b$)$ Consider an equilibrium model of a simple demand and supply of a particular good as follows:

$F^1$:

$F^2$:$Q^{**}=S(P^{**},R),S_{P^{**}}>0,S_R<mn\; id="EditorElement\_1981263">0</mn>$

where $Q^{**},P^{**},Y,R$ are respectively, equilibrium quantity and price, income, and the price of an input, used in the production of the good.

i$)$ Express both the demand and the supply equations above in their implicit version. $(2$ marks$)$

ii$)$ Next, totally differentiate the functions just obtained in i$).$

$(4$ marks$)$

iii$)$ Now, assuming $R$ changes while $Y$ remains fixed, rewrite your findings in ii$)$ in the $Jx=B$ form.

$(5$ marks$)$

$1$

BEEQ$2013$ MATHEMATICAL ECONOMICS

FIRST SEMESTER $2023/2024$ SESSION

MATRIC NO$.$:

iv$)$ Next, evaluate the effect of an increase in the price of input $($R$)$ on the equilibrium quantity and price of the good in the market.

$(10$ marks$)$