Question

3. Find the optimal bundle for a consumer with $500 budget whose preference is represented by U(m, n) = 2m + 2n when a) Pm = 10, Pn = 20 (5 points) b) Pm = 20, Pn = 10 (5 points) 4. Show income and substitution effect on graph when price of a normal good decreases. (10 points)

Answer 1

Question 3

The utility function is of substitute goods so only one of them will be consumed depending on the relationship between MRS and price ratio.
MRS = MUm/MUn = $\frac{\frac{\partial U}{\partial m}}{\frac{\partial U}{\partial n}} = \frac{2}{2} = 1$

a. Price ratio = Pm/Pn = 10/20 = 0.5
So, MRS > price ratio. Thus, only m will be consumed.
m = Budget/Pm = 500/10 = 50
So, m = 50; n = 0

b. Price ratio = Pm/Pn = 20/10 = 2
So, MRS < price ratio. Thus, only n will be consumed.
n = Budget/Pn = 500/10 = 50
So, m = 0; n = 50

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