Question

Carina buys two goods, food F and clothing C, with the utility function U = FC + F. Her marginal utility of food is MU_F= C + 1 and her marginal utility of clothing is MU_C= F. She has an income of 20. The price of clothing is 4.

a) Her demand for food is represented by F = 20/P_F , where P_F is price for Food. True/False.

b) Calculate the income effects on Carina’s consumption of food when the price of food rises from 1 to 4.

c) Calculate the substitution effects on Carina’s consumption of food when the price of food rises from 1 to 4.

d) Determine the numerical size of the compensating variation (in monetary terms) associated with the increase in the price of food from 1 to 4.

Hint: Write the answers for b, c ,d as integer.  

Write the answer for (a) in one word. Note that the answers are spelling sensitive. Please write the spelling of the answers as stated on the questions. (e.g: If your answer is decreases, then in the box write decreases, not decrease.)

Answer 1

Answer (a): False

Correct Answer is F = 12/PF

Explanation : Given, MUF = C+1 and MUC = F

Tangency : MUF / MUC = PF / PC

C+1 / F = PF /4

4C + 4= PF /F ....... equation(1)

Budget Line : PFF + PCC = I

PFF + 4C = 20 .......... equation(2)

Substituting equation(1) into equation(2), we get

4C + 4 + 4C = 20

Thus, C=2 independent of PF

From Budget Line : PFF +4(2) = 20

So, the demand for F is F = 12/PF

Answer (b) : -3

Answer (c): -6

Explanation of (b) & (c) :

Initial Basket : From the demand for food in (a),

F = 12/1 = 12 and C=2,

and also, the initial level of utility is U = FC + F

= 12(2) + 12 = 36

Final Basket : From the demand for food in (a),

F = 12/4 =3 and C=2

Also, the final level of utility is U = 3(2) +3 = 9

Decomposition Basket : U = FC + F =36 ...equation(3)

Tangency Condition satisfied with Final Price,

MUF/MUC = PF/PC

C+1 / F = 4/4

C+1 = 4 ....... equation(4)

Now, equation(3) can be written as,

F(C+1) = 36

Putting equation(4) into rewritten equation(3), we get

(C+1)2 = 36 and thus C=5 also by equation(4), F=6

So, the decomposition basket is F = 6, and C=5

Income effect on F :

Ffinal basket - Fdecomposition basket

= 3 - 6

= -3

Substitution effect on F :

Fdecomposition basket - Finitial basket

= 6 - 12

= -6

Answer (d): -24

Explanation :

PFF + PCC = 4(6) +4(5)

= 44

So, Carina should need an additional income of 24 (plus her actual income of 20).

That's why the compensating variation associated with the increase in the price of food is -24