Question $3[30$ MARKS$]$

Anatu's utility function for good X and Y is given by U$($X$,$ Y$)=2$X$7$y$?.$ 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$=$S$.$ Also, the MU$,=4$XY and MU$,=4$XY$.$ Use the information above to solve the

problems below.

i

Write the budget Constraint of the consumer.

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$4$ marks

ii$.$

Derive the demand functions for good X and Y$.$

$12$ marks

ili.

What combination of X and Y maximizes the consumer's utility?

$6$ marks

iv$.$

Calculate the marginal rate of substitution between X and Y at equilibrium and interpret your results.

$4$ marks

v$.$

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

$20$