Consider a consumer who purchases two goods, X and Y. The utility function of th

Question

Consider a consumer who purchases two goods, X and Y. The utility function of the consumer is U(X, Y) = Y x

MUx = 1/2 Y x and MUy = x . Suppose the consumer has an income of $1500 and X has a price of $5 and Y has a price of $10.

What bundle of X and Y will be consumer purchase? What will be his utility level at the optimal bundle? Suppose the price of Y decreases to $1, what purchase decision will the consumer make? What will be her new utility level?

Compute the substitution and income effects associated with the reuction in the price levels of Y from $10 to $1.

Explanation / Answer

1500 = Px*X + Py*Y 1500 = 5X + 10Y where X and Y are the amount of X and Y that the consumer would buy U=Yvx the bundle of goods that will maximize the utility of the consumer subject to the budget constraint would be MUx/Px = MUy/Py 1/2*Y/vx / 5 = vx / 10 Y = X hence the quantity of Y = Quantity of X put this in budget equation 1500 = 5X + 10X (since Y=X) X = 100 Y = 100 these values of X and Y will maximise the utility of the counsumer given its budget constarint U(X, Y) = Y vx=100*10=1000 b) MUx/Px = MUy/Py 1/2*Y/vx / 5 = vx / 1 Y = 10X 1500 = 5X + 100X x=14.3 y=143 U(X, Y) = Y vx=143*3.78=540.76 substitution effect=143-100=43 income effect=0

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