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# ass 2 - ECONOMICS 5300 ASSIGNMENT 2 SOME PRELIMINARIES ON...

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ECONOMICS 5300 ASSIGNMENT 2 SOME PRELIMINARIES ON MICROECONOMICS AND REVIEW OF CHAPTERS 3 AND 5 1. THE PRODUCTION FUNCTION OF A FIRM IS GIVEN BY: Q = L 0.4 K 0.5 FOR Q = OUTPUT, L = LABOR, AND K = CAPITAL. a) DERIVE THE MARGINAL PRODUCTS OF LABOR AND CAPITAL. b) DOES THIS PRODUCTION FUNCTION HAVE THE PROPERTY OF CONSTANT RETURNS TO SCALE, INCREASING RETURNS TO SCALE, OR DECREASING RETURNS TO SCALE? DERIVE AND SHOW YOUR ANSWER. c) GIVEN YOUR ANSWER TO b) ABOVE, WHAT DOES THE RETURNS TO SCALE PROPERTY OF THE PRODUCTION FUNCTION IMPLY ABOUT COST CONDITIONS? ARE COSTS INCREASING, DECREASING OR CONSTANT AS PRODUCTION IS INCREASED? DERIVE YOUR ANSWER.

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2. SUPPOSE A PRODUCTION FUNCTION WHERE OUTPUT Y IS RELATED TO A SINGLE INPUT, X IN THE FORM, Y = X 0.9 . a) DERIVE THE TOTAL COST FUNCTION THAT IS DUAL TO THIS PRODUCTION FUNCTION IF THE PRICE OF THE INPUT, X, IS r. b) DERIVE THE AVERAGE AND MARGINAL COST FUNCTIONS FROM THE TOTAL COST FUNCTION THAT YOU DERIVED IN a) ABOVE 3. THE DEMAND FUNCTION FOR PIPE WRENCHES IS GIVEN BY: Y = 0.4P -1.05 , FOR Y = QUANTITY OF PIPE WRENCHES DEMANDED, AND P = PRICE OF PIPE WRENCHES.
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