5.2.2 Scale and Sulstitution Effects Consider the market for netbooks, which is perfiectly competitive with firms who are price takers in both input and output markets. Production of netbooks requires labor (L) and computer chips ( k ). There is a large number of identical tirms, with the representative firm having production function: y=f(L,K)=L1k} (a) Show whether the techuology exhibits increasing decreasing or constant returns to scale. (b) The price of labor is w and the price of a computer chip is r. State the firm's cost minimization problem and write the Lagrangian. Having done all the hard work on Problem Set 5 of finding the conditional input demand functions, you know that they will take the following forms: L2=(3)1y2K4=(r2)1y2 and the minimum cost function will be C+(w,r,y)=2akir+g2 (c) Assuming the market price of a nethook is p, ase the cost function to state the firm's profit maximization problem. Then find the profit maximizing supply function y=y(w,r,p) (meaning find y as a function of w,F, and p ). (d) Assume that p=8 and r=1, and suppone the price of labor has increased from w=1 to w=4. Do the following to decompose the total change in the demand for labor into the scale and substitution effects: i. Find the optimal level of output at the original wages ii. Using that output level, find the optimal quantity of labor demanded when wages are at the original level of y=1. iii. The substitution effect will come frum just the change in wage, holding output constant; so find how much labor would be demanded if the firm had to pay ay =4 and produced the ariginal level of output. Write the substitution effect as the change in labot demanded. iv. Find the new optimal level of output with the new wage. v. Using the new optimal bevel of output and the new wages, find the new quantity of labor demanded by the reposentative firm. Use this to compute the scale effect. vi. On a graph with capital and laboe on the aves and an isoquant and isocost, illustrate the scale and substitution effects graphically. (e) Can you use this to explain why US. based firms are increasingly moving their production abroad? 5.2.2 Scale and Sulstitution Effects Consider the market for netbooks, which is perfiectly competitive with firms who are price takers in both input and output markets. Production of netbooks requires labor (L) and computer chips ( k ). There is a large number of identical tirms, with the representative firm having production function: y=f(L,K)=L1k} (a) Show whether the techuology exhibits increasing decreasing or constant returns to scale. (b) The price of labor is w and the price of a computer chip is r. State the firm's cost minimization problem and write the Lagrangian. Having done all the hard work on Problem Set 5 of finding the conditional input demand functions, you know that they will take the following forms: L2=(3)1y2K4=(r2)1y2 and the minimum cost function will be C+(w,r,y)=2akir+g2 (c) Assuming the market price of a nethook is p, ase the cost function to state the firm's profit maximization problem. Then find the profit maximizing supply function y=y(w,r,p) (meaning find y as a function of w,F, and p ). (d) Assume that p=8 and r=1, and suppone the price of labor has increased from w=1 to w=4. Do the following to decompose the total change in the demand for labor into the scale and substitution effects: i. Find the optimal level of output at the original wages ii. Using that output level, find the optimal quantity of labor demanded when wages are at the original level of y=1. iii. The substitution effect will come frum just the change in wage, holding output constant; so find how much labor would be demanded if the firm had to pay ay =4 and produced the ariginal level of output. Write the substitution effect as the change in labot demanded. iv. Find the new optimal level of output with the new wage. v. Using the new optimal bevel of output and the new wages, find the new quantity of labor demanded by the reposentative firm. Use this to compute the scale effect. vi. On a graph with capital and laboe on the aves and an isoquant and isocost, illustrate the scale and substitution effects graphically. (e) Can you use this to explain why US. based firms are increasingly moving their production abroad