You are a wine collector and you have $1000 to fill a small wine cellar. You are choosing between Pinot Noir priced at $30 per bottle and Pinot Grigio priced at $15 per bottle. You know that your utility function is given by U=15N 0.8

G 0.2

. a. How many bottles of Pinot Noir and how many bottles of Pinot Grigio will you have in your wine cellar? How much utility does this combination give you? b. Assume Pinot Grigio goes on sale for $10 per bottle. How does this change your consumption of wine? c. Based on the change you found in part b, isolate the income and substitution effects. d. You get a $100 raise. Assuming no change in your utility function and the original prices of wine, how much does your utility increase as a result of the raise?

a. To determine how many bottles of Pinot Noir and Pinot Grigio you will have in your wine cellar, we need to find the combination that maximizes your utility function. Given the utility function U = 15N^0.8 * G^0.2, we want to allocate our $1000 budget in a way that maximizes U.

Let's assume you buy x bottles of Pinot Noir and y bottles of Pinot Grigio. Since the price of Pinot Noir is $30 and Pinot Grigio is $15, the following equation can be used to represent the budget constraint:
30x + 15y = 1000

To find the combination that maximizes utility, we can solve this equation by substitution or elimination methods. However, since it is the utility function that is provided and not preferences, it is not possible to determine the exact combination and the corresponding utility.

b. If Pinot Grigio goes on sale for $10 per bottle, the following equation can be used:
30x + 10y = 1000

c. To isolate the income and substitution effects, compare the change in consumption of Pinot Grigio when the price decreases. Changes in consumption can be attributed to the substitution effect.

d. To determine how much your utility increases as a result of a $100 raise, we need to calculate the marginal utility of income. Since your utility function is U = 15N^0.8 * G^0.2, we can calculate the marginal utility of income as the derivative of the utility function with respect to income:

dU/dI = ∂U/∂N * ∂N/∂I + ∂U/∂G * ∂G/∂I

Since your utility function does not include the variable I (income), the marginal utility of income is zero. Therefore, your utility does not increase as a result of the raise.

Utility increase after change in price: https://brainly.com/question/33788461

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