At that time, the overall cash supply was a lot smaller relative to the GNP than it is today. There just wasn’t that much cash around. This was a HUGE political issue at the time. The populist movement was getting started around that time, and their big issue was the tight money supply and its effect on midwestern farmers. Remember William Jennings Bryan and his Cross of Gold speech in 1896?
The Ingalls family didn’t see much cash. Even in later years when they were more prosperous, they used relatively less cash than we would today. (I haven’t read the books in ages, so I’ll talk in terms of the TV show.) Ma would sell eggs to Mr. Olsen’s store, and buy goods there. He gave her credit for the eggs, not cash. She would then “spend” the credit in the store. This seems like a decent enough arrangement until you consider that by taking credit rather than cash, Ma was locked into shopping only at the Olsen’s store. There wasn’t any place else to shop in Walnut Grove, of course, but if she had had some cash, she could have taken it on her occasional trips to Mankato, and bought at Kato-Mart, which had much lower prices and a bigger selection.
In light of that situation, the role of Mrs. Olsen changes dramatically. She was portrayed as an overbearing greedy busybody, but she was basically played for a laugh. But considering that she was in charge of the only store in town, she becomes significantly less benign. Would someone like her have inflated prices? Certainly. Sold inferior goods for premium prices? Of course. Refused to let people return defective items? Yup. Many story lines on the show focused on her conflicts with her husband, who was basically a decent guy, but quite a wimp. He tried to deal fairly with the Ingalls family and other townspeople, and she would step in and try to work things to the store’s advantage. On the show, the fair and the good always won out, but in real life? I doubt it. Think of what it would have been like to have to shop with the real Mrs. Olsen. It would have been a real problem. And the limited cash flow prevented people from taking their money elsewhere. It also meant that a new store was unlikely to open. An established store run by a prosperous family could afford to let people buy on credit. It would be a lot harder for a start-up to do that.
So, to make a long story short, the “value” of the shiny penny was far more than its actual buying power, especially in 1870, when the Ingalls were much poorer than they were in the Walnut Grove years. It represented the very rare opportunity for the girls to have some actual buying power of their own.