## Question

###### Kirpa is trying to decide how many hours to work each week. Her utility is given by the following function: U(C,H) = C2 H3 , where C represents weekly consumption and H represents weekly leisure hours...

Kirpa is trying to decide how many hours to work each week. Her utility is given by the following function: U(C,H) = C^{2} H^{3} , where C represents weekly consumption and H represents weekly leisure hours. Her marginal utility with respect to consumption is MU_{c} = 2CH^{3} , and her marginal utility with respect to leisure is MU_{H} = 3C^{2} H^{2} .

A) Find Kirpa's optimal H, L and C when w=$7.50 and a = $185.

B) Suppose w increases to $15. Kirpa subsequently changes her weekly labor hours to 37.4 hours per week.

i) 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 points on the graph and label any axis intercepts.

ii) Indicate the substitution and income effects for leisure 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?

iii) 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?

C) Find the wage at which Kirpa will choose to work 40 hours/week.

D) Graph Kirpa's labor supply curve based on w=$7.50, w=$15, and the wage you calculated in part C).

E) Suppose the entire market of labor consists of 2 individuals, Kirpa and Demi. Demi's labor supply function is given below:

Q^{S}_{L} = { min(90,(w^{2} / 10}, w>=10 and 0, w<10}

Graph the market labor supply curve for w=$7.50, w=$15, and the wage you calculated in part C).