Exercise Set 2
THE HECKSCHER-OHLIN MODEL: THE FIXED COEFFICIENTS VERSION

I. Objectives

1. To obtain the PPF
2. To obtain the output at full employment
3. To obtain the factor prices, for given output prices
4. To illustrate the Rybczynski Theorem
5. To illustrate the Stolper-Samuelson Theorem

II. Model

• An economy produces two goods - Computers and Steel
• Two inputs - Labor and Capital
• Input-output coefficients are fixed
• Perfectly competitive markets
• Both factors are fully employed

III. Notation

• L: Labor force
• K: Capital stock
• a_ij: Number of units of Input i required to produce 1 unit of Good j,   i = L, K; j = C, S
• P_j: Price of Good j,   j = C, S
• W: Wage rate
• R: Rent on capital (the "price" of capital)

Questions

1. Choose values for the input-output coefficients, labor force and capital stock:

   a_LC = __________,     a_KC = __________, a_LS = __________,     a_KS = __________
   
   L = ___________, K = ___________.

2. Based on the preceding numbers, we conclude that [computers / steel] is the capital-intensive good and [computers / steel] is the labor-intensive good. Explain.

3. Write down the conditions for full-employment for each input. Using the equations, sketch the "full-employment lines." Indicate the intercepts and slope of each line.

4. Compute the outputs of computers and steel that are consistent with full employment of labor and capital. Indicate the values on the graph.

5. Suppose the amount of labor increases.
   • Using a higher value for L, obtain the output produced of both goods.

   • Sketch the results on the graph.

   • The increase in labor leads to [an increase / a decrease] in the output of computers and [an increase / a decrease] in the output of steel. This result is consistent with the [Rybczynski Theorem / Stolper-Samuelson Theorem]. Explain.

6. Choose values for the output prices:   P_C = _________,     P_S = _________.

7. Using the zero-profit conditions, obtain the equilibrium values of input prices. Provide a sketch with W and R on the two axes, and indicate the equilibrium values. Assume that these are the autarkic input prices.

8. Let's say that, after trade occurs, the price of computers rises.
   • Assuming that the zero-profit condition continues to hold, the outcome is [higher / lower] wages and [higher / lower] rent on capital. Explain.

   • This result illustrates the [Rybczynski Theorem / Stolper-Samuelson Theorem]. Explain.

   • Show the results on the graph.

9. Labor unions in the U.S. and EU argue that trade between developed countries and developing countries will lead to declining wages in the former (and rising wages in the latter.)
   • Using the Stolper-Samuelson Theorem, provide a justification for the argument.

   • Is it possible that, even if the SS theorem holds, not all workers in the developed countries stand to lose from trade? Explain.

   • Provide arguments that weaken the extreme implications of the theorem. (Hint: Think of reasons why factor equalization may not occur in real life.)