Question

Nora consumes only two goods (food and clothing) and her preferences for these goods can be represented by the following utility function

UF,C=F2C $wHQOGMxEDKuywAAAABJRU5ErkJggg==$

where F is the quantity of food consumed and C is the amount of clothing consumed respectively. Suppose Nora’s allocated monthly income on the two goods is $M $AHtd9LKYhu4mwAAAABJRU5ErkJggg==$ and the prices of the two goods (food and clothing) she prefers are $PF $bx6L+sIphTgAAAABJRU5ErkJggg==$ for food and $PC for clothing.

Using the above information write Nora’s utility maximization problem stating clearly the objective function, the budget constraint and the nonnegativity condition. (Hint: Food is on the horizontal axis and clothing on the vertical axis. You do not need to use the Lagrange multiplier to answer this question. Use the simple equilibrium condition of the consumer to solve this.)   

Can someone solve this but use the simple equilibrium condition rather than using lagrange?

Answer 1

Au U=f²c Max: F2c subject to {Budget constraint ů ProF + Pooc=M INon Neratinto y u F70 ? contains J u c70 condition Simple Equilibrium - MRS = Price Ratio MRS z ou OF su 3 с MRS = I FC F2 . MRS z ас F Price Ratio = PF

MRS - Price Ratio o f = ac Pc Pe - 0 AS PE F + Pe. C=M - i Subsituting value of f in Pro fac pe ) + Pc.cz M 0 , we get PF Qc Pc + Pc . C z M 3 colc M Subsituting value of et in f we get Beste coc) 3Pc TC M

_At qilux 1 г Н 3 Pc ² z 2 3 M Pe