Econ100BIntermediate Economics

1) The employment of teaching assistants (TAs) by major universities can becharacterized as a monopsony. Suppose the demand for TAs is W=30,000 -125n, whereW is the wage (as an annual salary) and n is the number of TAs hired. The supply of TAsis given by W=1000+75n.a. If the university takes advantage of its monopsonist position, how many TAs will ithire?What wage will it pay?b. If, instead, the university faced an infinite supply of TAs at the annual wage level of$10,000, how manyTAs would it hire?2) Jane’s Labor Supply ProblemSuppose Jane is a qualified craftswoman who can help produce widgets. Her utilityfunction depends on her consumption of two goods: stuff and leisure. She spends herentire income on stuff. Her utility maximization problem is as follows:

This is because the budget constraint implies that for each hour she works, she can buy anadditionalPwunit(s) of stuff.Fornow, assume that Jane is a price-taker in both the market for stuff (where she buys)and the market for labor (where she sells).(2a) Suppose the price of stuff is $10 (p=10). How much does Jane work if her wage is$5 per hour (w = 5) ?(2b) What aboutw = $10? w = $15? Sketch Jane’s labor supply curve.(2c) At w = 10, doesthe substitutioneffect dominate the income effect or vice versa ?Briefly explain your answer.OPTIONAL: This particular labor supply curve does not backward-bend for anypositivewage. Can you prove this? HINT: need to show thatwLfor all w > 0.(2d) Suppose the price of stuff went up from $10 per unit to $15 per unit. How muchdoes Jane work if her wage is $5 per hour (w = 5) ? What about w = 10 ?w = 15 ?(2e) Suppose Jane used to make a wage of $10 per hour (w = 10) when the price of stuffwas $10 (p = 10). Now that prices are $15 (p = 15), how much of a pay raise does Janeneed in order to achieve the same utility as before? This is known as the inflationproblem in macroeconomics.3) Jack’s Labor Demand ProblemJack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker inthe widget (output) market. His production function is as follows2Q=F(K,L)=4(KxL)−LInthe short-run, Jack’s capital is fixed at 5 units (K = 5). In the long-run, he canacquiremore capital by paying r for each unit of additional capital. Given a price of p for hiswidgets, Jack’s short-run profit maximization problem can be written asmax(,)[]−−=PxFKL−wL+rKL= P × [ 4 (5 × L) − L2 ] − [ wL + 5r ]Assume for now that Jack is a price-taker in the labor market as well. The going wage isw = $10, price for widgets P = 5, and factor price for capital r = 15(3a) What is Jack’s short-run marginal product of labor? What is Jack’s short-runmarginal revenue?