Question

II. Ms. Caffeine enjoys coffee (C) and tea (T) according to the function U(C, T) = 3C + 4T.

a. What does her utility function say about her MRS of coffee for tea? What do her indifference curves look like?

b. If coffee and tea cost $3 each and Ms. Caffeine has $12 to spend on these products, how much coffee and tea should she buy to maximize her utility?

c. Draw the graph of her indifference curve map and her budget constraint and show that the utility maximizing point occurs only on the T-axis where no coffee is bought.

d. Would this person buy any coffee if she had more money to spend?

e. How would her consumption change if the price of coffee fell to $2?

Answer 1

1) Marginal rate of substitution (MRS) is the rate at which a consumer is willing to substitute good 1 (Coffee) for good 2 (Tea). MRS is estimated as Change in Tea / Change in Coffee.

MRS = 4 / 3

2) Tea and Coffee are perfect substitutes.

3) Marginal rate of substitution (MRS) is the slope of Indifference Curve. Indifference curve in the instant case look like in the form of straight line.

4) Ms. Caffeine will get maximum satisfaction by consuming more units of tea. The marginal utility (MU) of tea is more than the marginal utility (MU) of coffee. Thus, Ms. Caffeine will spend the entire $ 12 on buying Tea. Thus, the quantity of tea that Ms. Caffeine should buy to maximze her utility = 12 / 3 = 4 Units of Tea.

Conclusion:- 4 Units of Tea and 0 Units of Coffee will maximise the utility of Ms. Caffeine.

6) Ms. Caffeine will buy Tea only if she had more money to spend as the consumption of tea will maximize her satisfaction. She will not spent any money on buying the coffee.