Closed Economy vs. Open Economy

  1. Closed Economy

The idea here is to compare the best outcome in a closed economy with that in an open economy. This problem is similar to one's occupational choice problem. There are thousands of different jobs, and most people usually choose at most one or two jobs, instead of personally producing everything they need.


 (auto = self, arkein = rule, defend in Greek) = Self sufficiency

Autarky imposes a stringent condition on production: xi = yi


maximize u(x1,x2)
subject to (s.t.): xi = yi, (a stringent restriction)

( xi = consumption of good i, yi = production of good i)
aL1 y1 + aL2 y2 = L (L = labor supply)

Figure 2. Equilibrium in a closed economy

How does one solve the utility maximization problem of a closed economy?

As the above diagram shows, the maximum welfare is achieved at the tangency point between the highest indifference curve and the PPF. Thus, when a maximum is attained, the two curves must have the same slopes. Marginal cost of good 1, measured in terms of the resources used up or the other good sacrificed is represented by the slope of the PPF, and called the marginal rate of transformation (MRT), i.e.

 MRT ≡ aL1/aL2 (opportunity cost or relative price of 1 in autarky)

Consumers' willingness to pay for a good is often represented by the slope of the indifference curve is called the marginal rate of substitution (MRS),


(MUi = marginal utility of good i.)

Equilibrium condition

 Thus, the consumption point which satisfies the following equilibruim is the solution to the problem (willingness to pay for good 1 = its opportunity cost),

MRS = aL1/aL2



  2. An Example of Autarky
 Problem to solve

Given u = y1y2, MRS = y2/y1, aL1 = 2, aL2 = 1, L = 120,

find the solution for the closed economy's problem.
(u = utility)

 MRT = ?

First, note that MRT (Marginal Rate of Transformation) = slope of PPF is

MRT ≡ aL1/aL2 = 2.

Note that MRT is the relative price of good 1 in autarky.

 autarky restriction In a closed economy, production must be equal to consumption in each industry. That is,

x1 = y1, and x2 = y2 .

Thus, a closed economy's problem is to choose y1 and y2 to

maximize u = y1y2 s.t. PPF: 2y1 + y2 = 120.

eq. condition:


Recall that the equilibrium condition for this problem is:

y2/y1 = MRS = MRT = 2.

Substitute this equilibrium condition (y2 = 2y1) into the PPF to obtain,

2y1 + y2 → 2y1 + 2y1= 120,

or y1 = 30, and hence y2 = 60. It follows that uA = y1 × y2


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  3. Open Economy

No tariffs and non transportation costs imply the law of one price. That is, p*1 and p*2 prevail in all countries (output price equalization).

The open economy's problem is to choose y1, y2, x1 and x2 to maximize u(x1, x2), subject to a single constraint that the total value of consumption is equal to that of production, i.e.,

p*1x1+ p*2x2 = p*1y1 + p*2y2

(expenditure = income)

1 Complex problem = 2 simple problems This is a complicated problem of choosing 4 unknown variables, subject to a constraint. However, it can be decomposed into two simpler problems.
 Step I

 Maximize GDP = p*1y1 + p*2y2 (GDP = NDP = net domestic product in the absence of depreciation.)

subject to: aL1y1 + aL2y2 = L (PPF)

To find a solution, eliminate one of the two varibles, expressing one in terms of the other. Then

GDP = NDP = p*1y1 + p*2[L/aL2 - y1aL1/aL2]

 Slope of GDP
(How much GDP increases as y1 increases by 1 unit)

 p*1 - p*2[aL1/aL2],

which is positive iff (if and only if)

 p*1/p*2- aL1/aL2 is positive.

If  p*1/p*2- aL1/aL2 > 0


 International price of good 1 (in terms of units of good 2) is higher than its autarky price, then GDP is rising in good 1.

then choose a maximum y1 = L/aL1, as shown above.

Accodingly, y2 = 0.

If  p*1/p*2

- aL1/aL2 < 0


 International price of good 1 (in terms of units of good 2) is lower than its autarky price, then GDP is falling in good 1.

then choose a minimum y1 = 0, as shown above.


Finland's organic grain

Finland's shipyard builds cruise ships.

Finland's food production: due to short growing season Finland has an absolute disadvantage in grain production. On the grounds of "food security,"however, Finland produces wheat. 29% of Finnish farm income is from the European subsidy. (More food production means less income.)

South Korea's beef: In South Korea, meat production is costly, more than ten times the price in the world market.

Kobe beef price: $1300 per pound

If  p*1/p*2- aL1/aL2 = 0


 International price of good 1 (in terms of units of good 2) is equal to its autarky price, then GDP is invariant. There are no gains from trade.


Unless  p*1/p*2= aL1/aL2 , specialize in one product.

Do not produce the product in which the country has no comparative advantage. The less you produce this product, the better.

Step II maximize u(x1,x2)

s.t. I = p*1x1 + p*2x2. (s.t. = subject to)


Equilibrium Condition: MRS = p*1/p*2

Figure 3. Utility maximization: UF is higher than UA.



  4. An Example of an Open Economy
 problem Given u = x1x2
MRS (slope of Indifference curve) = x2/x1,
p*1 = 3, p*2 = 1, aL1 = 2, aL2 = 1, and L = 120.
Step 1 

maximize 3y1 + y2, subject to 2y1 + y2 = 120.

Note that

p*1/p*2 = 3/1 > 2/1 = aL1/aL2.

That is, GDP is rising with y1. Thus, the country should specialize in good 1.

y1 = 60 = L/aL1, y2 = 0.

GDP = I (national income) = 3 × 60 + 1 × 0 = 180.

In the next step, use this income to maximize utility by choosing the right consumption bundle.

 Step 2   maximize u = x1x2, subject to 3x1 + x2 = 180

 Equilibrium condition is:

MRS = x2/x1 = 3/1 = p*1/p*2, or

x2 = 3x1.

Substitute the above equilibrium condition into the budget line

p*1x1 + p*2x2 = 180 to get

3x1 + x2 = 6x1 = 180.

x1 = 30, x2 = 90, uF = 30 × 90 = 2700.

UF = 2700 > UA = 1800.

(UF = utility under free trade,

UA = utility under autarky.

You are halfway through the math portion in this course).

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  5. Homework 1

Given: U = x1x2, MRS = x2/x1, L = 300, aL1 = 3, aL2 = 2, p*1 = 2, p*2 = 1,


1. Closed Economy: Find y1, y2, and UA

2. Open Economy: Find y1, y2, x1, x2, UF.

3. Compare UA and UF and sketch solutions in 1 and 2.

Pudong, Shanghai
Shanghai General Motors Corporation (in Pudong) is a joint venture between GM and Shanghai Automobile to produce automobiles.

The Reclining Buddha in Jade Buddha Temple, Shanghai.

 Yuyuan Garden, Shanghai