Question

"Jon consumes chicken (C) and rice (R) for his meals. The price of a unit of chicken is $6, and the price of a unit of rice is $2.

Jon's utility function is: U = (3C)*(2R)

Jon has $132 to spend on chicken and rice."

a) For U = 100, which of the following (C,R) points are on the indifference curve?

1. (30,20)

2. (10.35)

3.(4,54)

4. (0,50)

b) Is the indifference curve linear or non-linear?

c) Determine Jon's optimal bundle of chicken and rice to consume, given his budget and utility function.

d) Now rice goes on sale for $1 per unit of rice. Now determine Jon's optimal bundle of chicken and rice to consume.

e)  If there is a supply disruption and there is no chicken to purchase, what happens to Jon's utility? (Budget is still $132.)

Answer 1

I have answered the first four parts for you. I hope it helps. Please don't forget to upvote.

a) For U=100, Let us check the RHS= 3C*2R separately for all these points.

For (30,20), RHS = (3*30)*(2*20) = 3600

For (10,35), RHS = (3*10)*(2*35) = 2100

For (4,54), RHS = (3*4)*(2*54) = 1296

For (0,50), RHS = (3*0)*(2*50) = 0

Since none of these points give LHS=RHS=100, therefore, none of these points lie on the Indifference curve.

b) Clearly, U = (3C)*(2R) = 6C*R, so, the the utility function is cobb-douglas. Therefore, Indifference curves will be non-linear.

C	1	2	4	10	100/6
R	100/6=16.67	8.33	4.167	1.67	1

If we join all these points with a smooth curve on a (C,R) plane, we will get the IC for U=100. And, as we can see, it is not linear.

c) The utility maximizing bundle can be obtained by forming lagrange to maximize the utility with respect to the budget constraint 6C+2R=132.

Max U = 6CR

Subject to constraint: P_C*C + P_R*R = 132 => 6C+2R=132

Therefore, Jon's optimal bundle is (11,33) in this case.

d) The utility maximizing bundle can be obtained by forming lagrange to maximize the utility with respect to the budget constraint 6C+R=132.

Max U = 6CR

Subject to constraint: P_C*C + P_R*R = 132 => 6C+R=132

Therefore, Jon's optimal bundle is (11,66) in the case of a reuction of $1 in the price of rice.