Alper Duman Lecture Notes 3: Cost Minimization 22/03/2022 9/17 Exercises = Show that if f(x1, x2) = x1 + x2 then c(W1, W
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- Alper Duman Lecture Notes 3 Cost Minimization 22 03 2022 9 17 Exercises Show That If F X1 X2 X1 X2 Then C W1 W 1 (85.75 KiB) Viewed 45 times
Alper Duman Lecture Notes 3: Cost Minimization 22/03/2022 9/17 Exercises = Show that if f(x1, x2) = x1 + x2 then c(W1, W2, y) = min(wi, wzly Show that if f(x1, x2) = min(x1, x2) then c(W1, W2, y) = (W1 + w2]y = 22/03/2022 11 / 17 Lecture Notes 3: Cost Minimization Alper Duman
n = 4y/4 - 2y - y = 4y$/4 - 3y = 1 Questions on Profit Maximization 1. Consider a firm that has a production function 1/4 1/4 y = f(x1, x2) = 2x1/4x2/4 facing input prices wi = 2 and wz = 4. Assume that the output price p= 8. What will be the profit maximizing output level? What will be the profit? If this firm is divided up into two equal-size smaller firms, what would happen to its overall profits? Why? year?
Quiz Consider the production function f(x1, x2) = 4x1" X3 1/2 1/3 What is the returns to scale? Show your work. What is the TRS for the above production function?
Cost Minimization Problems be om O Production function is f(x1, x2) = min(x1,2x2). . What are the conditional factor demands if y = 10 • If the firm faces wi and w2 as input prices, what is the cost function? 1/3 1/3 Production function is f(x1, x2) = x1'ºx??o and the firm faces W1 and W2 as input prices. Show that cost function is C(W1, W2, y) = 2w1/?w???y3/2 1/2 2 Alper Duman Lecture Notes 4: Cost Curves 29/03/2022
Lecture Notes 3: Cost Minimization 22/03/2022 2 / 17 Profit Maximization Cobb-Douglas Problem In 2020, the town axi services. Let trip of a taxi rid acity of 20 trips be given by D(A red in rides per Assume y = f(x1, x2) = x;'°*? 1/3 1/3 If the input prices are wi and W2 what is profit maximizing y level of output? What is the profit? . the competitive m number of ride equilibrium? s had not change had become DNA day, what was to e was 10% and were expected market price of viam anodionosobo 121 នាង នា Log Alper Duman Lecture Notes 3: Cost Minimization 22/03/2022 4/17
Quiz Touchie MacFeelie publishes comic books. The only inputs he needs are old jokes and cartoonists. His production function is Q = 0.1J1/2_3/4. where J is the number of old jokes used, L the number of hours of cartoonists' labor used as inputs, and Q is the number of comic books produced. Touchie MacFeelie's irascible business manager, Gander Mac- Grope, announces that old jokes can be purchased for $1 each and that the wage rate of cartoonists' labor is $2. • Suppose that in the short run, Touchie is stuck with exactly 100 old jokes (for which he paid $1 each) but is able to hire as much labor as he wishes. How much labor would he have to hire in order produce Q comic books? . Write down Touchie's short-run total cost as a function of his output . Write down his short-run marginal cost function . Write down his short-run average cost function Alper Duman Lecture Notes 4: Cost Curves 29/03/2022 9 / 9