I need help with this question 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 followsQ=20L-L2²Q=F(K,L) = 4(KxL) - L²In the short-run, Jack's capital is fixed at 5 units (K = 5). In the long-run, he can acquiremore 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 as>(rental rate of capital)max 7=PxF(K,L)-[WL + FK]LTT-BxQ-WL-rk1 = 5(201-2²)-10L-75= P x [4 (5 x 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? (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 buygiven the prevailing prices. How much widgets does Jack make? What is Jack's profit?OPTIONAL: Although Jack acts as a price taker, is the widget market competitive forthis 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 followinginverse 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 widgetmarket.(3f) As a monopolist, does Jack buy more or less labor? Briefly explain why. No need tosolve for the profit maximizing quantity of labor. But you can if you want (algebraicallytedious).(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 lesscapital given the choice? In the medium/long run, what would we expect to happen to thefactor price of capital (r), assuming w and p remain unchanged?(31) Suppose Jack is a monopsonist in the labor market and faced a labor supply curvesimilar to the labor supply curve you derived for Jane (Question 2). Would Jack buy moreor less labor as a monopsonist ? Briefly explain why.

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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=201-2² - L² Q=F(K,L)=4(KxL) 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 ४८ >(rental rate of capital) max 7=PxF(K,L)-[WL + FK] L TT-BxQ-WL-rk IT = 5(201-2²)-10L-7 =Px [4 (5 x 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?