And why do they want me to eat his lunch?

A twenty-five cent meal in 1940 would be $3.84 today (courtesy of 'the inflation calculator'). Not really all that inexpensive.

What if Peterson objects?

I agree with Dave. There is probably no baby in the carriage. I imagine the mother took the child inside the diner with her.

Just leave the kid in the perambulator and catch a quick bite.

Its amazing how often we see things in Shorpy photos that would be considered irrational and even illegal today. I can't imagine why a mother would even think of leaving her baby unattended outside a store.

[What makes you think there's a baby in there? - Dave]

Would the mother carry the baby in her arms while shopping?

[In case it's not ultra-obvious: This is a restaurant. - Dave]

Oops, so it is. I better get my glasses fixed. :-/

One has to wonder if Martin Kane, private eye, is inside pitching the merits of Model pipe tobacco under the pretense of investigating the missing infant. Hap was left to fend for himself a thousand miles straight east, surrounded in his shop by his first love: endless supplies of Dill's Best, Old Briar, Model and Tweed pipe tobacco.

One has to wonder how anyone could serve a dinner for 25 cents, even in 1940, so we can only imagine what incredible gastronomic delights might have been on their dollar menu. I'm having trouble just trying to think of something edible that one can buy today for 2 bits and I keep coming up empty.

To the point, nothing else, just EAT !
And for you Chesterfield fans "Made for smokers like yourself."

Similar to this scene, and about the same time - my mother left my elder sister in the baby carriage while she went into the store (apparently a common thing back then). When she came out, the baby was gone. She screamed and shoppers came a-runnin'. They fanned out and caught a woman with my sister a block away. Her own baby had died and she needed a replacement I guess.