A consumer can spend her fixed income of $200 on two products, food (F) and luxu

Question

A consumer can spend her fixed income of $200 on two products, food (F) and luxuries, (L). The consumer’s tastes are represented by the utility function U = F L. Food sells for $2 per unit and luxuries sell for $5 per unit.

(a) Draw the budget constraint of the consumer and explain your diagram. (5 marks)

(b) Compute the amount of each good in the consumer’s optimal basket. Explain your steps. (5 marks)

(c) Assume that the government adds a tax of $1 to the price of luxuries. How does it affect the optimal consumption of the individual? (5 marks)

(d) Under the same conditions as in part (c), compute both the equivalent variation and the compensating variation associated with the new tax. Are these bigger, smaller or the same as the revenues that the government raises through the tax? (5 marks)

Explanation / Answer

a) Budget constraint : p1x1 +p2x2 = M

PF = 2; PL = 5; M = 200

2F+5L = 200

F=0 then L = 40

L=0 then F = 100

B) Optimal choice: max U s.t. PF +PL =M

Z = FL -G(PF+PL -M)

Differentitate Z with respect to F

= L - GPf =0 ; L/Pf = G 1

Diff. w.r.t. L

= F - GPl =0 ; F/Pl = G 2

Diff. w.r.t. G

= -Pf -Pl +M =0

From 1 and 2

F/PL = L/PF

F = LPL/PF

F = L (5/2)

2F + 5L = 200

2(5L/2) + 5L =200

10L = 200

L = 20

F = 5/2 * 20 = 50

Consumer's optimal basket is (F,L) = (50,20)

C) Now PL = PL +1

2F + 6L = 200

After tax F = 6/2 * L

2 (3L) + 5L = 200

11L = 200

L = 18.18

F = 3*18.18 = 54.54

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