Profit-Maximization

Putting Activity Decisions Together Separate output decisions from input decisions optimal output quantity by assuming production function and fixing prices of inputs (wage) Profit-maximizing output levels determined by finding output such that MR = MC MR fixed at P (competitive assumption) MR fixed less than P (other market structures) Marginal Cost Curve derived by production function and fixed input price

Then examin optimal INPUT decision Fix price of output and get Marginal Revenue Product (multiplying Marginal Physical Product of variable by price of output) sometimes by MR if MR < Price

activity level of firm (using inputs, producing outputs) analyzed in 2 separate ways convetional treatment = artificial when output rate determined, rate of input use is determined too

chapter 19 Varian (combines decisions in 1 analytic structure****

Economic Profit profit is modeled as function of input & output prices inputs: j = 1 m to make product output: i = 1 n

output levels (rates) : y1 yn input levels (rates): x1 xm

product prices (output): p1pn input prices: w1wm

Competitive Firm takes all output&input prices as given constants economic profit generated by production plan (x1xm, y1yn):

= p1y1 + + pnyn w1x1 - wmxm

Economic Profit suppose firms stream of periodic economic profits : o, 1,2 r = rate of interest PV of firms economic profit streamPV = 0 + 1/(1 + r) + 2/(1 + r)^2 + Competitive firm maximize its PV of profit

firm Short-Run: x2 = ~x2 production function: y = f(x1,~x2) fixed cost: FC = w2~x2 profit function: = py w1x1 w2~x2

Short-Run Iso-Profit Lines $ iso-profit line : all production plans that yield profit level of $

Short-Run Profit-Maximization problem: locate production plan that attain highest possible iso-profit line given constraint on choices of plans(constraint = production function)

Marginal revenue product of input 1: p x MP1 Rate at which revenue increased with the amount used in input 1

p x MP1 > w1 Profit increased with x1p x MP1 < w1 profit decreased with x1

Comparative Statics of SR Profit-Max What happens to SR Profit-Max production plan as output price p changes? Increased in output price, no change in input price increased profitability, will induce firm to produce more isoprofit line increase in p causes: reduction in slope reduction in vertical intercept increase in firms output level(supply curve slopes up) increase in level of firms variable input(demand curve shifts out)

what happens to SR Profit-Max production plan as variable input price w1 changes? Increase in input $, no change in output price decrease profitability, induce firm to produce less increase in w1 causes: increase in slope no change in vertical intercept decrease in firms output level(supply curve shifts inward) decrease in level of firms variable input(demand curve slopes down)