1. INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 1 FPE and Stolper-Samuelson; tool: Lerner diagram Let’s look at point A on the blue X = 1 isoquant for good X Isoquants of a good cannot intersect (the same combination of capital and labor would then give rise to 2 different levels of output, which is nonsense), so this must be the isoquant of a good. L K X = 1 A Suppose we look at another isoquant through point A, dashed green different Y = 0.5 Let’s say it’s the isoquant Y = 0.5 Suppose p x = 1, then the value of production along the X = 1 isoquant equals 1  1 = 1 Similarly, along the Y = 0.5 isoquant, provided p y = 2 (2  0.5 = 1) These are the unit value isoquants

2. INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 2 One unit of cost for the producer is given by wL+rK = 1 L K In the figure this is given by a straight line with slope w/r and intercept 1/r for K and 1/w for L. 1/r 1/w X = 1 B Y = 0.5 C Note that at point B the value of production of good X is 1 and the cost is also 1 At any other point on the X = 1 isoquant the cost of production is higher Similarly, for point C on the Y = 0.5 isoquant Production of both goods simultaneously is only possible if this figure is consistent FPE and Stolper-Samuelson; tool: Lerner diagram

3. INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 3 FPE and Stolper-Samuelson; tool: Lerner diagram

4. INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 4 Given the prices of final goods p x and p y the unit value isoquants are determined exactly. They are drawn here in the figure L K X = 1 Y = 0.5 There is only isocost line which touches these two isoquants 1/r 1/w B CThis determines the values 1/r and 1/w This implies that if trade between two countries equalizes the prices of final goods and these two countries have identical CRS production functions, then the reward to factors of production w and r are also equalized (FPE) one exactly FPE and Stolper-Samuelson; FPE

5. INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 5 There is a one-to-one correspondence between the prices of final goods and the reward to factors of production Similarly, the prices of inputs w and r give the unit cost line There is only isoquant for good X which touches it L K 1/r 1/w X = 1 B Y = 0.5 C This determines the price p x Similarly, there is onlyisoquant for good Y which touches the isocost line; this determines the price p y one exactly one exactly FPE and Stolper-Samuelson; FPE

6. INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 6 FPE and Stolper-Samuelson; Stolper - Samuelson Take a situation as depicted in the figure and note that good X uses relatively more capital than good Y (slope of line through origin) L K 1/r 1/w X = 1 B Y = 0.5 C Suppose the price of good X increases to p x = 5/4; this shifts the unit value isoquant for good X to 0.8 inward B’ C’ 1/w’ 1/r’ As a result the isocost line touching the unit value isoquants rotates counter-clockwise To touch at B’ and C’ 1/r to 1/r’, so r 1/w to 1/w’, so wrises falls

7. INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 7 L K 1/r 1/w X = 1 B Y = 0.5 C B’ C’ 1/w’ 1/r’ This is the Stolper-Samuelson theorem To summarize: the price of good X rises, this results in a rise in the rental rate of capital (the input used intensively in the production of good X) and a fall in the wage rate (the other input) It generalizes to arbitrary settings in terms of ‘friends’ and ‘enemies’: if the price of a final good rises the reward to some input rises and to some other input falls Also note that the rise in r and the fall in w causes a substitution away from capital in the production of both goods X and Y FPE and Stolper-Samuelson; Stolper - Samuelson