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Production Functions Review

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Production Function (Definition): Q=f(x,y,z,...)

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describes how inputs are used to produce an output.

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Single Input Review

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Marginal Product (MP):

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- equals (dq/dz) - the derivative of the production function.

- "additional output from increasing input."

- generally diminishing

- "additional output from increasing input."

- generally diminishing

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Marginal Revenue (MR):

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equals the price of the output.

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Multiple Inputs Review

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Isoquants (contour lines of production function)

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- represent different combinations of inputs that produce the save level of output.

- shape of curve depends on how substitutable inputs are.

- shape of curve depends on how substitutable inputs are.

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Shapes of Isoquants:

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- Cobb-Douglas (downward sloping convex)

- Perfect substitutes (Linear "straight line")

- Perfect complements (L-Shaped)

- Perfect substitutes (Linear "straight line")

- Perfect complements (L-Shaped)

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Slope of Isoquant

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equals the Marginal Rate of Technical Substitution (MRTS).

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Marginal Rate of Technical Substitution (MRTS), where z1 and z2 are inputs

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- equals the negative ratio of marginal products.

= -(dq/dz1)/(dq/dz2) <--- partial derivatives.

= -(dq/dz1)/(dq/dz2) <--- partial derivatives.

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Optimal hiring (or purchasing) rule for multiple outputs

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MRTS = -(w1/w2)

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Cost Functions Review

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Average Cost (AC) Curve has no vertical intercept.

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Marginal Cost (MC) cuts AC and Average Variable Cost (AVC) at their minimums.

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If price equals minimum AC, firm will make zero economic profits

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If price falls below minimum AC, firms will shut down in the long run.

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In the short run, a firm will operate as long as it covers its variable cost.

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Calculating Cost Functions

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Fixed Cost, if TC = 100 + 2q^2 + 3q

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= 100

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Variable Cost, if TC = 100 + 2q^2 + 3q

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= 2q^2 + 3q

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Marginal Cost, if TC = 100 + 2q^2 + 3q

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= (dTC/dq) = 4q + 3

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Average Cost, if TC = 100 + 2q^2 + 3q

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= (TC/q) = (100/q) + 2q + 3

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Average Variable Cost, if TC = 100 + 2q^2 + 3q

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= (VC/q) = 2q +3

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Fixed Cost:

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the part of Total Cost that does not vary with output.

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Variable Cost:

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the part of Total Cost that varies with output.

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Marginal Cost:

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- the rate at which cost changes as output changes.

- "the slope of the cost function."

- "the slope of the cost function."

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Average Cost:

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Total Cost divided by Total Quantity Produced.

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Average Variable Cost:

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Variable Cost divided by Total Quantity Produced.

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Cost Minimization Review

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Cost Minimization:

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the choice of factors that minimize production costs can be determined by finding the point on the isoquant that has the lowest associated isocost curve.

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Cost Function: C(x,y,z,...):

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measures the minimum costs of producing a given level of output at given factor prices.

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Sunk costs are not recoverable

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Cost Curves Review

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Average Cost Function:

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measures the cost per unit of output.

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Average Variable Cost Function:

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measures the variable costs per unit of output.

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Average Fixed Cost Function:

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measures the fixed costs per unit of output.

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Marginal Cost Function:

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measures the CHANGE in costs for a given change in output.

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Firm Supply Review

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Profit Maximization Condition:

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- MR = MC

- P = MC

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**REMEMBER*******- MR = MC

- P = MC

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Profit (pi) = Total Revenue (TR) - Total Cost (TC)

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Average Profit:

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= Average Revenue (AR) - Average Cost (AC) = Price (pi) - Average Cost

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Happy Firm:

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= P > AC

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Unhappy Firm:

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= P < AC

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Firms in the Short Run:

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- to stay in business: P > AVC

- shut down point: P < AVC

- shut down point: P < AVC

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Profit Per Unit

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= P - AC

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Industry Supply Review

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Industry Supply:

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= the sum of firm supply curves.

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Price Taker:

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- "n" is fixed in the short run.

- "n" is variable in the long run.

- "n" is variable in the long run.

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Monopoly Review

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A firm with market power faces a downward sloping demand curve.

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to sell more units, it must cut its price.

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Game Theory and Oligopoly Review

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Nash Equilibrium:

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- "a best response to a best response."

- there may be another option with higher payoffs for both players, but it is not the equilibrium.

- there may be another option with higher payoffs for both players, but it is not the equilibrium.