Question $3[30$ MARKS$]$

Anatu's utility function for good $x$ and $Y$ is given by $U(x,Y)=2x^2{Y}^2.Px,Py$ and $M$ are the

price of good $x,$ price of good $Y$ and consumer income respectively. If $M=200,Px=4$ and

$Py=5.$ Also, the $)x$ and $)y.$ Use the information above to solve the

problems below.

i$.$ Write the budget Constraint of the consumer.

$4$

ii$.$ Derive the demand functions for good $x$ and $Y.$

iii. What combination of $x$ and $Y$ maximizes the consumer's utility?

iv$.$ Calculate the marginal rate of substitution between $x$ and $Y$ at equilibrium and interpret

your results.

v$.$ Sketch the budget line for this goods and state TWO reasons that may lead to a shift in

the budget line.

$50,\frac{700}{5}=$

$4$ marks

$12$ marks

$6$ marks

$4$ marks

$4$ marks