Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function is given by the following equation U(L, C) = (C – 30)(L – 12). Luke receives $50 welfare payment per day. Show all the steps, with definition of every new notation used in the steps. a) Suppose that Luke's hourly wage is $5. Find Luke's daily budget constraint equation and graph it. b) If Luke's wage is $5 per hour worked, what is Luke's optimal consumption, (L", C*)?
Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function is given by the following equation U(L, C) = (C – 30)(L – 12). Luke receives $50 welfare payment per day. Show all the steps, with definition of every new notation used in the steps. a) Suppose that Luke's hourly wage is $5. Find Luke's daily budget constraint equation and graph it. b) If Luke's wage is $5 per hour worked, what is Luke's optimal consumption, (L", C*)?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function is given by the following
equation
U(L, C) = (C – 30)(L – 12).
Luke receives $50 welfare payment per day. Show all the steps, with definition of every new notation used in the steps.
a) Suppose that Luke's hourly wage is $5. Find Luke's daily budget constraint equation and graph it.
b) If Luke's wage is $5 per hour worked, what is Luke's optimal consumption, (L*, C*)? ·
c) Assume that the wage is an unknown variable, w. What is Luke's leisure demand L(w)?-
d) What is Luke's reservation wage, the lowest wage Luke is willing to work for? -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e441362-b166-4df8-bd10-42c2bc6dba65%2Fe3b86b05-d5e2-445b-9402-adc8a0542dcd%2Fpf9dlk_processed.png&w=3840&q=75)
Transcribed Image Text:Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function is given by the following
equation
U(L, C) = (C – 30)(L – 12).
Luke receives $50 welfare payment per day. Show all the steps, with definition of every new notation used in the steps.
a) Suppose that Luke's hourly wage is $5. Find Luke's daily budget constraint equation and graph it.
b) If Luke's wage is $5 per hour worked, what is Luke's optimal consumption, (L*, C*)? ·
c) Assume that the wage is an unknown variable, w. What is Luke's leisure demand L(w)?-
d) What is Luke's reservation wage, the lowest wage Luke is willing to work for? -
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