Question

Suppose Lisa's utility function is 4XY, where X is the consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is given by MUX=4Y, and the marginal utility of Y is given by MUY=4X .
a. Suppose Lisa wants to obtain a utility level of 48 utils. For each of the following, calculate the consumption of pizza (Y) that corresponds with the given consumption of beer (X) when U=48 .
i. Bundle 1: Beer = 2; Pizza = __________
ii. Bundle 2: Beer = 3; Pizza = __________
iii. Bundle 3: Beer = 4; Pizza = __________
iv. Bundle 4: Beer = 12; Pizza = ____________

Answer 1

Answer:

Bundle 1: Beer = 2; Pizza = 6

Bundle 2: Beer = 3; Pizza = 4

Bundle 3: Beer = 4; Pizza = 3

Bundle 4: Beer = 12; Pizza = 1

Explanation:

Given that;

Lisa utility function UF(X,Y) = 4XY

where;

X = beer

Y = Pizza

$MU_X = 4Y$

$MU_Y = 4X$

The utility level = 48

so, UF(X,Y) = 4XY

putting different values of X (i.e beer ) given to us in this equation, we can calculate the values of Y(i.e pizza) to fulfill the utility

So; when X (beer) = 2

48 = 4×2×Y

48 = 8Y

Y = 48/8

Y = 6

Thus, Bundle 1: Beer = 2; Pizza = 6

when X (beer) = 3

48 = 4×3×Y

48 = 12 Y

Y = 48/12

Y = 4

Thus; Bundle 2: Beer = 3; Pizza = 4

when X (beer) = 4

48 = 4×4×Y

48 = 16 Y

Y = 48/16

Y = 3

Thus; Bundle 3: Beer = 4; Pizza = 3

when X(beer) = 12

48 = 4×12×Y

48 = 48 Y

Y = 48/48

Y = 1

Thus; Bundle 4: Beer = 12; Pizza = 1