High production costs affect prices because firms must have prices that are high enough to cover the costs of production. If a firm charges a price that is lower than its costs of production (technically, a price that is lower than its average variable costs) it will go out of business. This is because it will be losing more money by making the product than it would if it simply shut down.
Of course, firms cannot simply raise their prices to offset high production costs if other competitors can produce more cheaply or if customers will not pay the higher price. However, high production costs do affect prices since firms will either have to raise prices high enough to cover their costs or go out of business.