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profit maximizing firm

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the firm chooses inputs and output with the sole goal of maximizing economic profits

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economic profits

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total revenue - total costs

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marginal revenue

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change in total revenue as a result of a change in output

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profit maximization FONC

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MR=MC

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profit maximization SOSC

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second derivative of profit must be less than zero

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elasticity of demand

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percentage change in quantity demanded resulting from a one percent change in price

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marginal revenue product

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extra revenue a firm receives

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short-run supply curve

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shows how much firm can produce at various prices and is the positively sloped part of short-run marginal cost curve

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market price falls below Ps and average cost curve

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firm should stop production and pay off fixed costs in mean time

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profit function

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shows maximal profits as a function of the prices the firm faces (P,v,w)

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properties of profit function

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1. Homogeneity

2. Non-decreasing in output price P

3. Non-increasing in input prices w and v

4. Convex in output prices

2. Non-decreasing in output price P

3. Non-increasing in input prices w and v

4. Convex in output prices

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homogeneity

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Doubling input prices would exactly double profits (describes why inflation would not change manufacturing plans)

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non-decreasing in output price

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deriv of profit function with respect to price gives supply function (q star) which is greater than or equal to zero

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non-increasing in input price

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deriv of profit function with respect to input prices is less than zero

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convex in output prices

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if a firm can vary two input prices they would make at least the amount of profits made when only varying one input price

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derivative of profit with respect to an input price

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a small increase in the price of an input would reduce profits in proportion to how much the input is used

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derivative of profit with respect to price of output

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a small increase in the price of the output will increase profits by how much the firm is producing

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how do firms choose their level of production in SR/LR?

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Intersection of price (marginal revenue=price) and marginal cost curve

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exit price

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if below this price the firm should exit the market

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exit price value

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the minimum of the long-run average cost curve

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short-run phenomenon

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shut down

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long-run phenomenon

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exit

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shut down price depends on what?

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revenues and variable costs

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when does a firm shut down?

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when the revenue is less than variable cost--> same as saying when price is less than average variable cost curve

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FOC for profit maximization

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RTS of l for k = w/v

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SOC for profit maximization

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1. second partial derivative for each input must be less than 0

2. determinant function > 0 (cannot be a saddle point)

2. determinant function > 0 (cannot be a saddle point)

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what do labor and capital demand curves look like?

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competitive market it is horizontal

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what are profits at the shut down price?

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there is no profit only fixed costs (-vk)

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what is producer surplus made of?

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current profits plus fixed costs. Actually paid minus must be paid (VC)

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marginal revenue product

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the extra revenue a firm receives when using an additional unit of an input

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formula for marginal revenue product

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MRP of l= deriv of revenue with respect to l TIMES price

MRP of k= deriv of revenue with respect to k TIMES price

MRP of k= deriv of revenue with respect to k TIMES price

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Hotelling's Lemma gives us...

answer

shows results of envelope theorem and labor/capital choice functions and firm's supply function