Production of bikes requires 6 workers for every 2 machines, such that bikes are produced according to:
F(K,L)=min(6K,2L)
1) Setup the short run cost minimization problem when K=3
2) Solve for short run optimal amount of labor Lsr(q) and short run minimized cost Csr(w,r,q)
3) Now suppose the bike shop can freely choose capital (K) and labor (L). Set up long run cost minimization problem
4) Solve for the long run optimal amount of capital K*(w,r,q) and labor L*(w,r,q), and the long run minimized cost C*(w,r,q)
5) Compare and contrast the methods for solving the short run and long run cost minimization problems. Why do the two problems require different methods for solving?
6) Suppose this is a consumer theory problem. Setup and solve the expenditure minimization problem for a consumer with utility u(x,y) = min(2x,6y). Identify the compensated demand functions and the minimized expenditure function
7) Compare and contrast the problems and solutions for part 4 and 6. How are they similar? How is the economic interpretation different?
Production of bikes requires 6 workers for every 2 machines, such that bikes are produced according to:
F(K,L)=min(6K,2L)
1) Setup the short run cost minimization problem when K=3
2) Solve for short run optimal amount of labor Lsr(q) and short run minimized cost Csr(w,r,q)
3) Now suppose the bike shop can freely choose capital (K) and labor (L). Set up long run cost minimization problem
4) Solve for the long run optimal amount of capital K*(w,r,q) and labor L*(w,r,q), and the long run minimized cost C*(w,r,q)
5) Compare and contrast the methods for solving the short run and long run cost minimization problems. Why do the two problems require different methods for solving?
6) Suppose this is a consumer theory problem. Setup and solve the expenditure minimization problem for a consumer with utility u(x,y) = min(2x,6y). Identify the compensated demand functions and the minimized expenditure function
7) Compare and contrast the problems and solutions for part 4 and 6. How are they similar? How is the economic interpretation different?
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