Suppose that Mark\'s utility function from consuming tuna and Samson is given by

Question

Suppose that Mark's utility function from consuming tuna and Samson is given by U = 2X + 3Y, where X represents the consumption of tuna and Y represent the consumption of salmon. Right now, he has a budget of $100. What is the marginal rate of substitution. If the price of tuna is optimal consumption $6 per pound and the price of salmon bundle (X, Y) for Mark to consume? If the price of tuna is $4 per pound and the price of salmon is $8 per pound, what is the optimal consumption bundle (X, Y) for Mark to consume?

Explanation / Answer

(a) The utility function is linear. Whenever the utility function is linear, solve for the optimal consumption as follows:

MUX = 2
MUY = 3

MRS = MUX/MUY = 2/3

(b)

Utility per unit of dollar spent on good X = MUX/PX = 2/6 = 0.33
Utility per unit of dollar spent on good Y = MUY/PY = 3/7 = 0.43

Since utility per unit of dollar spent on good X is less than utility per unit of dollar spent on good Y, all the income will be spent on good Y.

X = 0
Y = 100/7 = 14.29 units

(c)

Utility per unit of dollar spent on good X = MUX/PX = 2/4 = 0.5
Utility per unit of dollar spent on good Y = MUY/PY = 3/8 = 0.375

Since utility per unit of dollar spent on good X is more than Utility per unit of dollar spent on good Y, all the income will be spent on good X.

X = 100/4 = 25 units
Y = 0

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