Final answer:
Eileen's consumption in equilibrium with a reduced budget of $10 and the price of movies at $1 would depend on the maximization of marginal utility. Without specific updated marginal utility values, she will aim to use her entire budget to get the highest satisfaction, potentially consuming up to 10 movies.
Step-by-step explanation:
The question given is concerned with how much of each good will Eileen consume in equilibrium if the prices of movies drop to $1 while her movie budget shrinks to $10. At the optimal point of consumption known as Point S, the ratio of marginal utility to price for T-shirts matches the ratio of marginal utility to price for movies, which is given as 22:14 for T-shirts and 11:7 for movies. With a new budget constraint of $10 and a price drop to $1 for both goods, the consumption decision will be based on the maximization of marginal utility while staying within the budget limit.
As both goods have the same price, the decision will be driven by the marginal utility. If Eileen were consuming one T-shirt and six movies at the previous prices and budget, we must assume the marginal utilities were then maximized. With a reduced budget and reduced prices, assuming preferences and marginal utilities remain constant, Eileen would potentially consume up to 10 movies, as T-shirts are not mentioned in the price drop information. However, without specific marginal utility values for the new scenario, a precise distribution cannot be given, only that she will allocate her $10 budget to achieve the highest possible utility.