**Labor (Competitive Market)**- Find MRP
_{L}(demand for labor curve)- MRP
_{L}= (MR)(MP_{L}) - MR = P = MC
- MP
_{L}= derivative of given production function

- MRP
- Find the firm's profit maximizing quantity of labor
- Maximum profit = MRP
_{L}= w à solve for L

- Maximum profit = MRP
- If asked to graph the MRP
_{L}line:- Set L = 0 to find the y-intercept (wage)
- Set MRP
_{L}= to 0 for the x-intercept (labor)

- Set L = 0 to find the y-intercept (wage)

**Long-run equilibrium (Competitive Market)**- Find MC
- MC = derivative of the given cost function
- MC = P = MR

- MC = derivative of the given cost function
- Find ATC
- ATC = total cost function divided by q
- P = MR = ATC

- ATC = total cost function divided by q
- Set MC = ATC (because in the long-run all fixed costs become variable)
- Solve for q, which equals the long-run equilibrium quantity
- NOTE: q is the quantity for one firm

- Solve for q, which equals the long-run equilibrium quantity
- Substitute q into the MC function and solve for p, which is the long-run equilibrium market price
- Substitute p into the demand function (Q
_{D}) to find the total quantity demanded.- NOTE: Q
_{D}is the quantity for the entire industry.

- NOTE: Q
- Find the total number of firms operating in the long-run by this formula:
Total Demand (Q

_{D})

q

- Substitute the market price into the Q
_{D }function to find Q_{D}

- Find elasticity of demand: E
_{D}= (P/Q)(-b)- (-b) is the coefficient of variable cost, i.e. the slope of the Q
_{D}function. It is always negative for the linear demand function (Q_{D}= a-bP)

- (-b) is the coefficient of variable cost, i.e. the slope of the Q

**Short-run equilibrium (Competitive Market)**- Find MC and AVC
- AVC = derivative of total variable costs as given in the cost function
- You might as well find ATC too, just in case he asks you a long-run question as it relates to the originally short-run scenario. See Quiz 3 wheat markets example.

- AVC = derivative of total variable costs as given in the cost function
- MC = Q
_{S}(the supply curve) above AVC, and firm will produce only if P > AVC, so rearrange MC function to find Q_{S}

- Remember: MC = P
- NOTE: a firm will produce in the short-run if P < ATC because in the long run fixed costs will become variable. So, in the short-run the firm is only concerned with meeting AVC, so as long as P > AVC the firm will produce.
- NOTE: review the notes regarding the impact of sunk costs on short-run equilibrium.

- Remember: MC = P
- Set Q
_{S }= Q_{D}to find short-run equilibrium price

**Taxes/Subsidies**- Set price buyers pay = to sellers receive + the tax: P
_{b}= P_{s}+ Tax OR - Set price sellers receive = to price buyers pay + subsidy: P
_{s}= P_{b}+ Subsidy - Set Q
_{D}= Q_{S}

- Substitute P
_{b }or P_{s}into the Q_{D}or Q_{S}function (depending what you are solving for, the price paid by buyers or the price received by sellers) and solve for price. - Substitute the price you calculated back into the P
_{b }= P_{s}+ Tax or P_{s }= P_{b }+ Subsidy formula, again depending what you are solving for. - E
_{D}= ∆P_{b}

_{ }P*

- Set price buyers pay = to sellers receive + the tax: P
**Monopoly**- Find the inverse linear demand curve (aka industry demand curve) if it is not given to you. All you do is take the Q
_{D}equation and rearrange the variables to solve for P. - Find MC, Total Revenue (TR), and MR
- TR = (P)(Q); i.e. substitute the linear demand curve for P and multiply the entire function by Q to find TR.
- Remember: the marginal function is always the derivative of the total function
- NOTE: MR has the same intercept as the inverse linear demand curve but the slope is multiplied by 2.
- Example: inverse linear demand curve: P = 700+5Q so
MR = 700+10Q

- TR = (P)(Q); i.e. substitute the linear demand curve for P and multiply the entire function by Q to find TR.
- Set MC = MR to find profit maximizing Q
- Substitute Q into the inverse demand function to find P
- Profit = (P)(Q) – total cost function

- Find the inverse linear demand curve (aka industry demand curve) if it is not given to you. All you do is take the Q

**Multi-plant Monopoly**- Same steps as above but with new rules:
- MR must = MC at each plant to maximize profit, so MR = MC
_{T}= MC_{1 }= MC_{2}

- Q
_{T}= Q_{1 }+ Q_{2}

- To find Q
_{T}, rearrange MC_{1 }and MC_{2 }to solve for Q_{1}and Q_{2}, then add them together to find Q_{T}(total Q).

- To find Q
- Profit = Revenue – Total Cost = (P)(Q
_{T}) – (C_{1})(Q_{1) }– (C_{2})(Q_{2})

- Same steps as above but with new rules:
**Multi-market Monopoly**- Same steps as multi-plant monopoly
- MR must = MC in each market to maximize profit, so MC = MR
_{1}= MR_{2}

- Profit = Revenue in each market – Cost = P
_{1}Q_{1}+P_{2}Q_{2}– C(Q_{1}+ Q_{2})

- Same steps as multi-plant monopoly

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