Learn Farsi: قیمت بعضی از مرغ‌ها گران است. - The price of some of the chickens is high.

ba'zi means "some". When you want to say "some of the [things]", you use ba'zi az followed by a plural noun. Here, az acts like "of", and morgh-ha is plural, so ba'zi az morgh-ha means "some of the chickens".

Is there an unseen Ezafe connector after qeymat (price)?

Yes, there is an Ezafe connecting qeymat to the phrase that comes after it. You pronounce it as qeymat-e ba'zi az morgh-ha. This connects "price" to "some of the chickens", giving us "the price of some of the chickens".

The English translation says the price is "high," but doesn't geran mean "expensive"?

Exactly! In English, you typically say an item is "expensive" but its price is "high". In Farsi, it is very common and natural to use geran (expensive) directly with the word qeymat (price) to describe a high price.

Why does the sentence end with the singular verb ast (is) if we are talking about plural chickens?

The main subject of the sentence is qeymat (the price), which is a singular noun. Even though it is the price of multiple chickens (morgh-ha), the verb must agree with "price", so we use the singular ast.