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# Principles of Microeconomics ECON 10011

ND

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This 0 page Class Notes was uploaded by Dr. Tracy Kulas on Sunday November 1, 2015. The Class Notes belongs to ECON 10011 at University of Notre Dame taught by Staff in Fall. Since its upload, it has received 40 views. For similar materials see /class/232729/econ-10011-university-of-notre-dame in Economcs at University of Notre Dame.

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Date Created: 11/01/15

Econ 1001 1 Utility Maximization and Cost Minimization Practice Problems Utility Maximization Problems lSuppose your utility derived from consuming slices of pizza P and burgers Bcan be described by the function UQp QB 4QpQB Therefore your marginal utility of pizza is 4QB and marginal utility of burgers is 4QP Assume pizza costs 150 a slice and burgers cost 2 each If your income to spend on food is 12 a week how many slices of pizzas and how many burgers will you eat Maximize UQp QB 4QPQB subject to the budget constraint 15Qp 2QB 12 First set MUpPP MUBPB 4QB 15 4Qp 2 6QP 8Q QB 75QP Then substitute this into your bud get constraint 15Qp 275Qp 12 3Qp 12 QP 4 And QB 3 2 Carrie s utility from shirts and pants can be described by UQs Qp 3QSQP QS 2Qp Her marginal utility of shirts is 3Qp l and marginal utility of pants is 3Qs 2 If her income is 280 and shirts cost 10 and pants costs 20 what is Carrie s utility maximizing number of S and P 14 Shirts and 7 Pants 3 Alice has an income of 24 dollars a week and her utility function for cappuccinos and lattes is UQc QL 2QCQL 3Qc 2QL Her marginal utility for cappuccinos is therefore 2QL 3 and her marginal utility for lattes is 2Qc 2 If cappuccinos cost 3 each and lattes cost 2 each what is her utility maximizing combination of cappuccinos and lattes 6 Lattes and 4 Cappucinos 4 Peter wants to buy tulips and lilies for his garden He has an income of 60 and tulip bulbs are 250 each and lilies are 5 each If his utility function for tulips and lilies is UQT QL 6QTQL then MUT 6QL and MUL 6QT What is his utility maximizing number of tulips and lilies 12 Tulips and 6 Lilies 5 Ellen s utility function for CD S and DVD S is UQc QD ch2 Q1337 So MUC 12Qc39 2 QDW and MUD 37Qc 2 QD3947 If CD S cost 7 and DVD S cost 12 and Ellen s income is 156 how many CD S and DVD S will She buy Hint note that MRS can be reduced to a very Simple form 12 CD S and 6 DVD S CostMinimization Problems 1 Suppose a rm has the production function QL395K395 Q is output of shirts per month and K and L are the capital and labor used to produce the Shirts The marginal product functions are MPL 5Lquot5K395 and MPK 5L5K39 5 Find the costminimizing levels ofL and K to produce Q200 if the price of labor is 5 and the rental rate on capital is 20 Also calculate the total cost of producing 200 units Set MPKPK MPLPL 01 MPK MPL PK PL After simplifying you will end up with 10L 40K s0 L 4K Then substitute this back in the production function specifying that you will produce 200 shirts 200 4K 2K 2 200 2K So you find that K 100 L 400 Then we know that TC PLQL PKQK So TC 5400 20100 TC 4000 2 Suppose a firm can use wool or cotton to make sweaters and the production function for the firm is Q WC The marginal product functions are MPW C and MPc W If wool costs the firm 2 a bag and cotton costs 1 per bag what will the costminimizing combination of wool and cotton be if they want to produce 200 sweaters What will the total cost of that production be assuming no other costs besides raw material C20andW10 TC40 3 The production function for a company is Q 8AB 8B where Q are units produced A is one factory and B is another The marginal product functions are MPA 8B and MP3 8A 8 The cost ofusing factory A is 10 per minute and the cost ofusing factory B is 50 minute What is the costminimizing combination of factories A and B that will allow the company to produce 4000 items a minute Also calculate the minimum cost of producing 4000 items per minute A49andB10 TC990 4 The production function for heating water at Notre Dame is FE G 10E 2G where E is units of electricity and G is units of natural gas The marginal product functions are MPE 10 and MPG 2 If electricity costs 05 per unit and natural gas costs 02 per unit what is the costminimizing combination of electricity and natural gas per day that will allow Notre Dame to produce 200000 gallons of hot water per day Also calculate the minimum cost of producing 200000 gallons per day Note that MPEPE 200 and MPgPG 100 The MP per dollar is always higher for E so use all E 200000 10E E 20000 The TC will be 2000005 1000 5 WalMart can hire either experienced skilled or inexperienced unskilled workers S or U and has the production function Q 2OSU 208 Q is customers checked out per hour The marginal product functions are MP3 20U 20 and MPU 208 Find the costminimizing levels of S and U to get Q 2000 ifthe price of skilled labor is 10 an hour and the price of unskilled labor is 6 an hour Also calculate the total labor cost of waiting on 2000 customers per hour S 775 U 1191 TC 14896

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