F18: u(C,L)= 4ln(c)+7ln(L) mrs= 7c/4L available hours is 283. alpha= 0.31 z=3.9
ID: 1142348 • Letter: F
Question
F18: u(C,L)= 4ln(c)+7ln(L) mrs= 7c/4L available hours is 283. alpha= 0.31 z=3.9
19 Points) Household Choices. Profit, taxes and government spending are unknown for this question. Do not assume they are zero but assume that the economy is in equilibrium a) [8 Points] Would the household above prefer (45 C, 35 L) or (35 C, 45 Ly would the househol prefer (35 C, 45 L) or (33.9 C, 46 L)? ex. (5 C, 3 L) means C-5 and L 3 b) [6 Points] Suppose the household above chose leisure to be 155.2, how many hours of labor would the household provide to the market? What would the value of wages be in this case? c) [5 Points] Instead, suppose leisure is half of that mentioned in b) causing wages to be 4.3964. Find the level of consumption taken by the household [15 Points] Firm Choices. Consider a firm with production as follows:Explanation / Answer
Utility function is given by - u(C,L) = 4ln(C) + 7ln(L)
a) A rational person will chose a combination of consumption anz leisure to maximize his utility function.
For a combination of - (45C,35L)
U(C,L) = 4*ln45+7*ln35
= 4*3.80 + 7*3.55
= 40.05
For a combination of - (35C,45L)
U(C,L) = 4*ln35 + 7*ln45
= 4*3.55+ 7*3.80
= 40.80
Therefore we can say that between these two, a person will choose a combination of (35C,45L) because that increases his utility more than the other combucombin.
For a combination - (33.9C,46L)
U(C,L) = 4*ln33.9 + 7*ln46
= 4*3.52+ 7*3.82
= 40.82
Further, we can say that rhe combination (33.9C,46L) will give even more utility than the other two combinations.
c) We know that
wT - wL = wh = C
w - value of wage
T - total hours available
L - leisure hoyrs
h - working hours
C- consumption
Given that leisure hours = 155.2/2 = 77.6
Working hours = h = T- L = 283- 77.6 = 205.4
According to the equation,
wh = C
4.3964*205.4 = C = 903.02
Consumption = 903.02
b) Suppose leisure is 155.2 hours then total hours being 283, working hours = 127.8
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