Expecially b,c. Thanks 3. Albert consumes two goods: Chips (C) and DVDs (D). Albert's preferences can...

U(C,D) =5C + 3D^1/2

P_C and P_D

_{Income = M}

a)

Slope of alberts indifference curve =- MUx/MUy

MUx = MUc = 5 {differentiating U(C,D) =5C + 3D^1/2 w.r.t C}

MUy = MUd= 3*(1/2)*D^(-0.5) {differentiating U(C,D) =5C + 3D^1/2 w.r.t D}

Slope of indifference curve = MUc/MUd = -3.33*(D^0.5) = MRS

Since the slope of the indifference curve is equal Marginal Rate of Substitution

Slope of Budget Constraint = Py/Px = Pd/Pc

b) For Utility Maximization

MU of Product C /Price of C = MU of Product D/Price of D

5/Pc = 1.5(D^-0.5)/Pd

Pc/Pd = 5/1.5(D^-0.5)

i.e the slope of the Budget Constraint should be equal to the slope of the indifference curve at the utility maximization point , the point where the tangent to the indifference curve meets the budget constraint..

c)

U(C,D) =5C + 3D^1/2

at

C = 0

U(C,D)= 3D^1/2

MUc=0

MUd=1/2*3*D^-0.5

MUc/MUd = 0

at

D =0

U(C,D)= 5C

MUc=5

MUd=0

MUc/MUd = infinite

hence the range of relative price of chips and dvds is 0 to infinite

M/Pd Indifference Curve D in units MUd MUc Budget Constraint M/Pc C in units