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Answer :
Mark wants to maximize the utility of his wife with a fixed amount of money, $60. The price of a box of chocolates is $10, and the price of a bottle of wine is $15. Doug's wife's utility function is U = C2W2, where C is the number of chocolate boxes, and W is the number of wine bottles.
We need to find the Marginal Rate of Substitution (MRS) of Mark's wife. Let's first determine the formula for MRS . Marginal Rate of Substitution (MRS):It is the amount of one good that an individual is willing to give up to obtain an additional unit of another good while maintaining the same level of satisfaction.
The formula for MRS is as follows: MRS = M U x / M U y, where M U x is the marginal utility of good X and M U y is the marginal utility of good Y. Now let's calculate the MRS of Mark's wife. The marginal utility of chocolates (M U c) can be calculated as follows: MU c = 4CW²
The marginal utility of wine (M U w) can be calculated as follows: M U w = 4C²WTo calculate the MRS, we need to take the derivative of M U c with respect to W and the derivative of M U w with respect to C.MRS = d C / d W = M U c / M U w = (4CW²)/(4C²W) = W/C.
Therefore, Mark's wife's MRS is W/C. Now we need to find the number of boxes of chocolates and bottles of wine that Mark should buy to maximize his wife's utility.
To do this, we need to use the budget constraint, which is:$10C + $15W = $60Solving the above equation, we get:2C + 3W = 12Solving the above equation with the utility function, we get : C = W.
Therefore, Mark should buy equal numbers of boxes of chocolates and bottles of wine to maximize his wife's utility. So, he should buy 2 boxes of chocolates and 2 bottles of wine. Therefore, the MRS of Mark's wife is 1.
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