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?

Question

Quizplus · Accepted Answer

Since Nick insists on consuming y at three times the rate he consumes x, his endowment can be expressed as 20x + (3*20)x = 80x for x and 75y for y. Since the price of x is twice the price of y, we can express the budget constraint as 2pxx + pyy = I, where I is Nick's income from trading his endowment (which is zero in this case) and px is the price of x. Substituting py = px/2 and y = 3x, we get:

2pxx + (px/2)(3x) = 80px
4x^2 + 3x^2 = 80
x^2 = 16
x = 4

Therefore, Nick's gross demand for x is:

20 + 3(20) = 80 units of y 
4(20) = 80 units of x

Total expenditure on x = 80px = 4(80) = 320. Therefore, the correct answer is 23.

Nick Insists on Consuming 3 Times as Much of Y