Answer to Question #242661 in Microeconomics for Sunshine

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 graph

Answer 1

Budget line is a locus of all those combinations of two goods which a consumer can afford.

$p_1\times q_1 + p_2\times q_2 = m$

This is the equation of budget line.

Law of equi marginal utility states that a consumer will continue to consume two good till he get the equal marginal utility in terms of money so

$\frac{MU_x}{px} = \frac{MU_y}{p_y}$

Here marginal utilities of good x and good y in terms of money and to calculate MU in terms of money, we'll divide the MU of gooda by their price level.

a)According to equilibrium marginal law

$\frac{MU_x}{p_x} = \frac{MU_y}{p_y}\rArr \frac{MU_1}{p_1} = \frac{MU_1}{p_1}$

so

q₁=5 units

q₂=1 unit

b)$TU=10+5+4+2.5+2+2=25.5 \space units$

c) Budget line $p_1\times q_1 + p_2\times q_2 = m$

m=income

$4 q_1 + 10 q_2 = m$

at equilibrium level $4\times 5+10\times1=30\space naira$

if consumer income is 30 naira then he can afford

$q_1=\frac{30}{4}=7.5\space units\\q_2=\frac{30}{10}=3\space units$

d)