Micro Economics Study Guide

1. Labor (Competitive Market)
   
   1. Find MRP_L (demand for labor curve)
      
      1. MRP_L = (MR)(MP_L)
         
      2. MR = P = MC
         
      3. MP_L = derivative of given production function
         
   2. Find the firm's profit maximizing quantity of labor
      
      1. Maximum profit = MRP_L = w à solve for L
         
   3. If asked to graph the MRP_L line:
      
      1. Set L = 0 to find the y-intercept (wage)
         
      2. Set MRP_L = to 0 for the x-intercept (labor)
         
         

         
          

2. Long-run equilibrium (Competitive Market)
   
   1. Find MC
      
      1. MC = derivative of the given cost function
         
      2. MC = P = MR
         
   2. Find ATC
      
      1. ATC = total cost function divided by q
         
      2. P = MR = ATC
         
   3. Set MC = ATC (because in the long-run all fixed costs become variable)
      
      1. Solve for q, which equals the long-run equilibrium quantity
         
      2. NOTE: q is the quantity for one firm
         
   4. Substitute q into the MC function and solve for p, which is the long-run equilibrium market price
      
   5. Substitute p into the demand function (Q_D) to find the total quantity demanded.
      
      1. NOTE: Q_D is the quantity for the entire industry.
         
   6. Find the total number of firms operating in the long-run by this formula:
      

      Total Demand (Q_D)
      

q

1. Substitute the market price into the Q_D function to find Q_D
   

1. Find elasticity of demand: E_D = (P/Q)(-b)
   
   1. (-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)
      

 

1. Short-run equilibrium (Competitive Market)
   
   1. Find MC and AVC
      
      1. AVC = derivative of total variable costs as given in the cost function
         
      2. 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.
         
   2. MC = Q_S (the supply curve) above AVC, and firm will produce only if P > AVC, so rearrange MC function to find Q_S
      
      1. Remember: MC = P
         
      2. 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.
         
      3. NOTE: review the notes regarding the impact of sunk costs on short-run equilibrium.
         
   3. Set Q_S = Q_D to find short-run equilibrium price
      

 

 

1. Taxes/Subsidies
   
   1. Set price buyers pay = to sellers receive + the tax: P_b = P_s + Tax OR
      
   2. Set price sellers receive = to price buyers pay + subsidy: P_s = P_b + Subsidy
      
   3. Set Q_D = Q_S
      
   4. 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.
      
   5. 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.
      
   6. E_D = ∆P_b
      

   
   P*
   

   
    

2. Monopoly
   
   1. 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.
      
   2. Find MC, Total Revenue (TR), and MR
      
      1. TR = (P)(Q); i.e. substitute the linear demand curve for P and multiply the entire function by Q to find TR.
         
      2. Remember: the marginal function is always the derivative of the total function
         
      3. NOTE: MR has the same intercept as the inverse linear demand curve but the slope is multiplied by 2.
         
         1. Example: inverse linear demand curve: P = 700+5Q so
            

            MR = 700+10Q
            

   3. Set MC = MR to find profit maximizing Q
      
   4. Substitute Q into the inverse demand function to find P
      
   5. Profit = (P)(Q) – total cost function
      

 

 

1. Multi-plant Monopoly
   
   1. Same steps as above but with new rules:
      
   2. MR must = MC at each plant to maximize profit, so MR = MC_T = MC₁ = MC₂
      
   3. Q_T = Q₁ + Q₂
      
      1. To find Q_T, rearrange MC₁ and MC₂ to solve for Q₁ and Q₂, then add them together to find Q_T (total Q).
         
   4. Profit = Revenue – Total Cost = (P)(Q_T) – (C₁)(Q₁₎ – (C₂)(Q₂)
      

      
       

      
       

2. Multi-market Monopoly
   
   1. Same steps as multi-plant monopoly
      
   2. MR must = MC in each market to maximize profit, so MC = MR₁ = MR₂
      
   3. Profit = Revenue in each market – Cost = P₁Q₁ +P₂Q₂ – C(Q₁ + Q₂)