doubt from workouts

[riyaf]

6.13 (1) Here is a puzzle for you. At first glance, it would appear that
there is not nearly enough information to answer this question. But when
you graph the indifference curve and think about it a little, you will see
that there is a neat, easily calculated solution.80 DEMAND (Ch. 6)
Kinko spends all his money on whips and leather jackets. Kinko's
utility function is U(x; y) = min(4x;2x+y), where x is his consumption
of whips and y is his consumption of leather jackets. Kinko is consuming
15 whips and 10 leather jackets. The price of whips is $10. You are to
nd Kinko's income.
(a) Graph the indifference curve for Kinko that passes through the point
(15;10). What is the slope of this indifference curve at (15;10)?
What must be the price of leather jackets if Kinko chooses this point?
 Now, what is Kinko's income?

answers : slope of IC= -2
              price of leather jackets=$5
              income =$200

Also, please explain the shape of the IC. Why isn't L-shaped ?

[Atika Gupta]

workoutdoubt.JPG

u=min[4x,2x+y]
If, 4x<2x+y, u=4x
    4x>2x+y. u=2x+y
   4x=2x+y, u=4x=2x+y

In the fig. I have drawn both u=4x and u=2x+y. Their intersection point is B. After point B, 2x+y>4x. Hence, u=4x. Before B , 4x>2x+y. Hence, u=2x+y. Thus, IC is given by ABC.

At (15,10), u=2x+y=40. Hence, it lies before B. Slope=-2
For it to be consumer eqbm, MRSxy=px/py. That is, 2=10/py. that is, py=5

and M=10(15)+5(10)=200

[RajEco]

Should it be like this ? Please confirm.@atika

[Atika Gupta]

Yes my mistake. this is the right shape.