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Unformatted text preview: ugging the optimal values of food an housing into the utility function, we have
, 1259.9 A6) What is the optimal value of the Lagrange multiplier? Is it positive or negative? How
would you interpret the value?
Either of the first two firstorder conditions will work. In the first condition,
.
∙ This means that a $1 relaxation of the budget constraint raises utility by 0.04. This means
there is a positive marginal utility of income.
A7) Your third firstorder condition is the budget constraint. Replace the net income figure
$30,000 with the variable Y representing income and compute the equations representing demand
for food F and housing H. You should have an equation that includes coefficients and Y. This should be the formula for the Engel curve shown in Figure 2. Interpret the formula for the Engel
curve for housing H.
The budget constraint will be
. Then the reduced form equation for food
can be derived by inserting H=4F into the budget constraint. We have
or The reduced form demand for housing is derived from or The Engel curve shows that as income rises, demand for housing rises and so housing is a
normal good. The s...
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 Fall '07
 CORINNELANGINIER

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