Answer to Question #188011 in Microeconomics for Addo Benjamin

Question

John is a School of Agriculture graduate and consumes 2 goods: Yoghurt and Bread. Akua also earns a typical student income from the parents, GHS 400 a month. She can either spend it all on Yoghurts and get 50, or she can spend it all on Bread and get 200 loaves.

 

a.      Given this information, construct the equation for John’s Budget Line.

 

b.      John gets a research grant and her income increases to GHS 800 per month. What is the new equation of her budget line? What if income stays constant at GHS 400 and the price of Yoghurts increase to GHS10?

c.     Assume that prices are the same as used in part a. If the marginal utility of a Yoghurt is 20, what is the marginal utility of Bread if she is maximizing her utility?

Answer 1

(a)

Let Yoghurt quantity be, Y

and Bread quantity be B.

Let total income be M, which is 400 in this case. 

Now a general budget line equation is,

$YP_Y+BP_B=M$

Now, if all income is spent on yoghurt, John is able to buy 50 units,

$P_Y=\frac{400}{50}$

$P_Y=8$

Similarly, if spent on bread, he is able to buy 200 units,

$P_B=\frac{400}{200}$

$P_B=2$

Therefore, the budget equation will be,

$8Y+2B=400$

(b)

Now, if income increases from 400 to 800 the budget line will become,

$8Y+2B=400+400$

$8Y+2B=800$

If income remains the same, but the price of yoghurt is increased to 10 then, the budget line will become,

$10Y+2B=400$

(c)

Now, the utility-maximizing equation is,

$\frac{MU_Y}{P_Y}=\frac{MU_B}{P_B}$

MUY is given as 20, therefore,

$\frac{MU_Y}{P_Y}=\frac{20}{8}=2.5$

Putting this equal to the division of MUB and PB,

$\frac{MU_B}{P_B}=2.5$

$\frac{MU_B}{2}=2.5$

${MU_B=}{2.5}\times2$

${MU_B}=5$

Therefore, the marginal utility of bread will be 5.