Question

Hadi Utility function for two goods (sweets and cookies ) is U=3SC. Sweets are price at RM0.50 each and cookies at RM0.25.

a. Calculate Hadis’s Marginal Utility (MU) for both sweets and cookies

b. Write an expression for Hadi MRS between sweets and cookies .
      c. Determine Hadi’s optimal mix of sweets and cookies .
d. If Hadi has RM5 per week to spend on cookies and sweets, how many of each should she purchase per week?

Answer 1

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Hadi Utility function for two goods (sweets and cookies ) is U=3SC

price of sweets (Ps) = 0.50

price of cookies (Pc) = 0.25

a)

Hadis’s Marginal Utility (MUs) for sweets = dU/dS = 3C

Hadis’s Marginal Utility (MUc) for cookies = dU/dC = 3S

b)

Hadi MRS between sweets and cookies (MRSsc) = MUs/MUc

= 3C/3S

= C/S

c)

Hadi’s optimal mix of sweets and cookies can be determined by equating the slope of the utility function with the slope of the budget line =>

The slope of the Utility function is MRSsc = C/S

The slope of the budget line = Ps/Pc = 0.50/0.25 = 2

in equilibrium => MRSsc = Ps/Pc

C/S = 2

C = 2S

d)

If Hadi has RM5 per week to spend on cookies and sweets the quantity purchase is given by =>

5 = Ps*S + Pc*C

5 = 0.50*S + 0.25*C

Since   C = 2S

5 = 0.50S + 0.25*(2S)

5 = 0.50S + 0.50S

S = 5

Since   C = 2S

C = 2*5 = 10

she should purchase 5 sweets and 10 cookies per week.