Question

A budget line is Y = 500 = pAA+pBB = 5A + 10B. Also, the marginal rate of substitution = MRS = =MUB/MUA = -3A/B. Assuming the entire budget is spent on apples and bananas, how many apples are consumed?

Answer 1

Utility maximizing Condition :

(i) In order to maximize utility a consumer consumes that combination of goods where MRS = Slope of Budget line

(ii) As It is given that entire budget is spent then hence it should also satisfy Budget constraint i.e.  5A + 10B = Y = 500

From (i) MRS = -3A/B (Note that Here MRS is defined as MU_B/MU_A, this means that Bananas are on horizontal axis and vertical axis)

From (ii) Slope of Budget line = dA/dB => 5dA/dB + 10 = 0 => dA/dB = -10/5 = -2

Hence MRS = Slope of Budget Line => -3A/B = -2

=> B = 1.5A.

Putting this in Budget Constraint 5A + 10B = Y = 500 we get :

5A + 10*1.5A = 500

=> 20A = 500

=> A = 25

Hence, Total number of apples are consumed = 25 apples.