Question

If she spends all of her income on trouser and shoe during Christmas shopping, Rahel can afford 8 trousers and 8 pairs of shoes. She could also use her entire budget to buy 16 trousers and 4 pairs of shoes. If the price of a trouser is 400 Birr, then A) How much is Rahel’s income allocated for Christmas shopping? B) What is the budget line equation of Rahel? C) If Rahel’s utility function is U=T0.8S0.2, where T is Trousers and S is Pair of Shoes. What is the optimal combination of Trousers and Pair of Shoes for Rahel?

Answer 1

A) If Pt = 400, then:

$400×8 + Ps×8 = 400×16 + Ps×4,$

4Ps = 3,200,

Ps = 800 Birr.

So, Rahel’s income allocated for Christmas shopping is: 400×8 + 800×8 = 9,600 Birr.

B) The budget line equation of Rahel is:

$400Qt + 800Qs = 9,600.$

C) If Rahel’s utility function is U=T0.8S0.2, where T is Trousers and S is Pair of Shoes, then the optimal combination of Trousers and Pair of Shoes for Rahel occurs at:

$MUt/Pt = MUs/Ps.$