Econ 103 Practice Problems #5 l. Let U-10XY\". MU,-1 OY 12, MU,-5XY12, Px=$5, Py

Question

Econ 103 Practice Problems #5 l. Let U-10XY". MU,-1 OY 12, MU,-5XY12, Px=$5, Py=$20 and i=$ 180 a). What is the equation for the budget line? b). What is the equation for MRS? c). Interpret your MRS equation. d). What is the equation for the income consumption curve? e). What is the equilibrium level of X, Y and U? f). What is the equibium level of MUx, MUy and MRS? Let Px change to S10. g) What is the equation for the new income consumption curve? h). Why do we need a new ICC? i). What is the new equilibrium level of X', Y' and U? j). What is intermediate point for both X and Y? k). What are the S.E. and LE.? Is X a normal good? Explain. I). In a diagram, show the old and new equilibrium points, the ICCs, budget lines, the utility curves, intermediate point, S.E. and LE

Explanation / Answer

a. Budget Line Equation = I = Px.X+ Py.Y

180 = 5X + 20 Y

b. MRS = MUx/MUy = 10Y1/2 / 5XY-1/2

MRS = 2 Y/X

c. It means if you want to consume one unit of X you will have to sacrifice two units of Y.

d. Income consumption curve is the relationship between income and consumption of good X as well as good Y.

AS per law od equi marginality, at equilibrium MUx/PX = MUy/Py

10Y1/2 / 5 = 5XY-1/2 / 20

2Y/X = 1/4

X = 8Y

Substitute in budget equation

I = Px. 8Y + Py.Y

ICC for Y, Y = I /(8Px + Py)

Y = X/8

ICC for X = I ( Px + Py/8)

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