What is the ( long-run ) optimal choice of L and K for a given Q, w, and r? In other words, provide a formula for the optimal choice of labor L∗(w, r,Q) and capital K∗(w, r,Q) as a function of the parameters Q, w, and r.

Auniversity spent $1.8 million to install solar panels atop a parking garage. these panels will have a capacity of 400 kilowatts (kw) and have a life expectancy of 20 years. suppose that the discount rate is 20%, that electricity can be purchased at $0.10 per kilowatt-hour (kwh), and that the marginal cost of electricity production using the solar panels is zero. hint: it may be easier to think of the present value of operating the solar panels for 1 hour per year first. approximately how many hours per year will the solar panels need to operate to enable this project to break even? a. a.3,696.48 b.14,785.92 c.9,241.20 if the solar panels can operate only for 8,317 hours a year at maximum, the project (would/would not)break even?

Suppose that xtel currently is selling at $40 per share. you buy 500 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker. the rate on the margin loan is 8%. a. what is the percentage increase in the net worth of your brokerage account if the price of xtel immediately changes to (a) $44; (b) $40; (c) $36? (leave no cells blank - be certain to enter "0" wherever required. negative values should be indicated by a minus sign. round your answers to 2 decimal places.) b. if the maintenance margin is 25%, how low can xtel’s price fall before you get a margin call? (round your answer to 2 decimal places.) c. how would your answer to requirement 2 would change if you had financed the initial purchase with only $10,000 of your own money? (round your answer to 2 decimal places.) d. what is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if xtel is selling after one year at (a) $44; (b) $40; (c) $36? (negative values should be indicated by a minus sign. round your answers to 2 decimal places.) e. continue to assume that a year has passed. how low can xtel’s price fall before you get a margin call? (round your answer to 2 decimal places.)

Suppose the government enacts a stimulus program composed of $600 billion of new government spending and $300 billion of tax cuts for an economy currently producing a gdp of $14 comma 000 billion. if all of the new spending occurs in the current year and the government expenditure multiplier is 1.5, the expenditure portion of the stimulus package will add nothing percentage points of extra growth to the economy. (round your response to two decimal places.)