Question

Given that Rumbi’s budget line is 25 = 4Qcake + Qtea and the price of tea is R10. what is Rumbi's income and the price of cake ?

Answer 1

The equation for the budget line will be, $25=4Q_c+Q_t$

From the budget line above, the X- intercept will be 4units while the Y-intercept will be 1unit.

$P_t(price\ of\ tea)=R10$

$P_c(price\ of\ cake)=?$

$Q_c=4$

$Q_t=1$

$M(income)=?$

$Income(M)= (P_c\times Q_c)+(P_t \times Q_t)$

$M=P_cQ_c+P_tQ_t$

The budget line has intercept $Q_t=1unit$ and $P_t=10$ then Income will be;

$1\times10=R10$

Therefore, Rhumbi's income will be $R10$

Price of cake $(P_c)$ is the point of interception with the Y-axis.

$10=(P_c\times4)+(10\times0)$

$10=4P_c$

$P_c=R2.5$

Therefore, the price of the cake will be $R2.5$