Question

2. Suppose labor (L) and capital (K) are fixed proportion inputs, and that each unit of output must be produced with exactly 5 units of labor and 2 unit of capital. The price of a unit of labor is w, and the price of a unit of capital is r. a. Write down the production function. (5 points) b. Derive the equation for the expansion path. (3 points) c. Derive the equation for the long-run total cost function. (6 points) d. Graphically depict the labor demand curve. (3 points) e. Assume that a unit of the firm's output can be produced using either 5 units of labor and no capital, or 2 units of capital and no labor. That is, labor and capital are perfect substitutes. Moreover, assume w=r. i. Write down the firm's production function. (6 points) ii. Derive the equation for the firm's long-run total cost function. (5 points)

Please make sure you label each part of the question, and please make sure to show ALL of your math work! Please make sure your handwriting is clear and easy to read. Thank you!

Answer 1

Answer Given that suppose (abon (L) and Capital (k) are Fixed proportion inputs, and that each unit of output must be produced with exactly5 Units of labar and 2 unit of capital a) write down the Production function The tired proportion Prodin function is . G = min { 4 1 2 } a is pure unit labour requirement b is Py unit Capital requirement a = min. 23 1 / } b) Derive the equation for the to expansion peut At the equiliborium. = 2.5k This is the equation for expansion Path.

c) Derive the equation for the long-run total Cost function. Then the long run,Q=1=2.5K L=Q,K=0.4 A. Total cost of the firme (= WL tok (= wa +x (0.44) :: LRTC= (w+0.4 x)Q. d) Graphically depict the labor demand curre The labor demand is : MRPL = W. or P.MPL=W Lion, PdQzW or, p=w .: WIPEL OL real wage. / - L

labor demond in infinitely elastic at real - wage (w/p) .. e) Assume that a unit of the firm's output Can be produced using either 5 units of labor and no Capital, of 2 units of capital and no labor The perfect Substitute Production function in (1) Derive the equation for the firm's long-run total cost function. At equilsbrium : mph + W on. Mape 5.0+<* MPL < MP MPK or MPL CMP

Then this implies each dolly invested in labor give lower return than that of k. then the firm choses only K AQA sle Fun TC = WL trk 2WX0+ VK : = v. 2a ...RTC=28a.