Question 10 A firm uses inputs L (labor) and K (capital) to produce a single output. The two inputs are perfect complements in the firm's production function and must be used in a 1:1 ratio lest the firm waste resources. The price of labor is w = $25, and the price of capital is r = $10 The optimal input combination to produce q = 1,000 units of output is _* = K* = 20, as shown in the graph below (next page). Consider the firm's total cost when it produces q = 1,000. Assume there are no fixed costs. Which of the following alternatives is correct? (a) The firm's total cost is ( = min(wL, rK} = 20($10) = $200 (b) The firm's total cost is C = wL = 20($25) = $500 (c) The firm's total cost is C = wL + rK = 20($25 + $10) = $700 (d) The firm's total cost is C = q(w + r)/ min{K*, L-} = 1,000($25 + $10)/20 = $1,750K A C (1,000) isocost line isoquant K= 20-.. 4 =1,000 L' - 20 C(1,000)Question 11 Consider the same information in question 1D. Sketch a graph of the firm's isocost line at the current prices and outputlevel {w = 25, r = 113.6; = LDUD). Place capital {Kl in the vertical axis. Let C be the total cost associated with vour isocost {its level on the implicit third axis}. Suppose the price of labor changes to w\" = 15. In vour graph, draw a new isocost line associated with the same total cost if as before, but reflecting the new price of labor. Finallv, draw a new isoouant reflecting the level of output, E\". that can be produced if the firm incurs in this same total cost C at the new price levels. Which of the following alternatives is correct? la} The new isoouant has the same shape as the previous one. but has shifted to the left lb] The new isoouant touches the new isocost line in a point on the 45-degree line W = L] it} The new isocost line has the same slope as the previous one, but has shifted to the right id] The new isocost line has the same int-intercept but a different v-intercept Question 12 Consider the same information in questions liilI and 11. In particular, consider that the firm has the same tech nologv and that the price of capital has remained at r : 10 while the price of labor changed from w = 25 to vv' : 15. Before the price change, the firm was producing , : LUDCII units of output at the total cost of C dollars. After the price change, if the firm spends the same C dollars, it will produce tTunits of output. Which of the following alternatives is correct? [a] The firm will produce the same output as before, d\" : t7, using K' = L" : 20 [b] The firm will produce the same output as before, d\" : ti, using ft\" = L" s: 20 [cl The firm will produce more output than before, (3' la- tT, using K" = L' 1:5 2i) [d] The firm will produce more output than before, o' '.:=- d, using K\" = 2:], and L\" 3: 2E]