1. Suppose that a firm has the production function Q(K, L) - KL, with MPL - K an
ID: 1102442 • Letter: 1
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1. Suppose that a firm has the production function Q(K, L) - KL, with MPL - K and MPK - L. Furthermore, suppose that, in the short run, the firm's level of capital is fixed at K-5. (a) Find the firm's short-run, cost-minimizing quantity of labor LSg as a function of Q and w. (b) Now suppose that the price of labor and the price of capital are both 1. That is, w-1 and r = 1. Find the firm's short-run total cost function TCR. Identify which portion of the firm's total cost function represents the firm's fixed costs, and which portion represents the firm's variable costs (c) On a graph with Qon the horizontal axis, and dollars on the vertical axis, plot the firm's fixed cost curve (SFC), variable cost curve (SVC), and total cost curve (STC). Be sure to label the curves, as well as the axes (d) Find the optimality condition that the firm's choice of capital and labor must solve in order for it to be cost-minimizing in the long run. Use this optimality condition, along with the firm's production function, to find the firm's conditional labor and capital demand equations as functions of Q, r, and w e) Now, use the prices given above, write the firm's long-run total cost function TCLR Identify which portion of the firm's total cost function represents the firm's fixed costs, and which portion represents the firm's variable costs (f) On a separate graph from part (c), plot the firm's short-run total cost curve and long-run g) Now suppose that the price of capital has increased from r-1 to r- 4. Find the firm's (h) On the same graph as part (f), plot the firm's new short-run and long-run total cost total cost curve. new short-run total cost function and long-run total cost function. curvesExplanation / Answer
a) The condition for cost minimisation in short run is wL/wK = MPL/ MPK. , wl/wk=K/L, (K=5) so, wL/wk= 5/L
L=5(WK/WL)
b)Cost function= wL+ r K, L+K. since capital is fixed at 5 units it is the fixed factor and Lbaour is the variable factor.
d) To be cost minimising, w/r= MPl/MPk
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