Final answer:
When the price of good x increases, and with the utility function U=min {x, 2y}, the substitution effect results in the consumer substituting away from good x to good y, which becomes relatively cheaper. The magnitude of this effect depends on the specific details of prices and income.
Step-by-step explanation:
The question is asking about the substitution effect of a price increase for a good in the context of indifference curve analysis. In economics, when the price of a good, in this case good x, increases, consumers are expected to substitute away from x towards good y, which has become relatively less expensive. The indifference curve approach indicates that the substitution effect is the change in consumption that arises purely due to the change in relative prices while holding the consumer's utility constant. An individual's demand response to a price change is typically decomposed into a substitution effect and an income effect. The substitution effect captures the change in consumption of goods due to the change in prices only, disregarding the effect of any change in purchasing power.
For the utility function given, where U=min {x, 2y}, if the price of x increases and assuming x and y are both normal goods, the substitution effect would lead the consumer to demand more of good y relative to x. The specific magnitude of this effect depends on the consumer's preferences as expressed through their utility function. A detailed analysis would require additional information such as actual prices and income levels in order to quantify the substitution effect in this scenario.