Georgina consumes only grapefruits and pineapples. Her utility function is U (x comma y )equals x to the power of 0.8 end exponent y to the power of 0.2 end exponent, where x is the number of grapefruits consumed and y is the number of pineapples consumed. Georgina’s income is $105, and the prices of grapefruits and pineapples are $4 and $3, respectively. How many grapefruits will she consume?

21

Explanation:

Given that:

The utility function U(x, y) =

The budget line income is:

105=4x +3y

The equation MRTS is:

where;

and:

∴

Using the equation MRTS:

4x = 12y

x = 12y/4

x = 3y

Replacing the value of x into the budget line income, we have:

105 = 4x + 3y

105 = 4(3y) + 3y

105 = 12y + 3y

105 = 15y

y = 105/15

y = 7

Then, from x = 3y

x = 3(7)

x = 21

Thus, she will consume 21 gapefruits

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