Briefly explain the following:

Question

(a)Economic cost and accounting cost.
(b)Free market economy and mixed economy.
(c)Marginal utility theory and indifference curves analysis.

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3. please Answer the following questions about Lagrange multipliers and optimal
choice
(a) Let the utility function for good x and y be y + ln (x) (natural loga-
rithm). Write out the Lagrangian function and …rst order conditions.
Find the demand function. Find the income and substitution e¤ects
(in derivative form) of an increase in the price of good x, and y.
(b) Solve for the Cobb Douglas demand functions for utility function
u (x; y) = x�y � (in this case let � + � > 1). Also suppose that the
consumer has an endowment of x0 units of good x and y0 units of
good y (so the consumer maximizes utility subject to the constraint
that the value of chosen consumption is less than or equal to px0+qy0 .
Find the income and substitution e¤ects in derivative form.
(c) For utility function y +bx …nd the demand function when p < b and
q = 1. Can you …nd the Lagrangian multipliers for this case?

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