Answer to Question #285366 in Macroeconomics for minnie

Question

Consider a consumer whose utility function is given as: U (x, y) = xy, where x and y denote the quantities of goods x and y consumed. The budget constraint faced by the consumer is: 4x + 8y = 120, where 4 is the price of good x, 8 is the price of good y and 120 is the income of the consumer.

a) Find the optimal quantities for x and y consumed by the consumer. Show your solution diagrammatically

b)Following on the answer in a, now assume that the price of good x increases to 8. Find the new quantities consumed by the consumer

Answer 1

U(X,Y)=XY

$P_x=4$

$P_y=8$

4x+8y=120

a) For Utility Maximization,

$\frac{Mu_x} {Mu_y} =\frac{P_x}{P_y}$

$\frac{4} {8} =\frac{P_x}{P_y}$

4x=8y

x=2y

y=0.5x

From the budget line we have;

4(2y)+8y=120

8y+8y=120

16y=120

y=7.5

So, consumption bundle =(15,7.5)

b) Increase in price of x to 8

$P_x=8$

$P_y=8$

8x+8y=120

a) For Utility Maximization,

$\frac{Mu_x} {Mu_y} =\frac{P_x}{P_y}$

$\frac{8} {8} =\frac{P_x}{P_y}$

$\frac YX =1$

From the budget line we have;

8(y)+8y=120

8y+8y=120

16y=120

y=7.5

8x+ 8(x)=120

8x+8x=120

16x=120

x= 7.5

So, consumption bundle =(7.5,7.5)