In this question, we look into labor supply, i.e., the relationship between wage and quantity supplied...

 

  
 

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In this question, we look into labor supply, i.e., the relationship between wage and quantity supplied of labor. Suppose that there is a consumer who earns income by working. Let w be the wage rate (in dollars per hour.) If the consumer's income is exclusively from working, it is given by wl, where I is the number of hours she works. The consumer enjoys two "goods." One is consumption, and the other is leisure, the time spent not working. Let p = 1 be the price per unit of consumption, and L represent the time (in hours) he does not work. Let T be the total hours available per day. That is, L = T-1. Suppose this consumer's utility function is given by u(c, L) = 2 Inc +3 In L. (1) Formally write down this consumer's utility maximization problem. (2) Carefully draw the this consumer's budget set assuming T = 24, w = 1 and p₁ = 2; and indifference curves that goes through (c, L) = (6,6), (c, L) = (6,16), and (c,L) = (16,16). Also, carefully indicate the slopes of indifference curves at these points. 24 22 20 18 16 14 12 10 8 6 4 2 0 0 2 4 6 20 10 12 14 16 18 20 22 24 L (3) Derive the optimal labor supply, and then carefully draw the labor supply curve. 1 01 2 (4) You should notice something peculiar of the labor supply. This question asks you to investigate why. To see this, we look at the effect of increase in w. How do you refute if someone comes to you and argue that your solution must be wrong as follows: "Since w is the price of leisure, the higher price of leisure should induce this consumer to substitute his "leisure time" with consumption goods. Consequently, the supply of labor, i.e., T minus leisure time should increase as w increases. In this question, we look into labor supply, i.e., the relationship between wage and quantity supplied of labor. Suppose that there is a consumer who earns income by working. Let w be the wage rate (in dollars per hour.) If the consumer's income is exclusively from working, it is given by wl, where I is the number of hours she works. The consumer enjoys two "goods." One is consumption, and the other is leisure, the time spent not working. Let p = 1 be the price per unit of consumption, and L represent the time (in hours) he does not work. Let T be the total hours available per day. That is, L = T-1. Suppose this consumer's utility function is given by u(c, L) = 2 Inc +3 In L. (1) Formally write down this consumer's utility maximization problem. (2) Carefully draw the this consumer's budget set assuming T = 24, w = 1 and p₁ = 2; and indifference curves that goes through (c, L) = (6,6), (c, L) = (6,16), and (c,L) = (16,16). Also, carefully indicate the slopes of indifference curves at these points. 24 22 20 18 16 14 12 10 8 6 4 2 0 0 2 4 6 20 10 12 14 16 18 20 22 24 L (3) Derive the optimal labor supply, and then carefully draw the labor supply curve. 1 01 2 (4) You should notice something peculiar of the labor supply. This question asks you to investigate why. To see this, we look at the effect of increase in w. How do you refute if someone comes to you and argue that your solution must be wrong as follows: "Since w is the price of leisure, the higher price of leisure should induce this consumer to substitute his "leisure time" with consumption goods. Consequently, the supply of labor, i.e., T minus leisure time should increase as w increases.

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Answer 1 General guidance The answer provided below has been developed in a clear step by step manner 2 Step By Step Step 1 The labor market continues to recover but a stubbornly high rate of underemp... View the full answer