What would happen in a perfectly competitive market for apples in the short-run to the market and to individual producers if the price for pears...

If the price of pears goes up, the demand for apples will rise.  This will mean that the market for apples will see an increase in price and an increase in quantity demanded.  The individual farmer will see an increase in price.

This answer assumes that many people will see pears and apples as substitute goods.  That is, people are more or less willing to buy either pears or apples, depending on the price.  If...

If the price of pears goes up, the demand for apples will rise.  This will mean that the market for apples will see an increase in price and an increase in quantity demanded.  The individual farmer will see an increase in price.

This answer assumes that many people will see pears and apples as substitute goods.  That is, people are more or less willing to buy either pears or apples, depending on the price.  If the price of pears goes up, people will, ceteris paribus, buy more apples.  They will buy fewer pears because of the price increase and will go buy apples instead.

In perfect competition, the entire market faces a demand curve that has a negative slope.  When the price of pears goes up, the demand for apples rises.  The market demand curve retains its negative slope, but moves to the right.  This means that, ceteris paribus, the price of apples rises as does the quantity demanded.

In perfect competition, the individual producer does not face a sloped demand curve. Instead, the individual producer’s demand curve is perfectly horizontal.  The producer can sell as much as they can produce at the market price.  When the market price changes, the individual producer can sell at the new, higher market price.  However, because their demand curve is flat, they do not get to sell any more than they could before.  Even before, they could sell as much as they wanted.  This has not changed.

Thus, an increase in the price of pears will lead to an increase in the market price and market quantity demanded of apples.  Individual producers will see an increase in price but not in quantity demanded.  Please follow the link below and scroll down to “Section 02: Pure Competition in the Short Run” to find graphs that show these changes.