intersect the average cost at its minimum?
The average cost is AC(q) = C(q)/q. If we produce one more item and the additional item is cheaper
than the average cost, then it decreases. If we produce one more item and the additional item is
more expensive than the average cost, then it decreases.
With a convex cost, the marginal cost is increasing which implies that the marginal cost and average
cost must intersect once at the minimum of the average cost.
Individual supply of the firm
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ursulamoore33. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £8.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
69252 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy revision notes and other study material for 15 years now