Consider the model of a firm that produces final goods using R&D and components as inputs, with cost data as follows:
Components: Total costs of production = PC €¢ QC €¢ 100
Earnings of high-skilled labor = WH €¢ HC = 10
Earnings of low-skilled labor = WL €¢ LC = 40
Earnings of capital = R €¢ KC = 50
Share of total costs paid to high-skilled labor = 10/100 = 10%
Share of total costs paid to low-skilled labor = 40/100 = 40%
R&D: Total costs of R&D = PR €¢ QR = 100
Earnings of high-skilled labor = WH €¢ HR = 40
Earnings of low-skilled labor = WL €¢ LR = 10
Earnings of capital = R €¢ KR = 50
Share of total costs paid to high-skilled labor = 40/100 = 40%
Share of total costs paid to low-skilled labor = 10/100 = 10%
a. In which factor(s) is components intensive? In which factor(s) is R&D intensive?
b. Suppose that due to the opening of trade, the price of components falls by ˆ†PC/PC = -10%, and the price of R&D remains unchanged, ˆ†PR/PR = 0. Using the hint below, calculate the change in the wage of high-skilled and low-skilled labor.
We follow a procedure similar to that used in Chapter 4 when calculating the change in factor prices in the Heckscher-Ohlin model.
First, write the total costs in each activity as consisting of the payments to labor and capital:
PC €¢ QC = R €¢ KC + WH €¢ HC + WL €¢ LC, for components
PR €¢ QR = R €¢ KR + WH €¢ HR + WL €¢ LR, for R&D
Because we assume that 50% of costs in components or R&D are always paid to capital, then R €¢ KC = 0.5(PC €¢ QC) and R €¢ KR = 0.5(PR €¢ QR), so we can rewrite the above two equations as:
0.5(PC €¢ QC) = WH €¢ HC + WL €¢ LC, for components
0.5(PR €¢ QR) = WH €¢ HR + WL €¢ LR, for R&D
Taking the change in these equations:
0.5(ˆ†PC €¢ QC) = ˆ†WH €¢ HC + ˆ†WL €¢ LC, for components
0.5(ˆ†PR €¢ QR) = ˆ†WH €¢ HR + ˆ†WL €¢ LR, for R&D
Dividing the equations by (ˆ†PC €¢ Qˆ†) and (ˆ†PR €¢ QR), respectively, we can rewrite the equations as:

Use the cost shares and price change data in these formulas to get:

Now solve these two equations for the change in the high-skilled wage, (ˆ†WH/WH), and the change in the low-skilled wage, (ˆ†WL/WL).
c. What has happened to the relative wage of high-skilled/low-skilled labor? Does this match the predictions of the offshoring model in this chapter?

Transcribed Image Text:

(_)( Pe : Qc ) + (Th-人R-Qc) , for componcents -5%-(ara)(100) + (Th )(1000), Δ W// 40 for components WH 100 A for R&D WL / 100 0 W,八100