Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) . (a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has. (b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle? (c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?
Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) .
(a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has.
(b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle?
(c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?
The utility in terms of economics can be defined as the amount of satisfaction or happiness that a consumer gets from consuming goods and services. The utility is dependent on the bundles or combination of goods consumed by an individual, with greater quantities of goods gives greater levels of happiness or utility. Therefore, the utility function shows a positive relationship between the consumption of goods and services and the amount of utility received from that consumption.
The utility function for perfect substitutes is defined as U(X,Y) = aX + bY.
The optimal level of consumption is a rule that says when a consumer maximizes his/her utility, the marginal utility per dollar spent must be the same for all goods and services in the consumption bundle.
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