Impacts of Technological Change on Production, Productivity, and Labor Demand | ACE 551, Assignments of Agricultural engineering

Download Impacts of Technological Change on Production, Productivity, and Labor Demand | ACE 551 and more Assignments Agricultural engineering in PDF only on Docsity! Rhett Farrell ACE551 Fall2006 QPA Ex. 1 - Revised 1 1. Impacts of Technological Change on Production, Productivity, and Labor Demand In our model economy, production requires two inputs, capital and labor. For the short run considered in this analysis, capital inputs are fixed at 3 units; producers will adjust labor inputs to achieve the profit maximizing output quantity. Technology is represented in our production function (presented fully in the appendix) by three exogenously determined efficiency measures. Two of these measures are related to specific factor-saving technology and the third is factor neutral. To evaluate the impact of technology improvements on output, labor productivity, and labor demand in our model economy, a 10% increase (efficiency improvement) in factor neutral technology is simulated in the production function. Figure 1 shows the increase in production from the initial level of technology (Θ0=1.0) to the improved level of technology (Θ0=1.1). As the graph indicates, technology improvements shift the production function upward – greater output is now possible for every level of labor input. This point is reinforced by figure 2, which shows the marginal product of labor under each technology. The upward shift in the marginal product curve reflects the increase in productivity for each unit of labor with the improved technology. Figure 2 also reveals that the marginal productivity of labor decreases as additional labor is added. Figure 1: Shift in Production with 10% Technology Improvement 0 20 40 60 80 100 120 140 160 180 200 2 3 4 5 6 7 8 9 10 Qty Labor Q ty O ut pu t Θ0=1.0 Θ0=1.1 q1 q1 Figure 2: Shift in Labor Productivity with 10% Technology Improvement 0.0 5.0 10.0 15.0 20.0 25.0 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Qty Labor M ar gi na l P ro du ct (l ab or ) Θ0=1.1 Θ0=1.0 The production functions in figure 1 suggest output will increase with the introduction of efficiency improving technology, but calculating the expected change in output associated with this technology advance requires information beyond the production function. For a profit optimizing producer (a reasonable assumption for the producers in our economy), the increase in output associated with a 10% technology improvement has two components. The first component comes directly from the technical improvement in labor productivity. This value can be determined by comparing the output level from the pre- and post-technical improvement production functions at any level of labor input, and in figure 3 this is the vertical move from q1 to q2. The second component of the increase in output is an indirect result of the improvement in labor productivity: when input productivity increases, the input costs essentially decrease relative to the value of the output and the extra profit provides an incentive to increase production. In figure 3, this is the move from q2 to q3. To construct figure 3, an output price of $.057 and a wage rate of $1.00 are assumed. The numerical decomposition of the change in output associated with a 10% improvement in technology is provided in table 1. Given these price and wage assumptions, the increased labor use which results from the changing profit incentives as labor productivity increases accounts for over two thirds of the increase in output. 2 Figure 4: Comparing Production for Selected Elasticities of Substitution 0 20 40 60 80 100 120 140 160 180 200 2 3 4 5 6 7 8 9 10 Labor O ut pu t sigma=0.5 sigma=0.8 sigma=1.2 Figure 5: Comparing Marginal Productivity of Labor for Selected Elasticities of Substitution 0 5 10 15 20 25 2 3 4 5 6 7 8 9 10 Labor M P La bo r sigma=0.5 sigma=0.8 sigma=1.2 Next, the same simulation is used to examine the impact substitution between input factors will have on the supply function. Figure 6 presents the supply function for each elasticity and table 3 calculates the change in output and labor demand for a specific increase and decrease in the output price. Response in both output quantity and labor demand increase with the substitutability between production factors. Looking at the graph in figure 6, when σ = 0.5 the producer’s ability to respond to output price changes is clearly very limited. In 5 contrast, a small change in price prompts a large change in quantity when σ = 1.2. Since substitutability helps preserve the marginal productivity of labor (as shown in figure 5), the producer has greater ability to vary output with labor inputs when the elasticity of substitution is higher. Figure 6: Comparing Supply Curves for Selected Elasticities of Substitution 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.0 50.0 100.0 150.0 200.0 250.0 Output Qty Pr ic e sigma=0.5 sigma=0.8 sigma=1.2 Table 3: Factor Substitutability Impact on Supply and Labor Demand Price increases from $.057 to $.062 σ=0.5 σ=0.8 σ=1.2 Δ output 7.21 12.34 20.38 Δ labor demand 0.43 0.73 1.21 Price decreases from $.057 to $.052 σ=0.5 σ=0.8 σ=1.2 Δ output -8.23 -12.12 -16.42 Δ labor demand -0.45 -0.66 -0.90 Finally, the simulation is used to observe changes in the return to capital (the fixed factor) when the output price changes. The profit and loss from the same output price changes noted above are reported in table 4. As the table indicates, flexibility in the input mix maintains the highest returns to the fixed factor. Again, the ability to more easily alter 6 production by changing the level of labor inputs allows for a more desirable supply response to changes in output price. Table 4: Factor Substitutability Impact on Profit Price increases from $.057 to $.062 σ=0.5 σ=0.8 σ=1.2 Δ profit .1308 .1143 .1100 Price decreases from $.057 to $.052 σ=0.5 σ=0.8 σ=1.2 Δ profit -.1179 -.1143 -.1100 3. Substitutability among Factors and Factor Shares of Income In the final step of the simulation, the factor shares of income are studied to identify the change in labor income that occurs with change in the labor rate. For a given wage increase and wage decrease, the changes in labor’s share of production value are shown in table 5 and the changes in labor demand are shown in table 6. When substitutability among factors is low, the producer has less opportunity to respond to wage rate changes. Thus, table 5 reports the expected results, wage rate increases increase labor’s share of production value when substitution is difficult (and vice versa when substitution is easy). In addition, the change in labor demand in table 6 is more drastic when substitution is easiest. Figure 7 relates labor use to the wage rate and makes apparent that the largest labor use quantity responses occur when substitutability is highest between factors of production. 7