Suppose that a consumer had a utility function given by: U=XY3. This consumer has a budget of $48.Fill in the value of this consumer's demand function. X = Answer Question 6[input]*(1/Px).(For instance, if X = 4/Px, then X = 4 * (1/Px) and enter 4)

Question

BlackTom AI · Accepted Answer

We start by identifying the consumer's problem and the given utility function: U = X * Y^3 with a budget of 48 and prices Px and Py for goods X and Y, respectively. To find X as a function of Px (holding Py and income constant), we solve the utility maximization with a Lagrangian: L = X Y^3 + λ (48 - Px X - Py Y).

First-order conditions:
- ∂L/∂X = Y^3 - λ Px = 0 → λ = Y^3 / Px.
- ∂L/∂Y = 3 X Y^2 - λ Py = 0 → λ = 3 X Y^2 / Py.
Equating the expressions for λ gives Y^3 / Px = 3 X Y^2 / Py. Assuming Y > 0, divide both sides by Y^2 to get Y / Px = 3 X / Py, which leads to Y = (3 X Px) / Py.

Next, substitute Y back into the budget constraint: Px X + Py Y = 48. Replacing Y with (3 X Px) / Py yields
Px X + Py * (3 X Px / Py) = 48.
The Py terms cancel in the second term, giving Px X + 3 Px X = 48 → 4 Px X = 48.
Solve for X: X = 48 / (4 Px) = 12 / Px.

Thus X can be written as X = 12 * (1 / Px). In the requested format, this is X = 12 * (1/Px). So the numeric coefficient is 12, which aligns with plugging in the given structure. The result 12 is the appropriate coefficient multiplying (1/Px) to express X as a demand function of Px.

Suppose that a consumer had a utility function given by: U=XY3. This consumer has a budget of $48.Fill in the value of this consumer's demand function. X = Answer Question 6[input](1/Px).(For instance, if X = 4/Px, then X = 4 (1/Px) and enter 4)数值题

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Suppose that a consumer had a utility function given by: U=XY3. This consumer has a budget of $48.Fill in the value of this consumer's demand function. X = Answer Question 6[input]*(1/Px).(For instance, if X = 4/Px, then X = 4 * (1/Px) and enter 4)数值题