Question

Suppose a consumer had a utility function given by: U = X2Y0.5. If the price of Good X (Px) is $3 and the price of Good Y is $6 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $18.75? (Round to the nearest decimal place if necessary.)

Answer 1

Using the utility function we have MRS = MUX / MUY = 0.2X^-0.8Y^0.5 / 0.5X^0.2Y^-0.5 = 0.4Y/X

Slope of the budget line = PX/PY = 3/6 = 0.5

At optimal choice, MRS = PX/PY

0.4Y/X = 0.5

Y = 1.25X

Use this in the budget line equation

18.75 = XPX + YPY

18.75 = 3X + 1.25X*6

X = 1.8

Hence the quantity of good X is 1.8