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 are Paige's Hicksian demand functions?**- Option 1: \[ h_x(p_x, p_y, U) = \left( U - \ln\left(\frac{p_y}{4p_x}\right) + 1 \right) \cdot \frac{1}{4} - \frac{1}{4}; \quad h_y(p_x, p_y, U) = \frac{p_y}{4p_x} \]- Option 2: \[ h_x(p_x, p_y, U) = \frac{p_y}{4p_x}; \quad h_y(p_x, p_y, U) = \left( U - \ln\left(\frac{p_y}{4p_x}\right) + 1 \right) \cdot \frac{1}{4} - \frac{1}{4} \]- Option 3: \[ h_x(p_x, p_y, U) = \frac{p_x}{4p_y}; \quad h_y(p_x, p_y, U) = \left( U - \ln\left(\frac{p_x}{4p_y}\right) + 1 \right) \cdot \frac{1}{4} - \frac{1}{4} \]- Option 4: \[ h_x(p_x, p_y, U) = \frac{p_y}{2p_x}; \quad h_y(p_x, p_y, U) = \left( U - \ln\left(\frac{p_y}{2p_x}\right) + 1 \right) \cdot \frac{1}{2} - \frac{1}{2} \]- Option 5: \[ h_x(p_x, p_y, U) = \left( U - \ln\left(\frac{p_x}{4p_y}\right) + 1 \right) \cdot \frac{1}{4} - \frac{1}{4}; \quad h_y(p_x, p_y, U) = \frac{p_x}{4p_y} \]

Hicksian demand functions are also known as compensated demand functions. Hicksian demand functions…

Py 1 4px Py 4px ○ $ha (Pa, Py, U) = (U - In ( 1 ) + 1). —; hy (Px ›Py,U) = Ohr (Px, Py, U) - Py 4px Py ;hy (Pa, Py, U) = (U-In (P) + ○h (P, Py, U)=;hy = Oh (Pa, Py, U)= ; hy (Pa, Py, U)= Py 2px (Pa, Py, U) 1 4 = 1 1). ¼ - 4 4 Px (U - In ( 12₂ ) + 1) · 1 - 1 4 4 Py U-In ( 2 ) + 1) · 1/2 - 1/ 2

Py 1 4px Py 4px ○ $ha (Pa, Py, U) = (U - In ( 1 ) + 1). —; hy (Px ›Py,U) = Ohr (Px, Py, U) - Py 4px Py ;hy (Pa, Py, U) = (U-In (P) + ○h (P, Py, U)=;hy = Oh (Pa, Py, U)= ; hy (Pa, Py, U)= Py 2px (Pa, Py, U) 1 4 = 1 1). ¼ - 4 4 Px (U - In ( 12₂ ) + 1) · 1 - 1 4 4 Py U-In ( 2 ) + 1) · 1/2 - 1/ 2

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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