Question

6) (12pts.)A consumer who can only consume two goods has a preference relation over the bundles that are "smooth and is such that, the marginal rate of substitution of good 2 for good 1 at a bundle (41, 42) is: MRS2,191.42) = 3 If the price of good 1 is 3 TL/unit, price of good 2 is 6 TL/unit and the income of the consumer is 27 TL what is the bundle that the consumer will consume (i.e., what is the optimal bundle)? You have to show your calculations in order to get points.

Answer 1

We have given the MRS= $\frac{1}{2\sqrt q{_1}}$

We know that at optimality MRS = $\frac{p_1}{ p{_2}}$

=>

201

=>

2./q1

=>

V91 = 1

=>

91 = 1

Now,

The budget line is where M is the income of the consumer.

P1.01 + P2.42 = M

=> 3 + 6 x q2 = 27

=> q2 = 4.

So the optimal bundle is (1,4).