Final answer:
Selling public land allowed the state to raise revenue for governmental operations and encourage economic development, while giving it away promoted widespread settlement and improvements, along with supporting public works such as railroads.
Step-by-step explanation:
The advantages to the state in selling public land included the generation of revenue in an era devoid of federal income tax, providing funding essential for government functions without the need to incur large budget deficits, and stimulating economic growth and development. Selling land also enabled those with financial means to acquire prime lands, potentially boosting agricultural output and settlement expansion. On the other hand, giving away land, as seen through the Homestead Act and other initiatives, encouraged widespread settlement, improved lands, and facilitated public works like the construction of railroads, which served the broader public good by creating a nationwide transportation network.