Question

Expecially b,c. Thanks

3. Albert consumes two goods: Chips (C) and DVDs (D). Albert's preferences can be described by the utility function U(C,D) = 50 + 3D!. Albert has income M and the two goods have prices Pc and P» (chips and dvds). (a) Write out the expression for Albert's marginal rate of substitution (or slope of Albert's indifference curves when good C is graphed on the horizontal axis). (2 marks) (b) Write out Albert's utility maximization problem and derive Albert's demands for Chips and DVDs. (6 marks) (c) Determine a range on the relative price of chips, eg. > or <, where Albert chooses bundles with positive quantities of one good and zero quantities of the other good. Which good does Albert stop consuming? (4 marks)

Answer 1

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

P_C and P_D

_{Income = M}

a)

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

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