Question

A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold = 1, Py = 1, and I = 8. a. Solve for the Marshallian demand functions of x and y (your answer should have numbers, not variables. You should round your answers to three decimal places): * old 4 y = 4 b. What is the utility associated with these demands, prices, and income? u = 16 c. Suppose the price of x rises to P, new = 3. What is x at the new price? x = 1.778 d. What is the substitution effect (for x)?: Substitution Effect = -2.222 e. At the new price Pnew = 3. What is the Marshallian demand for x? ** new = 1 f. What is the income effect (for x)? Income Effect = 5

Answer 1

A consuuss Puetuence i o(ky)=xy Prold, 1, Py = 1 and I=8 Now, Maginal ability of a MUY = ou cry.u MUX S ax and Marginal utility ory su (xsy) . x muye Now, budget constaint, Iz Prold x + Py y 2) 8= x + y Condition will be utility manime'sine Now, Pxold a MUX py Μυγ =) = =) Y=x substituting y = x in the budget constraint we get ! 1 8= x +y =) ktu su 2x=82) X=4 As, x=y, y=4 Hunde as a Marshallin demand fractions - X* old = 4 y* = 4 Scanned with CamScanner

demand, pues and w utility assou atcel with these ůcome. (3)=18 SЩ, sғы X-8 = 4 2) ot*}} = 4*4 = 4 or = 16 4 Т= 7 4) P = 3, Ру - 1 Now, budget constraint Тя еx x+ Pч ч - = 3х + 8 Now, nt'lity Maimising condition, Иох . Ру пеш muy y = ) - эх substituting Y= 3x in the budget constaint, 3= 3х+2х =) Сх: е - Хя ), 33 x 1 and, as, y = 34 = 3x1 =3 -) Now, S= substituting 3х + у y=3 we get, 8. 3x +3 Scanned with CamScanner

o now, we have to find the decon position basket! toom (6) we know, ability on original indiftuence Now, from (bl we know, at Chuck! U= 16 2) Xy - 16 --- Also, targency condition requiest slope of Indifference caue= slope of new budg. Ilie, - Ž = 2 2) 7=3x sub stébeitig y = 3x in equation is w get! Xy: 16 =/(X*3x) = 16 =) 3 X²= 16 x = 5 213 and as Y = 3X 2 6.9 Now, substituting effect is [ for good x] = decomposition bundle - Initial bundle (2.3-4). 5 -17. Scanned with CamScanner