Question

Billie has $800 of income to spend on goods X and Y. The prices of goods X and Y are $200 and $10, respectively. Her utility function is U(X,Y) = X^0.5Y^0.5. How many units of good X does she purchase? How many units of good Y does she purchase?

Answer 1

Answer:

Given, Billie's income, Y=$800 and price of goods X , Px=$200, price of goods Y, Py=$10

Hence the budget constraint of Billie is 200X+10Y=800

And her utility function given as U(X,Y) = X^0.5Y^0.5

We know that utility is maximized when,

MUX PC MRS = MUY Py

Now,

OU(X,Y) MUX = 0.57 0.5 -=0.5.X0.5170.5 X0.5

Similarly,

aU(X,Y) -0.5X0.5Y". MUY = MUY -=0.5X0.570.5- 1 0.5.x0.5 y 0.5

Therefore,

MU: Prospe 200 Y MUY Py => 0.570.5 = 10 => ý = 20 => Y = 20x yos

Now plugging this value in the budget constraint we get, 200X+10Y=800=>200X+10*20X=800=>400X=800=>X=800/400=2

And hence Y=20X=20*2=40

Therefore she will purchase 2 units of good X and 40 units of good Y.