Question

Margaret spends all of her income on t-shirts (x1) and shoes (x2). Her preferences can be represented by the utility function u (x1, x2) = 2√x1x2

(a) [15 Points] Derive the demand functions for t-shirts and shoes in terms of the price of t-shirts (p1), the price of shoes (p2), and income (m). Show your result on a graph.

(b) [10 Points] Draw the Income Offer Curve and Engel Curves (one for each good).

(c) [10 Points] Draw the Price Offer Curve and Demand Curves.

(d) [5 Points] Suppose the price of shoes are $16, the price of a t-shirt is $16, and Margaret has $128 income. What is the optimal bundle of t-shirt and shoes (x1, x2) which gives her the highest utility?

Answer 1

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MUXI MUZ margtnal tliEY 0LA aginal MURE m MascE 22c2 MRSE 22 at optimal P2 22 221 also be same at 22 Scanned with CamScanner

Page No. Sothe demand function of r and m 2P2 Shoes thddftcren Corue budget line tCtshirtS and ih the Mar4ant wilL consame X ptlmal ahove diar am ith are the pundle Whtch his income Part B atter Curve Income Sheors cs Scanned with CamScanner tchirt

Epeturve en ged corvel for tshirtS Shoes 21 when the ncome ofthe t also increases RSaptimal consumptione offer am Ancre a ses The income ahoue Curve in the dta the income incre entas the optinalcansam ption ot Mrgaret also increases aboue exempER ARO Show diagram engel relattop income Shaes relation ship eases the Thre Shows Chip relation ship of chirt an & Linert as chown aboue the Curve with uhich is Scanned with CamScanner

Date Page No. Part C hae Prtce offer Curue shirts Demand Tet Den an Curve tor Shoes Curde Price tshict Shees uhen the price f the da d t'sdemand fallk Such YIses re lation ship is shown by the pnce In ahove e t tisthe 0f fer curue helow dia ram Dem an a corue for Shoes an a t-Shtrts Showint prtce inverse relatlon go0ds an d CScanned with CamScanner

Date Page No. Part D Price ot Shaes frice ot $16 -Shirt 16 Mar dart Tncome The optimal hundle will be MRSE X2 16 16 O+ 32 128 32 7 A s SO So ttez he will consume chirts and Shoes to hts utilitY maximie the incomeot at ScahneKwith CamScanner