A hole can be dug in one hour with a small shovel and in half an hour with a large shovel.
1. What is the RTS of labor time for shovel size?
2. What does the "one hole" isoquant look like? How much time would it take a worker to dig a hole if he or she used a small shovel for half the hole, then switched to the large shovel?
Answer
\(\boxed{\text{2. If a worker used a small shovel for half the hole and then switched to the large shovel, it would take approximately 0.67 hours (or 40 minutes) to dig the hole}}\)
Step 1 ：Let small_shovel_time = 1 hour and large_shovel_time = 0.5 hour
Step 2 ：Calculate the rate of work done by each shovel: small_shovel_rate = \(\frac{1}{1}\) = 1.0 and large_shovel_rate = \(\frac{1}{0.5}\) = 2.0
Step 3 ：\(\boxed{\text{1. The RTS of labor time for shovel size is 2.0}}\)
Step 4 ：Calculate the combined_rate: \(\frac{1}{2}\) small_shovel_rate + \(\frac{1}{2}\) large_shovel_rate = \(\frac{1}{2}\)(1.0) + \(\frac{1}{2}\)(2.0) = 1.5
Step 5 ：Calculate the time_taken to dig a hole using both shovels: \(\frac{1}{1.5}\) = \(\frac{2}{3}\) hours or 40 minutes
Step 6 ：\(\boxed{\text{2. If a worker used a small shovel for half the hole and then switched to the large shovel, it would take approximately 0.67 hours (or 40 minutes) to dig the hole}}\)
