A consumer has his preferences represented by the utility function U(x,y) = min {5x + 4y,...

A consumer has his preferences represented by the utility function U(x,y) = min {5x + 4y, 4x + 7y} if x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (10,10)

a. -4/7

b. -5/4

c. -4/5

d. -7/4

e. -5/7

Expert Solution

Utility function is given by :

U(x,y) = min {5x + 4y, 4x + 7y}

Now at (x,y) = (10,10) we have U = U(x,y) = min {5*10 + 4*10, 4*10 + 7*10} = 90 which lies on segment 5x + 4y (Because at 10,10 this segment will have lower value)

So equation of indifference curve at 10,10 will be U = 5x + 4y = 90 => y = (1/4)(90 - 5x)

Slope = dy/dx = (1/4)*(-5) = -5/4

Thus, Slope of indiference curve at (10,10) is -5/4

Hence, the correct answer is (b) -5/4

Rahul Sunny answered 2 years ago

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