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
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![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 \( p_x x + p_y y = I \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9c59a52-435e-40d4-a4cc-d95ba9c85ded%2F401eb31a-f2fb-4076-8823-0178bf228190%2Fgo590q_processed.png&w=3840&q=75)
Transcribed Image Text: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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9c59a52-435e-40d4-a4cc-d95ba9c85ded%2F401eb31a-f2fb-4076-8823-0178bf228190%2Frblug8i_processed.png&w=3840&q=75)
Transcribed Image Text:### 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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