Advanced Microeconomics/Production

Properties of Production Sets The production vector where represents an output, and an input Y is non empty Y is closed (includes its boundary) No free lunch - (no inputs, no outputs) possibility of inaction Free disposal Irreversability - can't make output into inputs Returns to scale: Non-increasing: Non-decreasing: Constant: Additivity: Convexity: Profit maximization Example Single Output where marginal revenue product Marginal revenue product is the price of output times the marginal product of input The first order conditions for profit maximization require the marginal revenue product to equal input cost for all inputs (actually) used in production, marginal rate of techical substitution Properties of profit functions and supply Profit functions exhibit homogeneity of degree 1 doubling all prices doubles nominal profit supply functions exhibit homogeneity of degree 0 Cost Minimization The optimal CMP gives cost function \funcd{c}{w,q} Example The ratio of input prices equals the ratio of marginal products The marginal cost of expansion through $z_1$ equals the marginal cost of expansion through The solution to the CMP gives factor demands, and the cost function Cost Functions gives positive economic profit, short run and long run In short run, fixed costs are irrelevant. Shut down if minimum efficient scale: No economic profits in the long run, given free entry for any firms enter, in the long run until