According to the production function scenario, with a 10% increase in capital per worker, and a 0.25% output gain per 1% capital increase, if initial output per worker is $1,000, what is the estimated output per worker after one year?

According to the production function scenario, with a 10% increase in capital per worker, and a 0.25% output gain per 1% capital increase, if initial output per worker is $1,000, what is the estimated output per worker after one year?

• A. $2,500
• B. $1,250
• C. $1,225
• D. $1,025

Answer: (D)

The main idea is applying the output change from a given capital change using elasticity. If output increases by 0.25% for every 1% increase in capital per worker, a 10% rise in capital leads to a 10 × 0.25% = 2.5% increase in output. Starting from $1,000 per worker, a 2.5% increase yields 1000 × 1.025 = $1,025 per worker. So the estimated output per worker after one year is $1,025.

The main idea is applying the output change from a given capital change using elasticity. If output increases by 0.25% for every 1% increase in capital per worker, a 10% rise in capital leads to a 10 × 0.25% = 2.5% increase in output.

Starting from $1,000 per worker, a 2.5% increase yields 1000 × 1.025 = $1,025 per worker.

So the estimated output per worker after one year is $1,025.