Question

请大师帮我解答这道中级微观经济学的题目，谢谢了

Jenny's utility is given as U(x,y)=min{2x,4y}. Let Px and Py prices of x and y, respectively, and m denotes her income. Then,
a)Find the ordinary demand functions for x and y.
b)Assuming that Px=Py=$1, show that the sum of the ordinary demands of x and y (x^*+Y^*) is equal to Jenny's income(M).

Answer 1

a)
由题设条件有，
2*x = 4*y ①
Px*x + Py*y = m ②
解由①②组成的联立方程组，得：
x = 2*m/(2*Px + Py) ③
y = m/(2*Px + Py) ④

b)
将
Px=Py=1$
m = M
代入③④：得：
X^* = 2*M/3
Y^* = 2*M/3
故：
x^*+Y^* = M