1. Closed Economy  
purpose  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: (i) find the industry in which one has a comparative advantage. There are thousands of different jobs, and most people usually choose at most one or two jobs, instead of personally producing everything they need. (ii) Long term goal: invest in areas in which one would have a potential comparative advantage. 
Autarky 
(auto = self, arkein = enough, sufficient, strong in Greek) = Self sufficiency Autarky imposes a stringent condition on production: x_{i} = y_{i} 
maximize u(x_{1},x_{2}) ( x_{i} = consumption of good i, y_{i} = production of
good i) 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 ≡ a_{L1}/a_{L2 }(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), MRS≡ MU_{1}/MU_{2} (MU_{i} = 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 = a_{L1}/a_{L2 } 
2. An Example of Autarky  
Problem to solve  Given u = y_{1}y_{2}, MRS = y_{2}/y_{1, } a_{L1} = 2, a_{L2} = 1, L = 120, find the solution for the closed economy's problem. 
MRT = ?  First, note that MRT (Marginal Rate of Transformation) = slope of PPF is MRT ≡ a_{L1}/a_{L2} = 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, x_{1} = y_{1}, and x_{2} = y_{2} . Thus, a closed economy's problem is to choose y_{1} and y_{2} to maximize u = y_{1}y_{2} s.t. PPF: 2y_{1} + y_{2} = 120. 
eq. condition: MRS = MRT 
Recall that the equilibrium condition for this problem is: y_{2}/y_{1} = MRS = MRT = 2. Substitute this equilibrium condition (y_{2} = 2y_{1}) into the PPF to obtain, 2y_{1} + y_{2} → 2y_{1} + 2y_{1}= 120, or y_{1} = 30, and hence y_{2} = 60. It follows that u^{A} = y_{1} × y_{2} =1800. 
3. Open Economy  
Peace promotes specialization and trade. Political instability forces countries to choose autarky (e.g., food safety). Agriculture in the Negev: Today's desert pioneers 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 y_{1}, y_{2}, x_{1} and x_{2} to maximize u(x_{1}, x_{2}), subject to a single constraint that the total value of consumption is equal to that of production, i.e., p*_{1}x_{1}+ p*_{2}x_{2} = p*_{1}y_{1} + p*_{2}y_{2} (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*_{1}y_{1} + p*_{2}y_{2} (GDP = NDP = net domestic product in the absence of depreciation.) subject to: a_{L1}y_{1} + a_{L2}y_{2} = L (PPF) To find a solution, eliminate one of the two varibles, expressing one in terms of the other. Then GDP = NDP = p*_{1}y_{1} + p*_{2}[L/a_{L2}  y_{1}a_{L1}/a_{L2}] 
Good 2 = numeraire  Assume: p*_{2} = 1 = p_{2}. [numeraire means "standard good."] p*_{1} = world price of good 1, p_{1} = autarky price of good 1 = a_{L1}/a_{L2}. p*_{1} >? < p^{A}_{1 }= a_{L1}/a_{L2} 
Slope of GDP function (How much GDP increases as y_{1} increases by 1 unit) 
p*_{1}  [a_{L1}/a_{L2}] > 0, which is positive iff (if and only if) p*_{1} p^{A}_{1} is positive. (the world price is higher than domestic price of good 1) 
If p*_{1} a_{L1}/a_{L2} > 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 y_{1} = L/a_{L1}, as shown above. Accodingly, y_{2} = 0. 
If p*_{1}  a_{L1}/a_{L2} < 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 y_{1} = 0, as shown above. 
Food safety: counterexample Finland's organic grain 
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.) Saudi Arabia's rice production in desert areas.
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}= a_{L1}/a_{L2}

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. 
Conclusion  Unless p*_{1}/p*_{2}= a_{L1}/a_{L2} , 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(x_{1},x_{2})
s.t. I = p*_{1}x_{1} + p*_{2}x_{2}. (s.t. = subject to) 
Equilibrium Condition: MRS = p*_{1}/p*_{2} Figure 3. Utility maximization: U^{F} is higher than U^{A}. 

Industrial Revolutions  
First industrial revolution  occurred in the 1800s in the textile industry in UK and spread througout Europe. specialization and division of labor, factories, iron and steel industry, steam engine the Age of mechanical production 
Second industrial revolution  occurred in the early part of the 20th century. noted for Henry Ford's assembly lines (1908), electricity (US houses were wired up with power in 1920), and mass production, especially in the automobile industry. the Age of mass production (e.g., automobiles, airplanes) 
Third industrial revolution  noted for personal computers, Internet and 3D printing. 1990s Democratization of communications. 
Fourth?  Artificial intelligence, robots, autonomous vehicles, Big data, and quantum computing (not materialized yet). US Representative Jake Auchincloss delivered a AIgenerated speech on a bill to create a USIsrael AI center. Need to preclude AIgenerated PhD theses. 
excessive use of robots raises production costs and defective products. 
4. An Example of an Open Economy  
problem  Given u = x_{1}x_{2} MRS (slope of Indifference curve) = x_{2}/x_{1}, p*_{1} = 3, p*_{2} = 1, a_{L1} = 2, a_{L2} = 1, and L = 120. 
Step 1  maximize 3y_{1} + y_{2}, subject to 2y_{1} + y_{2} = 120. Note that p*_{1}/p*_{2} = 3/1 > 2/1 = a_{L1}/a_{L2.} That is, GDP is rising with y_{1}. Thus, the country should specialize in good 1. y_{1} = 60 = L/a_{L1}, y_{2} = 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 = x_{1}x_{2}, subject to 3x_{1} + x_{2} = 180 
Equilibrium condition is: MRS = x_{2}/x_{1} = 3/1 = p*_{1}/p*_{2}, or x_{2} = 3x_{1}. Substitute the above equilibrium condition into the budget line p*_{1}x_{1} + p*_{2}x_{2} = 180 to get 3x_{1} + x_{2} = 6x_{1} = 180. x_{1} = 30, x_{2} = 90, u^{F} = 30 × 90 = 2700. U^{F} = 2700 > U^{A} = 1800. (U^{F} = utility under free trade, U^{A} = utility under autarky. You are halfway through the math portion in this course). 
