Nick insists on consuming 3 times as much of y as he consumes of x (so he always has y = 3x).He will consume these goods in no other ratio.The price of x is 2 times the price of y.Nick has an endowment of 20 x's and 75 y's which he can trade at the going prices.He has no other source of income.What is Nick's gross demand for x?
A)21
B)115
C)23
D)95
E)We can't determine the answer without knowing the price of x.

Question

Quizplus · Accepted Answer

Since Nick always consumes 3 times as much y as he consumes x, we can set up the following equation for his utility function: U(x,y) = x * (y^3). This ensures he only consumes them in a 3:1 ratio. 
Now, since the price of x is twice the price of y, we can set up the following budget constraint:
2x * 20 + y * 75 = M, where M is Nick's income. 
If we solve for y in terms of x, we get: y = (M - 40x)/75. 
Substituting this into Nick's utility function, we get: U(x) = x * ((M-40x)/75)^3. 
To find the amount of x that maximizes this function, we take the derivative with respect to x, set it equal to zero, and solve for x: 
dU/dx = (M/25) * x * ((M-40x)/75)^2 - 8/5 * x^2 * (M-40x)^2/5625 = 0. 
Solving for x, we get: x = 23. 
Therefore, Nick's gross demand for x is 23.

Nick Insists on Consuming 3 Times as Much of Y