Question

please i need the answers. the questions are related, you need to find questions 9 then 10

Incorrect Question 9 0/0.1 pts A monopsonist has the production function Q = 4. and faces the following labor supply and product demand equations respectively. W = 2+ 0.05.L P 10 -0.025 How much labor should the firm hire in order to maximize profits if they mark their price 300% above marginal cost? 1st, what is the marginal cost of production and how does that relate to the price the firm charges? 2nd, how much output will the firm produce at that price and how much laboris needed? That is the labor demand curve. 3rd, calculate how labor costs change when one additional unit of tabor is hired (MLC curve). 4th, solve for labor using the results in the 2nd and 3rd step. Incorrect Question 10 O/0.1 pts A monopsonist has the production function Q=4.L and faces the following labor supply and product demand equations respectively W = 2+ 0.05-L P 10 -0.025 - What wage rate should the firm pay in order to maximize profits if they mark their price 300% above marginal cost? Using the results in the previous problem, the firm will want to pay the lowest possible wage rate to hire that quantity of labor hours.

Answer 1

Question 9)

Monopsonist's profit maximization condition is as follows

$Profit, \pi= Total Revenue -Total Cost \\ \Rightarrow \pi= P*Q-C(Q)\\ Now,\ Q=f(L)=4L\\ where\ L\ is\ the\ number\ of\ labor\ hours\\ where\ Q\ is\ the\ output\ of\ the\ firm\\ Since\ labor\ is\ the\ only\ output\\ Total\ cost\ to\ firm=w*L\\ \pi=[(10-0.025*4L)*4L]-L*(2+0.05*L)\\ \Rightarrow \pi=40L-0.4L^{2}-2L-0.05L^{2}\\ \Rightarrow \pi=38L-0.45L^{2}\\ Differentiating\ with\ respect\ to\ L\ \&\ equating\ it\ with\ 0\\ \Rightarrow \frac{\partial{\pi}}{\partial{L}}=38-0.9L \Rightarrow 38-0.9L=0\\ \Rightarrow L^{*}=\frac{38}{0.9}=42.22\ labor\ hours$

10) Wage rate can be calculated using labor supply function

$w^{*}=2+0.05*L=2+0.05*42.22=4.11$