When deriving an individuals demand curve how do you find the optimal bundle if you are only given: price of 2 goods and income.
i.e-
price of wine: $35
price of beer: $12
Income= $419
To find the optimal bundle of goods when deriving an individual's demand curve, you need to compare the ratio of the prices of the two goods to the individual's marginal utility for each good. Here's a step-by-step guide:
Step 1: Determine the marginal utility for each good.
You need additional information to obtain the individual's marginal utility for wine and beer. Without this information, we can't proceed with deriving the demand curve accurately.
Step 2: Compare the ratio of prices to marginal utilities.
Assuming you have the marginal utility information for wine and beer, calculate the ratio of prices (wine/beer) to the ratio of marginal utilities (MUwine/MUbeer). The ratio should be equal to maintain the individual's optimal bundle.
Step 3: Calculate the quantity of wine and beer.
Let's assume, for example, the individual's marginal utility ratio is 2 and the price ratio is 2.5 (35/12). If MUwine/MUbeer = 2 and the price of wine/price of beer = 2.5, the individual would allocate more of their budget towards beer because the marginal utility per dollar spent is higher for beer.
Step 4: Allocate the budget.
To find the quantity of each good, you need to allocate the individual's income across the two goods. Using the price and quantity relationship, divide the income by the price of each good and then allocate accordingly.
For the example provided:
Price of wine: $35
Price of beer: $12
Income = $419
Assuming you have the marginal utility information, you can calculate the quantities of wine and beer as follows:
Quantity of wine = (Income / Price of wine) * (MUbeer / MUwine)
Quantity of wine = (419 / 35) * (MUbeer / MUwine)
Quantity of beer = (Income / Price of beer) * (MUwine / MUbeer)
Quantity of beer = (419 / 12) * (MUwine / MUbeer)
Please note that without the specific marginal utility information, it is not possible to provide the exact quantities of wine and beer.