|1. A Closed Economy's Problem|
elliptic production function
y12 + 4 y22 = KL, MRT = y1/4y2.
(Stars race around a supermassive blackhole of the Milky
Way in an elliptic orbit.)
|Utility and MRS||
U = x1x2, MRS = x2/x1
x1 = y1, x2 = y2.
|How to solve|
|2. An Open Economy's Problem|
K = 80, L = 100,
p*1 = p*2 = 1.
Choose y1 and y2 to Maximize GDP
|Step 2||Choose x1 and x2 to maximize U(x1,x2)
world prices: p*1 = p*2 = 1.
Budget Constraint: p*1x1 + p*2x2 = Io(income from step 1).
Production possibility frontiers, MRT, utility function, MRS, resource supplies and international prices are as follows:
PPF: y12 + 4 y22 = KL,
MRT = y1/4y2.
Utility: U = x1x2,
MRS = x2/x1
Prices: p*1 = p*2 = 2.
|A. Autarky problem||
Find y1, y2, UA, (p1/p2)A in autarky.
|B. Optimal production under free trade||Given international prices, p*1,
p*2, find optimal output, y1, y2, and Io
(maximized income) evaluated at world prices.
|F. Optimal consumption under free trade|| Find, x1, x2,
UF, z1 (= x1 - y1 = export,
if negative) and z2 (x2-y2= import, if
|G. Gains from trade||Evaluate the gains from trade, G = UF - UA.|
|S. Sketch||Sketch the solutions and carefully label points A, B, and F. This concludes the math portion of the course.|
|No more math from now on.|
Mauritz Escher, Amalfi coast