1) The employment of teaching assistants (TAs) by major universities can be

characterized as amonopsony. Suppose the demand for TAs is W=30,000 - 125n, where   W is the wage (as an annual salary) and n is the number of TAs hired. The supply of TAs is given by W=1000+75n.

a. If the university takes advantage of its monopsonist position, how many TAs will it hire? 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 many TAs would it hire?

2) 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 =  X + 24 − L

where P×X = w × L

and 0 < L < 24

Jane’s utility maximization problem can be rewritten using the following indirect utility function1that incorporates her budget constraint

max Indirect Utility =    w L +  

This is because the budget constraint implies that for each hour she works, she can buy an additional P/w 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).

(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 about w = $10? w = $15? Sketch Jane’s labor supply curve.

(2c) At w = 10, does the substitution effect dominate the income effect or viceversa ? Briefly explain your answer.

OPTIONAL: This particular labor supply curve does not backward-bend for any positive

wage. Can you prove this? HINT: need to show that L for all w > 0.

(2d) 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 ?

(2e) 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 inflation problem in macroeconomics.

3) Jack’s Labor Demand Problem

Jack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker in the widget (output) market. His production function is as follows

Q = F(K, L) = 4(KxL) − L2

In the short-run, Jack’s capital is fixed at 5 units (K = 5). In the long-run, he can acquire more capital by paying r for each unit of additional capital. Given a price of p for his widgets, Jack’s short-run profit maximization problem can be written as

−                                 −

max π= Px F(K, L) − [wL + rK]

L

= 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 is w = $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-run marginal revenue?