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Q1. Suppose a consumer has utility function (u) = xy where x and y are amounts of two commodities that this consumer consume. Suppose this consumer's income is $120, price of good x is $1/ unit and the price of good y is $4/ unit.
Maximize utility for this consumer.
Use the bordered Hessian to test the second-order condition.
Q2. Given the total cost function: C = x2 + 2xy + 2y2 for a firm producing goods x and y. The firm must meet a production quota of 2x + 3y = 40.
Minimize cost for this firm.
Q3. A consumer wants to maximize utility u (x,y) subject to the constraint PxX +PyY = B where x and y are amounts of two commodities that this consumer consume. Suppose this consumer's income is B, price of good x is Px and the price of good y is Py. Assume that the second- order sufficient condition is met so lH¯l = lJl ≠ 0. Find dx/dPx.
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In the above solution we have maximized the utility of the consumer with respect to the given budget constraint. This is one of the applications of economics in everyday life. Typically we have a budget constraint and we try to maximize our utility (satisfaction) with respect to what we have. This application of economics can be used to make best shopping decisions, provided you know how you value different things i.e. you know your utility function.
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