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Problem 2 (30 points): Kirpa is trying to decide how many bours to work each week. Her utlity is given by the following function: U(C,H)CH3, where C represents weekly consumption and H represents weekly leisure bours. Her marginal utility with respect to consumption is MUc -2cH, and her marginal utility with respect to leisure is MUH 3C3H Assume Kirpa has some assets a that she uses for weekly consumption, so that her weekly budget constralnt can be represented as follows: C-a+wl, where tw represents her hourly wage and L represents weekly labor hours. Assume Kirpa bas 112 waking hours that she is willing to devote to labor and leisure. (1) (5 points) Find Kirpa's optimal H, L, and C when w- $7.50 and a-$185. H-11L-L C 85 + 7,50 L (i) Suppose uw increases to S15. Kirpa subeequently changes her weekly labor hours to 37.4 hours per week. a (5 polnts) Graph the wage change and the resulting change in Kirpa's leisure and consumption Make sure you label your axes, show both optimal leisure-consumption polnts on the graph, and label any axis intercepts. b (5 polnts) Indicate the substitution and Income effects for lelsure on your graph. Note that leisure and consumption are both normal goods. Which effect dominated? Explain how you know. What can you conclude about the slope of Kirpa's labor supply curve based on this wage change? c (bonus 5 points) Calculate Kirpa's wage elasticity of labor supply. You will use the same formula used to calculate price elasticity of demand, treating wage as "price". Interpret the number you calculate. Is Kirpa's labor supply elastic or inelastic? (ii) (5 points) Find the wage at which Kirpa will choose to work 40 hours/week. (iv) (5 points) Graph Kirpa's labor supply curve based on w- $7.50, to $15, and the wage you caleu- lated in part (c). (v) (3 points) Suppose the entire market of labor consists of 2 individuals, Kirps and Demi. Dem's labor supply function is given below: min/00.210 te

Answer 1

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