1) Jane's Labor Supply Problem Suppose Jane is a qualified craftswoman who can help produce widgets. Her utility function depends on her consumption of two goods: stuff and leisure. She spends her entire income on stuff. Her utility maximization problem is as follows: max Utility = VX + v24 -L where PXX = W X L and 0 S L S 24 Jane's utility maximization problem can be rewritten using the following indirect utility function1 that incorporates her budget constraint max Indirect Utility = \\ L + v24-L L This is because the budget constraint implies that for each hour she works, she can buy an W additional P unit(s) of stuff. For now, assume that Jane is a price-taker in both the market for stuff (where she buys) and the market for labor (where she sells). (6a) Suppose the price of stuff is $10 (p=10). How much does Jane work if her wage is $5 per hour (w = 5) ? (6b) What about w = $10? w = $15? Sketch Jane's labor supply curve.(6c) At W = 10, does the substitution effect dominate the income effect or Vice versa ? Briey explain your answer. OPTIONAL: This particular labor supply curve does not backward-bend for any positive 6L wage. Can you prove this? HINT: need to show that 614 for all w > 0. (6d) Suppose the price of stuff went up from $10 per unit to $15 per unit. How much does Jane work if her wage is $5 per hour (w = 5)? What about w = 10 ? w = 15 ? (6e) Suppose Jane used to make a wage of $10 per hour (w = 10) when the price of stuff was $10 (p = 10). Now that prices are $15 (p = 15), how much of a pay raise does Jane need in order to achieve the same utility as before? This is known as the ination problem in macroeconomics