General Equilibrium

Question 1

3 basic assumptions of general equilibrium theory (i.e. can all markets clear?)

Answer 1

1. No frictions (no externalities, no distortionary taxes)
2. Price-taking (no market power)
3. Many agents

Question 2

What does the axis length of an edgeworth box represent?

Answer 2

Total endowment of good

Question 3

What characterises competitive equilibrium in an exchange economy model?

Answer 3

MRS(a) = MRS(b) = p1/p2

Question 4

What is a general competitive equilibrium?

Answer 4

1. Vector of prices and an allocation such that:
   (i) Firms maximise profits subject to production function
   (ii) Profits distributed to households
   (ii) Consumers maximise utility subject to budget constraint
   (ii) All markets clear (i.e. total demand equals total endowment of goods, so excess demand = 0)

Question 5

What assumptions needed for competitive equilibrium to exist in an exchange economy?

Answer 5

1. Consumer preferences are:
   (i) Continuous (small price changes don’t result in large jumps in quantity demanded)
   (ii) Monotonic (more = better)
   (iii) Convex (averages better than extremes)
2. W>0 (endowment > zero)

Question 6

What is a Walrasian equilibrium?

Answer 6

competitive equilibrium in an exchange economy

Question 7

Why might competitive/Walrasian equilibrium not exist?

Answer 7

1. If an individual’s demand is discontinuous, competitive equilibrium might not exist
   (i) e.g. agent might be endowed with a good they do not want to sell at any price
   (ii) some goods only come in discrete quantities

Question 8

How much profit do firms make in a competitive market w/constant returns to scale?

Answer 8

Zero

Question 9

What characterises competitive equilibrium in an production economy model?

Answer 9

MRT = MRS = w/p

Question 10

Illustrate and explain how increasing returns to scale might mean non-existence of competitive equilibrium in production economy model?

Answer 10

SEE NOTES (titled Non-existence: increasing returns to scale)

1. Initially not a competitive equilibrium
2. Change relative prices, rotating budget constraint to try and achieve competitive equilibrium
3. Due to increasing returns to scale, firm’s optimum jumps
4. Discontinuous jump = reason for non-existence

Question 11

Individual’s maximisation problem in exchange economy model? In words and equation

Answer 11

1. Maximise utility (function of consumption of x1 and x2)
2. Subject to constraint that total spending less than/equal to total value of endowments
3. max U(x) st px ≤ pw

Question 12

Consumer maximisation problem in production economy model? Words and equations

Answer 12

1. Maximise utility (function of leisure and consumption)
2. Subject to constraint that total spending equals total income
3. max U(x,1–L) st profit + w*L = px

Question 13

Firm maximisation problem in production economy model? Words and equations

Answer 13

1. Maximise profit (isoprofit line)
2. Subject to constraint of production function
3. max px-wL st x ≤ F(L)

Question 14

Draw diagram to show gain from trade following liberalisation (1 country and ROW)

Answer 14

SEE NOTES (now remove tariffs)

Question 15

Are consumers always better off when country opened up to world trade vs autarky?

Answer 15

Yes - ability to trade at any world prices other than autarky prices makes consumers better off

Question 16

Draw diagram to show that consumers in 2 autarkic countries benefit from trade (assuming consumers are identical)

Answer 16

SEE NOTES (trade result)

Question 17

Draw diagram to show how some consumers might be made worse off by trade if consumers are heterogeneous

Answer 17

SEE NOTES (if consumers different, then some may be made worse off by trade)

Question 18

Draw diagram to show how some producers might be made worse off by trade

Answer 18

SEE NOTES (producers may suffer from trade)

Question 19

Stopler-Samuelson theorem

Answer 19

1. increase in demand for a good raises demand for the factor used most intensively in its production
2. E.g. wage rises if demand for the labour-intensive good rises

Question 20

Rybczynski theorem

Answer 20

increase in a country’s endowment of a factor will cause increase in output of the good which uses that factor intensively and a decrease in the other

Question 21

What is the contract curve? What does it represent?

Answer 21

1. locus of points where MRS(a)=MRS(b)

2. Represents the set of all Pareto efficient points

Question 22

Walras’ law (words and equations)

Answer 22

1. aggregate net/excess demand for each good identical to zero (i.e. equal to zero for all possible prices, not just equilibrium prices):
2. (i) p1z1(p1, p2) + p2z2(p1, p2) = 0
   (ii) where z1(p1,p2) = xa1(p1,p2) + xb1(p1,p2) – wa1 – wb1

Question 23

Why does a firm with constant returns to scale make zero profits in a competitive market?

Answer 23

1. CRTS means AC=MC

2. When MC=AC, profits are zero

Question 24

3 key international trade concepts (Venables 2016 lecture)

Answer 24

1. Comparative advantage – country has comparative advantage in good 1 if it’s relatively more expensive under free trade vs autarky (i.e. p1/p2 < p1/p2)
2. Trade pattern – each country exports good in which it has comparative advantage
3. Gains from trade – trade enlarges consumption possibility set & enables consumer to reach higher indifference curve

Question 25

A country has a comparative advantage in good 1 if…

Answer 25

it’s relatively more expensive under free trade vs autarky (i.e. p1/p2 < p1/p2)