# Marginal utility and consumer choice when consumers

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Marginal Utility and Consumer Choice When consumers maximize utility: C F /P P MRS = C F C F /P P /MU MU = Since the MRS is also equal to the ratio of the marginal utility of consuming F and C

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Consumer Choice The utility is maximized when the marginal rate of substitution (MRS) is equal to the ratio of the prices MRS is equal to the ratio of marginal utilities. So at the optimal point the ratio of marginal utilities is equal to the price ratio.
Marginal Utility and Consumer Choice Rearranging, gives the equation for utility maximization: The left-hand side is the utility from1\$ spent on food. The right hand-side is the utility from 1\$ spent on closing. C C F F P MU P MU / / =

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Consumer Choice Food (units per week) Clothing (units per week) 40 80 20 20 30 40 0 Point B does not maximize utility because the MRS = -(-10)/10 = 1 is greater than the price ratio = 1/2 +10 F U 1 -10 C B
Consumer Choice 1\$ spent on food increases the utility by dU=U(F+dF,C)-U(F,C)=U F (F,C)dF dF=1\$/P F So, dU=U F /P F 1\$ spent on clothing increases the utility by dU=U(F,C+dC)-U(F,C)=U C (F,C)dC dC=1\$/P C So, dU=U C /P C

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Consumer Choice If MRS (=MU F /MU C ) > P F /P
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