Question

Given the following information:

Quantity (units) TU1 TU2
0 0 0
1 40 20
2 60 36
3 76 45
4 86 51
5 94 53

TU(Total utility)

Assume that P1 = 4 naira per unit and P2= 10 naira per unit:

a. What quantities of q1 and q2 does the consumer buy at the equilibrium point

b. Calculate the total utility that he derives at that point.

c. Calculate the budget line or income of the consumer

d. this result on a ggraph

Answer 1

Solution:

a.). The quantities of q1 and q2 that the consumer buys at equilibrium are as follows:

q1 = 5 Units

q2 = 1 Unit

At equilibrium: $\frac{MU1}{P1} = \frac{MU2}{P2} = \frac{8}{4} = \frac{20}{10} = 2 = 2$

This is displayed by the below table:

 

b.). The total utility that he derives at this point = (P1 $\times$ Q1) + (P2 $\times$ Q2) = (4 $\times$ 5) + (10 $\times$ 1) = 20 + 10 = 30

The total utility that he derives at this point = 30

 

c.). The budget line of the consumer:

Budget line: I = PxX + PyY

Where: I = Total income = 30

           Px = Price of P1

           Py = Price of P2

           X = Q1

           Y = Q2

30 = 4X + 10Y

 

d.). Budget line graph is as below: