Question

Now, assume that the demand in the fish market is given by: Demand: Quantity = 10, 100 − 100 ∙ Price 5. Find the equilibrium price and quantity, and represent the demand, supply, and equilibrium in a graph (with quantity in the horizontal axis and price in the vertical axis). 6. How much money is each firm making in profit? 7. If there is free entry to the fish market, how many firms will there be in equilibrium in the long run? Finally, imagine that the government sets a tax of $10 per unit on sellers. 8. Compute the equilibrium after tax and the tax revenue. 9. How much surplus do consumers lose due to the tax? And how much do sellers lose in aggregate profit? 10. The government decides to use the tax revenue to fully compensate consumers for their loss in consumer surplus due to the tax, and to use what- ever amount of money is left to partially compensate the sellers for their loss in profit. By how much money does the compensation fall short of the sellers’ loss?

Cost = 400 + Output + Output²

Answer 1

From the cost function MC = 1 + 2Q. Single firm supply function is MC = 1 + 2Q. This implies that Q = 0.5P - 0.5. For market supply curve we have 50Q = Qs = 25P - 25.

5. Equilibrium occurs when demand equals supply

25P - 25 = 10100 - 100P

125P = 10125

P* = 81 and Q* = 10100 - 8100 = 2000. With 50 firms, each firm produces 2000/50 = 40.

6. Profit for each firm = revenue - cost = 40*81 - (400 + 40 + 40^2) = 1200

7. If there is free entry to the fish market, long run price has AC = MC

400/Q + 1 + Q= 1 + 2Q

400/Q = Q

Q = 20 and MC = AC = 41. This is the long run price. At this price, quantity demanded in long run is Qd = 10100 - 100*41 = 6000. Each firm in the long run produces 20 units so there are 6000/20 = 300 firms in the long run.

Finally, imagine that the government sets a tax of $10 per unit on sellers.

8. This shifts the supply curve left. New supply is Qs = 25(P - 10) - 25 = 25P + 225

New equilibrium is at

25P - 275 = 10100 - 100P

125P = 9875

P* = 83 that buyers pay. Q (from new supply curve) = 25*83 - 275 = 1800. Price that sellers receive is 1800 = 25P - 25 or Pseller = $73

Tax revenue = 10*1800 = 18000.

9. Loss to consumer = (increased price)(quantity) + 0.5*(increased price)*(decreased quantity) = 2*1800 + 0.5*2*200 = 3800 and loss to producer =  (decreased price)(quantity) + 0.5*(decreased price)*(decreased quantity)

= 8*1800 + 0.5*(8)*(200) = 15200.

10. The government decides to use the tax revenue to fully compensate consumers for their loss in consumer surplus due to the tax, which is 3800 and to use the amount of money left which is 18000 - 3800 = 14200 to partially compensate the sellers for their loss in profit. Hence the compensation fall short of the sellers’ loss by $1000.