Please show work and steps 4. Melissa\'s utility function is U min (L, E 2, 2T)
ID: 1177006 • Letter: P
Question
Please show work and steps
4. Melissa's utility function is U min (L, E 2, 2T) where Lare lattes, E are eggs, and Tis toast. She is on a diet, and her calorie constraint for breakfast is Cbar J600 calories. Supposelattes have 300 calories, eggs have 100 calories, and toast also has 100 calories per serving. a. What type of utility function is this? Are these good complements, substitutes, or perfect substitutes? b. If she has to eat only whole servings, what will she have for breakfast, andhow many calories will she consume? If she can eat partial servings, how would your answer differ?Explanation / Answer
1. This is a Leontiff utility function. they are good for complements.
2. Since the utility is a minimum, if either L, E or T is 0, then U = 0. Thus she needs to have at least one of each. This gives her 300 + 100 + 100 = 500 calories already. Thus, with this, she would have a utility of 1/2 since L = 1, E/2 = 1/2, 2T = 2. Thus, to increase this we can either add one more 100 calories of E or one more hundred calories of T. Adding T would still make 1/2 the min, so having her eat 2 eggs would give 2/2 = 1 = E/2 so U = 1. Thus her utility is maximized with L = 1, E = 2, T = 1 and 600 calories with U = 1.
If fractional servings are allowed, again we cannot have 0 anything. To maximize the utility function in this case, we want the numbers L, E/2, and 2T to be equal, since if theyre not one is smaller than the others and this would be inefficient. Thus, L = E/2 = 2T and 300L + 100E + 100T = 600. L = 2T, E = 4T so we get 600T + 400T + 100T = 600 so T = 6/11, E = 24/11, L = 12/11.