4. Answer the following short questions: 2 (a) Can you find a utility function u(x1, x2)...

 

Transcribed Image Text:

4. Answer the following short questions: 2 (a) Can you find a utility function u(x1, x2) resulting in the following demand func- tions for the two goods 1, 2: -0.7 1(P1 P2, w)=wp 1 and 12(P1, P2, w)=wp20.3 where w > 0 is the income and p, P2 > 0 are the prices of the goods. (b) What is the cost function of a firm that buys labor input at price w > 0 and capital at price r? Suppose that the cost function is given by: 2gr if 2r <3w, c(q,r,w)= 3qw if 2r3w, where q is the quantity produced. What is the conditional labor demand of the firm if 2r> 3w? (c) Examine the long-run behavior (lim) of the solution of the following linear system with initial condition x = (1,0,0): 1 12 x1+1 0 1 1 2 10 (Hint: for one of the eigenvalues, consider the column sums of the matrix). 4. Answer the following short questions: 2 (a) Can you find a utility function u(x1, x2) resulting in the following demand func- tions for the two goods 1, 2: -0.7 1(P1 P2, w)=wp 1 and 12(P1, P2, w)=wp20.3 where w > 0 is the income and p, P2 > 0 are the prices of the goods. (b) What is the cost function of a firm that buys labor input at price w > 0 and capital at price r? Suppose that the cost function is given by: 2gr if 2r <3w, c(q,r,w)= 3qw if 2r3w, where q is the quantity produced. What is the conditional labor demand of the firm if 2r> 3w? (c) Examine the long-run behavior (lim) of the solution of the following linear system with initial condition x = (1,0,0): 1 12 x1+1 0 1 1 2 10 (Hint: for one of the eigenvalues, consider the column sums of the matrix).