# Simon ECON 435 – Assume the wage is $1000, and the cost

You only need to finish the first 10 questions to get the full mark.1. Assume the wage is $1000, and the cost of capital is $2. Fill out the following table. Is themarginal product of labor diminishing? 12 2. The firm’s short-run cost function () = 10 + 2 + , () = + 1.a. The price = 6. What is the optimal quantity and profit? Should the firm shut down inthe short-run? Why?b. If = 2, what is the optimal quantity and profit? Should the firm shut down in theshort-run? Why?c. At which price does the price just cover the firm’s variable cost ( = )?d. At which price the firm’s profit is 0?e. What is the firm’s supply curve in the short-run?Suppose there are 4 identical firms in the market, and the demand function is = 30 ?2 .f. What is the market supply curve? Compare the slope of the market supply curve withthe slope of the supply curve of a single firm. If there are 10 firms in the market, answerthese questions again.g. What is the market equilibrium (market price and quantity), profit and output of eachfirm?In the long-run suppose the demand function is = 30 ? 2 .h. What is the long-run equilibrium price, market output, output of each firm, and numberof firms?i. 1 Suppose the cost function becomes () = 10 + 2 2 + 2, () = + 2. What isthe long-run equilibrium price, market output, output of each firm, and number offirms? 3. Suppose the production function is = 0.6 0.7. Does it have IRS, CRS, or DRS?4. Suppose the cost function is () = 20 + 0.5 2 + . What are the FC, FC, ATC, AFC, AVC?The MC= + 1. Find out the quantity level at which ATC is minimized, the quantity at whichAVC is minimized. At which quantity is AFC minimized? ? , the wage is w,5. Suppose the production function is = ?. In the short-run capital is and the cost of capital is r. What is the cost function in the short-run? What is the MCfunction? Draw the diagram. (Hint 1: in both of the cost function and MC function we write???.2? the costs as a function of output q; Hint 2: = 2 )?,? 6. = 5, = 2, = 0.5 0.5 , = 2 = What are the optimal K and L that produces an output of 20, 40, and 60? Draw the graph to illustrate your solution, and drawthe expansion path in the graph. Draw the total cost function in a new diagram.7. Suppose = 2 + 3, w=5, r=1. What is the long-run cost function? Now suppose w=1 andr=5, what is the long-run cost function?8. Explain why in a perfectly competitive market each firm is a price taker (It wouldn’t set theprice higher or lower than the market price)?9. When MC is increasing, and MR is constant or decreasing, explain why at the optimalquantity MR=MC. (Use a graph if it is helpful.)?,? 10. = 2, = 3, = ?, = 2 ?.? = 2 What are the optimal K and L that produces an output of 10? Now suppose the wage increases to 4, get the optimal bundle ofK and L. Draw the graph to illustrate your solution.11. We usually assume the is diminishing. Explain why this assumption makes sense, ordoes not make sense.12. Remember Malthus theory? Explain why it worked three hundred years ago but doesn’twork today. (If you don’t remember it, google it on the internet.)13. Suppose the production function is = ?. Draw the isoquant at which = 10. Find outthe slope of the curve at the point of (K=10,L=10) graphically and mathematically? Is this?, ? slope larger or smaller than the slope at the point of (K=5, L=20)? (Hint: = 2?)2? 14. Suppose the production function is = 3 + 2. Draw the isoquant at which = 100.What is the slope of the line?15. Suppose the production function is = min?(, ). Draw the isoquant at which = 100.16. Suppose the production function is = ?. Does it have IRS, CRS, or DRS?17. Suppose the production function is = 0.3 0.7. Does it have IRS, CRS, or DRS? = 18. In the long-run all firms in a perfectly competitive market earn a 0 profit. Why are they stillin business if their profit is 0?19. If we assume that is increasing. Show that MC is increasing intuitively andmathematically.20. Suppose we have the following short-run ATC curves. Draw the long-run ATC curve. 21. Explain why when the LRATC is decreasing we have IRS, when the LRATC is stable, we haveCRS, and when the LRATC is increasing we have DRS? 22. Can you explain why a firm may have IRS? DRS? What is the optimal size of the firm if it hasIRS, DRS, or CRS?23. Suppose the wage is 10 and the cost of capital is 5. Draw the isocost line at which the cost isequal to 20. Draw another at which the cost is 60. What are the slopes of these two lines?24. Suppose the wage is w=4 and the cost of capital is r=2. It takes 2 unit of labor and 1 unit ofcapital to produce 1 unit of output. What is the long-run cost function? (If you can’t get thegeneral cost function, then calculate the costs at three different quantity levels.). Nowsuppose w=5 and r=1. What is the long-run cost function?25. When there are many firms in the market, explain why the demand curve faced by each firmis horizontal while the market demand curve is still downward sloping.26. In a same graph draw a typical MC, AVC, and ATC curves. Explain why the MC curve crossesthe other two curves at their minimums. Can you prove it mathematically? 27. Explain why a LRATC curve is below all SRATC curves? Draw the graph and show the changein the scale to return.