Exercise 8 Earned Income Tax Credit (Labor Market Application) Your utility from leisure (x 1 ) and consumption (x 2 ) is u x 1 2 x 2 Each day you are endowed with 24 hours of time ( 1 24) You could have 24 hours of leisure, but since consumption is an essential good you can trade time endowment for income at $10 hour wage Essentially your opportunity cost of leisure is p 1 10 of missed income Let the price of consumption be normalized to p 2 1 a)Your budget constraint is therefore 1 p 1 x 1 p 1 x 2 p 2 What is MU 1 What is MU 2 Find MRS and the optimal leisure consumption bundle (x 1 ,x 2 ) How many hours a day do you work Calculate and show graphically b)The labor income you make falls below the poverty line by $30 day The government decides to compensate with a lump sum welfare subsidy of S 30 Therefore your new budget constraint is S 1 p 1 x 1 p 1 x 2 p 2 What is the optimal leisure consumption bundle now Did your consumption increase by $30 How much are you working now Calculate and show graphically c)The Earned Income Tax Credit (EITC) was first introduced in 1975 and subsequently expanded It is essentially a negative tax (a subsidy rate, instead of a lump sum) that rotates the budget constraint instead of shifting it Let s 20 and the new budget constraint be 1 p 1 (1 s) x 1 p 1 (1 s) x 2 p 2 How does your answer in part b change Comparing S to p 1 s( x 1 ), which program costs the government more d)What if instead of a negative 20 tax on earned income, the government imposed instead a $12 hour minimum wage (p 1 ' 12) Discuss the implications of the two policies in this simple model and if you think it may differ in real life

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Exercise 8. Earned Income Tax Credit (Labor Market Application) Your utility from leisure (x 1 ) and consumption (x 2 ) is u=x 1 2

Exercise 8. Earned Income Tax Credit (Labor Market Application)

Your utility from leisure (x₁) and consumption (x₂) is u=x₁²x₂. Each day you are endowed with 24 hours of time (₁=24). You could have 24 hours of leisure, but since consumption is an essential good you can trade time endowment for income at $10/hour wage. Essentially your opportunity cost of leisure is p₁=10 of missed income. Let the price of consumption be normalized to p₂=1.

a)Your budget constraint is therefore ₁p₁ = x₁p₁ + x₂p₂. What is MU₁? What is MU₂? Find MRS and the optimal leisure-consumption bundle (x₁,x₂). How many hours a day do you work? Calculate and show graphically.

b)The labor income you make falls below the poverty line by $30/day. The government decides to compensate with a lump-sum welfare subsidy of S=30. Therefore your new budget constraint is S + ₁p₁ = x₁p₁ + x₂p₂. What is the optimal leisure-consumption bundle now? Did your consumption increase by $30? How much are you working now? Calculate and show graphically.

c)The Earned Income Tax Credit (EITC) was first introduced in 1975 and subsequently expanded. It is essentially a negative tax (a subsidy rate, instead of a lump-sum) that rotates the budget constraint instead of shifting it. Let s=20% and the new budget constraint be ₁p₁(1+s) = x₁p₁(1+s) + x₂p₂. How does your answer in part b change? Comparing S to p₁s(-x₁), which program costs the government more?

d)What if instead of a negative 20% tax on earned income, the government imposed instead a $12/hour minimum wage (p₁'=12). Discuss the implications of the two policies in this simple model and if you think it may differ in real life.