代做Intermediate Economics 100B Winter 2024 PROBLEM SET 2调试Haskell程序

Intermediate Economics 100B

Winter 2024

PROBLEM SET 2

Due February 3rd, 2024 by midnight

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?

(3b) What is Jack’s short-run marginal revenue product of labor?

(3c) Given that Jack is a price-taker in the labor market, how much labor would Jack buy given the prevailing prices. How much widgets does Jack make? What is Jack’sprofit?    OPTIONAL: Although Jack acts as a price taker, is the widget market competitive for this example? Look at Jack’s profit. At the going price of widgets, is P = MC?

(3d) Suppose that Jack is a monopolist in the widget market and faces the following

inverse demand for widgets: P(Q) = 30 − 0.25 Q. What is Jack’s marginal revenue now? marginal revenue product for labor?

(3e) Sketch Jack’s labor demand curve as a price-taker and as a monopolist in the widget market.

(3f) As a monopolist, does Jack buy more or less labor? Briefly explain why. No need to solve for the profit maximizing quantity of labor. But you can if you want (algebraically tedious).

(3g) Re-do (3c) assuming that K = 4 and K = 6.

(3h) Based on (3c) and (3g) and the prevailing prices, would Jack rather use more or less  capital given the choice? In the medium/long run, what would we expect to happen to the factor price of capital (r), assuming w and premain unchanged?

(3i) Suppose Jack is amonopsonist in the labor market and faced a labor supply curve

similar to the labor supply curve you derived for Jane (Question 2). Would Jack buy more or less labor as amonopsonist ? Briefly explain why.

4) The demand for labor by an industry is given by the curve L = 1200 − 10w, where L is    the labor demanded per day and w is the wage rate. The supply curve is given by L = 20w. What is the equilibrium wage rate and quantity of labor hired? What is the economic rent earned by workers?

5) Using the same information as in Exercise 4 above, suppose now that the only labor

available is controlled by a monopolistic labor union that wishes to maximize the rent earned by union members. What will be the quantity of labor employed and the wage rate? How does your answer compare with your answer to Exercise 4? Discuss.