Micro Economics

A firm purchases capital and labor in competitive markets at prices r=6 and w=4, respectively. With the firm's current input mix, the marginal product of capital is 12 and the marginal product of labor is 18. Is this firm minimizing its costs? If so, explain how you know. If not, explain what the firm ought to do.

Econ Proof/2470

Consider the problems of maximizing u(x) subject to px = y and maximizing v(u(x)) subject to px = y, where v(u) is strictly increasing over the range of u. Prove that x* solves the first problem if and only if it also solves the second problem. If this proof is in the Mas-Collel text or Varian text, let me know and I can look it up.

Consumption, income and leisure time

Consider the problem of maximizing u(c,l) subject to pc + wl = w + y, where c is consumption, l (element of (0,1)) is leisure time, and y is non-wage income. Prove that leisure must be a normal good for the labour supply function to be downward sloping. Pleas use direct methods and comparative statics.

Profit Maximization, Cost Minimization: Prove that profit maximization implies cost minimization but not vice versa.

Prove that profit maximization implies cost minimization but not vice versa. I'm looking for a mathematical proof (I think its involving convexity/concavity, I'm not quite sure?) The types of proofs we learned in class are: the proofs i learned in class are Direct Proof. Assume that A is true, deduce various consequences and use them to show that B must also hold. Contrapositive proof. Assume that B does not hold, then by deducing various consequences show that A cannot hold. Proof by contradiction. Assume that A is true and B is not true, then show that these assumptions imply a logical contradiction. I think the answer should satisfy one of the above. I'm not qui... click for more

Utility and Indirect Utility Mathematical Proof

Consider the problems of maximizing u(x) subject to px = y and maximizing v(u(x)) subject to px = y, where v(u) is strictly increasing over the range of u. Prove that x* solves the first problem if and only if it also solves the second problem. This is what I got, however i dont think its entirely correct. To solve the first problem: maximizing u(x) subject to px = y Assuming x is a one variable commodity bundle, Lagrangean equation: L = u(x) - b(px-y) First order condition: dL/dx = U'x - bp = 0 dL/db = px - y =0 from the second equation, x* = y/p To solve the second problem: maximizing v(u(x)) subject to px = y Assuming x is a one variable commodity bundle, Lagrangean ... click for more