2. An eyeglass manufacturer can produce eyeglasses according to the following production function: quK where K is the number of tiny screwdrivers the rm owns, and L is the number of workers the rm employs. Workers are paid a wage of TL : 1m] each, and tiny screwdrivers can be bought for a price of 1"}: = 4 each. a In the lon -run, ca ital and labor are both variable. To reduce units, what is g P P the mix of labor L and capital X that minimizes costs? Show your workl (Hint: you have two unknowns, L and H. You have two equations. the output condition Q : LK and the bang-for-the-buck condition MPLXT'L = MPKer. Solve the equations simultaneously to nd the right levels of L and K as a function of Q. It may help to simplify the bang-for-the-buck condition to get rid of any square roots before plugging it into the output function.) {b} 'What is the corresponding long-run lowest cost of producing Q units of goods? 'What is the long-run marginal cost of the Qm unit? New say that we are currently using 50f} tiny screwdrivers and 2E] workers. In the short- run we CANNOT HIRE 0R FIRE 'WDRKERS but we can buy or sell screwdrivers. [c] To produce Q units of output, how many tiny screwdrivers do we need, given that we are stuck with 2D workers? Solve as a function of Q, so that we can plug in to get the number of screwdrivers K for any possible quantity Q. {d} 'What is our short-run total cost of producing Q units? What is the short-run marginal cost of the Q\"L unit? Solve for this as a function of Q. {e} Sketch graphs of {i} the long- and short-run total costs from {b} and {d}, and {ii} the long- and short~run marginal costs. Draw these graphs with Q on the :r-axis, and dollars or dollars per unit on the yaaris