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 five Timbits would.

3.1a) (4 points) What is his marginal rate of substitution of Donuts for Timbits (MRSDT)? Draw Jin's indifference curve.

• MRSDT = ___________________________

3.1b) (2 points) What is his utility function that would represent his preferences?

• Jin's utility function: U(D, T) =______________________

3.1c) (4 points) If the price of Timbit is $0.25 per unit and the price of Donut is $2.5 per unit and Jin has $10 to spend on Timbits and Donuts, how many of each product would he purchase?

• Jin buys _________ Donut(s).
• Jin buys _________ Timbit(s).

3.2) (10 points) Jane likes to have Tea (T) with Cookies (C). She always has 5 cookies for every cup of tea.

3.2a) (3 points) Draw 2 indifference curves that describe her preferences with Tea (T) on the horizontal axis and Cookies (C) on the vertical axis.

3.2b) (3 points) What is her utility function that would represent her preferences?

• Her utility function: U(T, C) = ____________________________

3.2c) (4 points) If the price of a cup of tea, PT = $2 and the price of one unit of cookies, PC = $0.6 and Jane has $10 to spend on Tea and Cookies. How many of each product would she buy?

• She buys __________________ cup(s) of tea.
• She buys __________________ cookie(s).

3.3) (10 points) Suppose Anna's preferences can be represented by U(X, Y) = 5X0.4Y0.8.

3.3a) (4 points) What is her marginal rate of substitution of X for Y (MRSXY)?

• MRSXY = ____________________

3.3b) (6 points) Find the optimal bundle with the price per unit of X = $4 and the price per unit of Y = $2 and income = $48.

• The optimal bundle is (X*, Y*) = __________________________________