4. If an individual's utility function for coffee (x) and cream (y) is given by U(x, y) = min (x, 5y), write the demand function for coffee .

3. Suppose an individual's MRS (of steak for beer) is 2s/b and this person is currently consuming equal amounts of steak and beer. Suppose also that the price of a steak is $1 and a beer is $4. Then what should the individual do in order to increase utility? Explain in 3-5 sentences.

To derive the demand function for coffee, we need to determine how much coffee an individual will consume at different prices of coffee and cream.

The utility function given, U(x, y) = min (x, 5y), implies that the individual's utility depends on the minimum amount of coffee (x) and 5 times the amount of cream (y) consumed. This means that the individual values cream more than coffee, as the utility increases by 5 units for each unit increase in cream consumption.

Now, let's consider the individual's budget constraint. Suppose the price of coffee is denoted as P_x and the price of cream as P_y. The individual's income can be represented by M, and the budget constraint is given by P_x * x + P_y * y ≤ M.

Given that the price of coffee is P_x, the individual's utility is maximized when the ratio of the marginal utility of coffee to its price is equal to the ratio of the marginal utility of cream to its price. In other words, when MU_x / P_x = 5 * MU_y / P_y.

From the utility function U(x, y) = min (x, 5y), the marginal utility of coffee (MU_x) is 1, as the utility only increases when an additional unit of coffee is consumed. On the other hand, the marginal utility of cream (MU_y) is 5, as each additional unit of cream consumed increases the utility by 5 units.

Substituting these values, we have 1 / P_x = 5 * 5 / P_y. Simplifying, P_y / P_x = 1/25.

The demand function for coffee (x) can now be derived by substituting the budget constraint into the ratio obtained: x = (M - P_y * y) / P_x.

By substituting the derived P_y / P_x ratio, we get the final demand function for coffee as x = (M - (1/25) * P_x * y) / P_x.

Therefore, the demand function for coffee is x = (M - (1/25) * P_x * y) / P_x.