Paige has the utility function $ U(x, y) = \ln(x) + 4y $.Do not worry about corner solutions when answering the following questions; you can use the Lagrangian multiplier method. Paige's budget constraint is $ p_x x + p_y y = I $. ### What is the expenditure function?#### Options:1. **$E(p_x, p_y, U) = p_x g_x(p_x, p_y, I) + p_y g_y(p_x, p_y, I)$**2. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_y}{4p_x}\right) + 1\right) \cdot \frac{p_y}{4}$**3. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_x}{4p_y}\right) + 1\right) \cdot \frac{p_x}{4}$**4. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_x}{2p_y}\right) + 1\right) \cdot \frac{p_x}{4}$**5. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_y}{2p_x}\right) + 1\right) \cdot \frac{p_y}{4}$****Note:** - $ E(p_x, p_y, U) $ denotes the expenditure function.- $ p_x $ and $ p_y $ represent the prices of goods x and y, respectively.- $ U $ is the utility level.- $ \ln $ denotes the natural logarithm function.

Answered: Image /qna-images/answer/401eb31a-f2fb-4076-8823-0178bf228190.jpg

What is the expenditure function? ○ E(Pa, Py, U) = Pa 9a (Pa, Py, I) + Pygy (Pa, Py, I) PxGx O$E(Px, Py, U) = (U − In ( ₂ ) + 1). 4px Py 4 Px O E(P2, Py‚U) = (U − ln ( P ) + 1). 4 4 ○ E(Pz, Py,U) = (U − ln( P + 1)) . På 2Py

What is the expenditure function? ○ E(Pa, Py, U) = Pa 9a (Pa, Py, I) + Pygy (Pa, Py, I) PxGx O$E(Px, Py, U) = (U − In ( ₂ ) + 1). 4px Py 4 Px O E(P2, Py‚U) = (U − ln ( P ) + 1). 4 4 ○ E(Pz, Py,U) = (U − ln( P + 1)) . På 2Py

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

### What is the expenditure function?

#### Options:

1. **$E(p_x, p_y, U) = p_x g_x(p_x, p_y, I) + p_y g_y(p_x, p_y, I)$**

2. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_y}{4p_x}\right) + 1\right) \cdot \frac{p_y}{4}$**

3. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_x}{4p_y}\right) + 1\right) \cdot \frac{p_x}{4}$**

4. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_x}{2p_y}\right) + 1\right) \cdot \frac{p_x}{4}$**

5. **$E(p_x, p_y, U) = \left(U - \ln\left(\frac{p_y}{2p_x}\right) + 1\right) \cdot \frac{p_y}{4}$**

**Note:**
- $ E(p_x, p_y, U) $ denotes the expenditure function.
- $ p_x $ and $ p_y $ represent the prices of goods x and y, respectively.
- $ U $ is the utility level.
- $ \ln $ denotes the natural logarithm function.

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