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?

"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?

"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.(4,5)

4.(0,5)

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

Jon's utility function is:

U = 3C 2R

Price of a unit of chicken is, P_C = $6
Price of a unit of rice is, P_R = $2

Income, M = $132

a)

For,

U = 100
3C 2R = 100

The bundles;

1.(30,20)

3C 2R = U
3*30 2*20 = U
90 * 40 = U
U = 360 100

Therefore, bundle (30,20) does not lie on the indifference curve at U= 100

2. (10,35)

3C 2R = U
3*10 2*35 = U
30 * 70 = U
U = 210 100

Therefore, bundle (10,35) does not lie on the indifference curve at U= 100

3. (4,5)

3C 2R = U
3*4 2*5 = U
12 * 10 = U
U = 120   100

Therefore, bundle (4,5) does not lie on the indifference curve at U= 100

4. (0,5)

3C 2R = U
3*0 2*5 = U
0 * 10 = U
U = 0 100

Therefore, bundle (10,35) does not lie on the indifference curve at U= 100

b) The indifference curve for U = 100,

3C 2R = U
3C 2R = 100
R = 50/3C

C	1	2	3
R	16.67	8.33	5.55

Therefore, no the indifference curve is not linear, it is a curve convex to the origin.

c) Given,

Jon's utility function is:

U = 3C 2R

Price of a unit of chicken is, P_C = $6
Price of a unit of rice is, P_R = $2

Income, M = $132

Marginal rate of substituion;

MRS = MUc / MUr
= 3*2R / 3*2C
MRS = R / C

The optimal level of consumption is achieved when;

MRS = P_C / P_R
R / C = 6/2
R/C = 3
R = 3C

Putting this in budget constraint;

P_C C + P_R R = M
6C + 2R = 132
3C + R = 66
3C + 3C = 66
6C = 66
C = 11

R = 33

Therefore, the optimal bundle is ; (11,33)

d) Now, price of rice is; P'_R = $2

MRS = R / C

The optimal level of consumption is achieved when;

MRS = P_C / P'_R
R / C = 6/1
R/C = 6
R = 6C

Putting this in budget constraint;

P_C C + P'_R R = M
6C + R = 132
6C + 6C = 132
12C =132
C = 11

R = 66

Therefore, now the optimal bundle is ; (11,66)

e) Now, there is no chicken to purchase, C = 0

So,

P_C C + P_R R = M
0 +  P_R R = M
2R = 132
R = 66

When , chicken is 0 John'c utility function will be;

U = 3C 2R
U = 0 2R
U = 0