{'fraction_non_alphanumeric': 0.023977433004231313, 'fraction_numerical': 0.0, 'mean_word_length': 5.228070175438597, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The Theory of Quantity Discounts and Optimal Pricing

This paper explores a monopolist's optimal multi-tier quantity-discount prices and shows that only the last tier's marginal cost is relevant in determining the tier prices and each tier's price is equal to its preceding tier's marginal revenue. An increase in total output is associated with larger individual tiers' own and cumulative outputs (the stretching effect), and the increases in their cumulative outputs are smaller if their tiers are closer to the first one (the ripple effect). The pricing structure is further characterized by the tier-Lerner indices and the price elasticities defined on individual tiers' own and their commutative outputs.