Question

Question 3: (30 points) 3.1) (10 points) Jin buys only Timbits (T) and Donuts (D) at Tim Hortons. He views Donuts and Timbits as perfect substitutes. For him, one Donut would give him the same satisfaction as eight Timbits would 3.1a) (4 points) What is his marginal rate of substitution of Donuts for Timbits (MRSTD)? Draw Jin's indifference curve. • MRSTD = O BE de ole

please answer all the first four sub- parts.

Answer 1

Solution:

a) As Timbits and Donuts are perfect substitutes, the marginal rate of substitution is constant across all points on all indifference curves.

Since, 1 donut give satisfaction same as 8 timbits, that is 1 donut and 8 timbits are equally substitutable, marginal rate of substitution of donuts for Tidbits, MRStd = 1/8

The indifference curves are can be graphed as: with Timbits on horizontal axis and Donuts on vertical axis, parallel lines with slope of 1/8, as follows: (the end points plotted in the graph are 20 and 2.5)

Donuts 25 20 Timbits

b) The utility function for perfect substitutes can be written in the form: U(x, y) = ax + by

For given information, the utility function is:

U(T, D) = T + 8*D

c) For price of Timbits, Pt = $0.15 per unit and price of donuts, Pd = $2 per unit, along with income, M of $3, the budget line becomes:

Pt*T + Pd*D = M

0.15*T + 2*D = 3

Then, price ratio = Pt/Pd = 0.15/2 = 0.075 which is less than 0.125 (or 1/8).

As price ratio, Pt/Pd, is lower than MRStd, Jin will spend all the income on purchase of Timbits only, and no consumption of donuts (as relative additional satisfaction/benefit Jin gets from Timbits is more than relative additional price paid for it).

So, D = 0, and thus, using the budget line, T = 3/0.15 = 20.

Jin buys 0 Donut and 20 Timbits.