Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of cheese. If the total cost of x units of cocoa is x², the price of cheese is $8, and Casper's income is $174, how many units of cocoa will he consume? A) 9 B) 11 C) 12 D) 23 E) 24

Question

Quizplus · Accepted Answer

Casper's budget constraint can be expressed as:

xS1U1P1 + yS1U1P0 = I

Plugging in the given values:

xS1U1P1 + 8y = 174

Solving for y:

y = (174 - xS1U1P1)/8

Now, we can plug this into Casper's utility function:

U = 3x + y = 3x + (174 - xS1U1P1)/8

To maximize utility, we will take the derivative and set it equal to zero:

dU/dx = 3 - (1/8)S1U1P1 = 0

Solving for x:

x = 24/8 = 3

Therefore, Casper will consume 3 units of cocoa.

Casper's Utility Function Is 3x + Y, Where X Is