3. Utility for two goods is given by: U(x1.X2) 5x1 +10x2 a.) Find the demand fun
ID: 1140825 • Letter: 3
Question
3. Utility for two goods is given by: U(x1.X2) 5x1 +10x2 a.) Find the demand function for the optimized bundle of the two goods in terms of h(P1 P2.m). b.) If m-$100, p1-$3, p2 $4 what is the optimized bundle of goods? c.) If m-$100, P1 -$1, P2 $4 what is the optimized bundle of goods? 4. Utility for two goods is given by: U(x1,X2) min(x1,2x2) a.) Find the demand function for the optimized bundle of the two goods in terms of h(P1.P2.m). b.) If m-$100, p -$5, P2 $10 what is the optimized bundle of goods? 5. Utility for two goods is given by: U12)2x 12+x2 a.) Find the MRS for this utility function. b.) Set the MRS equal to the price ratio pi/P2 and solve for x1.Explanation / Answer
3..)
a)
goods are substitute to each other and utility function is linear. Corner solution will exist here.
MUx1 = 5
MUx2 = 10
MRSx1x2 = 5/10
= 0.5
Price Ratio = Px1/ Px2
If MRS > Px1/Px2
Only good X1 would consumed
Conversely, if MRS <Px1/Px2, only god X2 would be consumed.
b)
MRSx1,x2 = 0.5
Px1/Px2 = ¾
= 0.75
Price ratio is greater than MRS. Thus only X2 shall be consumed.
Quantity of x2 = 100/ 4
= 25
Utility = 10*25
= 250
Optimized bundle = ( 0 , 25)
c)
MRSx1,x2 = 0.5
Px1/Px2 = ¼
= 0 .25
MRS > Px1/Px2
Only good x1 shall be consumed.
When on X1 is consumed = 100/1
= 100 units.
Total utility = 100*5
= 500
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