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Firm Optimization 6. (8 points) Suppose a firm uses capital (X), labor (L), and energy (E) to produce output (Q). In the short-run, the firm cannot adjust its capital stock. The price of capital is r, price of labor is w, and the price of energy is e. The price of final output is p. In the short-run profit maximization problem, which of the variables K, L, E, Q. p, r, w, e are exogenous? 7. (10 points) Assume a firm has the production function is Q = VKL . To maximize the firm's profit, it satisfies the condition w = pMPL. In the short-run, the capital stock is 9. If the wage rate is $6 and the price p is $18, how much labor does the firm demand? Markets Consider the following cost function: c(q) =16+15q+4q' 8. (8 points) Find the firm's individual supply function. 9. (8 points) Find the firm's minimum efficient scale. 10. (8 points) Suppose there are 20 firms with this cost function. What is the market supply function? II. (8 points) What is the long-run supply function of the market?TeSuit IS TOO much Of 11. How can the externality be addressed. Name 3 ways. And explain. 12. Draw a graph of a good with a positive externality and explain whether the result is too much or not enough production. 13. How can the externality be addressed. Name two ways and explain. 14. There are some solutions that are theoretically possible but not realistic for solving externalities. Why do they fail in practice? 15. Explain what a specific example of a public good is and who takes advantage(abuses/defrauds) of them, how/why? 16. Explain what a specific common resource is and who takes advantage (abuses/defrauds) of them, how/why? 17. What could be done to correct question 15? 18. What could be done to correct question 16? 19. Economics may be a study of scarcity, but it is also a study of equity as well. Would you be happy with the solutions you put forward in questions 17 & 18? Why or why not? 20. Who pays their fair share of taxes?(this is a trick question) explain 21. Who pays their unfair share of taxes? (this is also a trick question) explain 22. Explain how at least three different types of taxes discriminate against some groups and are fair or unfair as we have chosen to implement them in the United States. 23. Why have we chosen to set taxes up this way do you think? 24. What are implicit and explicit costs? 25. Why does the production function's slope decrease? 26. Why does the average fixed cost curve decrease as output increases? 27. When do firms decide to shut down in the short or long term? Why is their decision different? 28. Why are Monopolies a concern for society? What can they do that would lead to a sub- optimal outcome? 29. What has been done to remedy a monopoly and do you think there are any monopolies today that need to be addressed?e. In what range must the international relative price of wheat fall? Why? 7. Suppose that: In Malaysia the unit labor requirement (ULR) to produce a pound of rice and a pencil are 2 and 4 hours of labor respectively; In Indonesia, the unit labor requirement to produce a pound of rice and a pencil are 4 and 6 hours respectively; each country has 20,000 hours of labor to allocate between the production of rice and pencils; and in autarky, Malaysia consumes 5,000 pounds of rice and 2,500 pencils. When trade PRW occurs, the world relative price of rice Pew becomes 3/5. a. Given that the marginal product of labor is the inverse of unit labor requirements, i.e. MPL = 1/ULR, derive the relationship between price ratio and the ratio of unit labor requirements. (hint: remember that w = P *MPL and that in autarky wages in both sectors are equal) b. Which country has the better technology? C. What are the autarkic (pre-trade) relative prices of rice and pencils respectively in each country? d. How many work hours are employed in the Pencil and Rice sector respectively in Malaysia? e. In which product will each country specialize? f . When specializing, how many units of rice and pencils will Malaysia produce? (hint: obtain total labor hours available from your answer in part d. above) Chapter 3: Specific Factors Model 8. How does the specific factors model differ from the Ricardian model? (list at least 3 for full points) 9. Suppose that land is specific to agriculture, capital is specific to manufacturing, and labor is mobile between sectors. If there is an increase in the amount of capital, holding the prices of agricultural and manufacturing goods constant, what happens to the equilibrium nominal wage rate and labor allocation? What happens to the rental rate of capital? What happens to the rental rate of land? 10. Suppose that land is specific to corn, capital is specific to automobiles, labor is mobile between sectors, and payments are as follows: Automobiles: Sales revenue = 400; payments to labor = 100; payments to capital = 300 Corn: Sales revenue = 300; payments to labor = 250; payments to land = 50 Holding the price of automobiles constant, suppose the increase in the price of corn is 10% and the increase in the wage is 5%. What is the impact of this on the rental of land and the rental of capital? Thought exercise: Question generation (This is due on Sunday, the gth of February, 2020 at 11:59PM) 11. Choose any topic above and construct an original multiple choice question (complete with question, at least 4 responses and the correct answer). In addition, provide the logic for what the question was designed to test.Consider a price-taking firm with this production function: q = 1 1/3 K1/3 1. (46 points) Operating in the short-run. a) (4 points) Show that the total cost function is TC = w ()q3 + rk b) (6 points) Show that the short-run supply function is q = ( (PK) 1/2 c) (6 points) What is the short-run supply function? Why? d) (6 points) Show that the profit-maximizing labor demand function is L = K1/2 () 3/2 The profit function is * = (3) p4/3 ( K ) 1/3 -rk 1 = TR - TC = Pq - (wl trk) = p(PK) 1/2 - WK1/2 ( ) 3/2 - rk = P3/2 ( K )1 3/2 3w - Wk1/2p3/2 (4)"(2) *- TK = P3/2 ( K 2- p3/2 ()"()()" - rK = p3/2 ( K 1/2 - P3/2 ( K \\1/2 (3w/ -rk = p3/2 (K (3 w/ (1 -1) -TK = (2)P3/2 (4 )1/2 3 w -rka) the marginal product of the 6" unit of labor? b) at what level of labor APL and MPL equal? c) the total cost of producing 455 units of output 3. Assume a firm with a production function (=1220404of and buying labor and capital with a market price of $5 per unit and $40 per unit respectively. If the firm has total outlay of $800, what combination of inputs( labor and capital) would the firm use in order to produce the maximum possible output. 4. Assume a firm with a production function of p= 2543X and buying labor and capital with a market price of $3 per unit and $12 per unit respectively. Find the optimal combination of labor and capital producing 1250 units of output. 5. Suppose the short - run cost function of a firm is given by: TC =60'-180' + Q + 100 Find: a) The expressions for TFC and TVC b) The expressions for AFC, AVC , AC and MC c) The minimum value of MC and the minimum value of AVC. d) What is the value of MC at the minimum AVC