Final answer:
The total output growth rate for Antegria with a 3 percent increase in labor force, capital stock, and TFP is approximately 9 percent, due to compounding effects on economic growth.
Step-by-step explanation:
The student's question pertains to calculating the total output growth rate in the hypothetical land of Antegria when the labor force, capital stock, and total factor productivity (TFP) all increase by 3 percent. To determine the total output growth rate, we cannot simply add the individual percentage increases together because the overall effect on output is multiplicative, not additive. In an economy, increases in labor force, capital stock, and TFP interact with each other and contribute to overall economic growth. Therefore, we apply the concept of compound growth rates to find that the total output growth will be more than any individual increase but less than their simple sum.Using the formula for compound growth (1+r)n, where r represents the growth rate and n the number of variables growing, we can understand that if one element grows by 3%, the growth factor is 1.03. When we have three factors growing at this rate, we multiply them to get the overall growth factor, which is 1.033 = 1.092727. Subtracting the base of 1, the total percent increase in output is approximately 9.27%, which when rounded to the nearest whole number, gives us a 9 percent growth. Thus, the main answer is b) 9 percent.In conclusion, the interplay of increased labor, capital, and productivity leads to a compounded effect on economic growth, exemplifying how small annual increases have significant impacts over time on an economy's GDP per capita.