The handmade snuffbox industry is composed of 100 identical firms, each having short – run total costs given by STC = 0.5q2 + 10q + 5 and short – run marginal costs by SMC = q + 10 where q is the output of snuffboxes per day.
a) What is the short –run supply curve for each snuffbox maker? What is the short – run supply curve for the market as a whole?
b) Suppose the demand for total snuffbox production is given by Q = 1,100 – 50P. What will be the equilibrium in this marketplace? What will each firm’s total short – run profits be?
c) Graph the market equilibrium and compute total short – run producer surplus in this case.
d) Show that the total producer surplus you calculated in part c is equal to industry profits plus industry short – run total fixed costs.
e) Suppose the government imposed a 3$ tax on snuffboxes in the industry described above.
i) How would this tax change the market equilibrium.
ii) How would the burden of this tax be shared between snuffbox buyers and sellers?
iii) Calculate the total loss of producer surplus as a result of the taxation of snuffboxes. Show that this loss equals the change in total short – run profits in the snuffbox industry. Why do not fixed costs enter into computation of the change in the short-run producer surplus?
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a) The short-run supply curve for each snuffbox maker can be determined by finding the quantity of snuffboxes each maker is willing to supply at different price levels. To find this, we need to equate the marginal cost (SMC) to the price level. In this case, SMC = q + 10.
To find the short-run supply curve for the market as a whole, we need to sum up the individual quantities supplied by each snuffbox maker at different price levels. Since there are 100 identical firms, we can multiply the quantity supplied by a single firm by 100.
b) To find the equilibrium in this marketplace, we need to set the quantity demanded equal to the quantity supplied. In this case, quantity demanded is given by Q = 1,100 - 50P. The quantity supplied is determined by the short-run supply curve. Set these two equations equal to each other and solve for the equilibrium price (P) and quantity (Q).
To find each firm's total short-run profits, we need to calculate the difference between total revenue and total costs. Total revenue can be found by multiplying the equilibrium price by the quantity produced by each firm. Total costs can be found by substituting the equilibrium quantity into the short-run total cost equation (STC).
c) To graph the market equilibrium, we plot the equilibrium price and quantity on a supply and demand graph. The equilibrium price is located at the intersection of the demand curve (Q = 1,100 - 50P) and the short-run supply curve. The equilibrium quantity is determined by substituting the equilibrium price into the demand curve.
To compute total short-run producer surplus, we need to find the area below the equilibrium price and above the short-run supply curve. This represents the difference between the price that firms receive and the minimum price they are willing to accept.
d) To show that the total producer surplus is equal to industry profits plus industry short-run total fixed costs, we need to calculate both of these. Industry profits can be found by multiplying each firm's total short-run profits by the number of firms (100 in this case) and then subtracting the industry fixed costs. Industry fixed costs can be found by multiplying the fixed cost per firm by the number of firms.
e) If the government imposed a $3 tax on snuffboxes, it would change the market equilibrium by shifting the supply curve upwards by the amount of the tax. The new equilibrium price would be higher, and the equilibrium quantity would be lower compared to the original equilibrium.
The burden of the tax would be shared between snuffbox buyers and sellers. Buyers would pay part of the tax in the form of a higher price, and sellers would also bear part of the tax in the form of lower profits. The exact distribution of the tax burden depends on the price elasticity of demand and supply.
To calculate the total loss of producer surplus as a result of the taxation, we need to find the difference between the original producer surplus and the producer surplus after the tax. This can be calculated by finding the difference between the areas below the equilibrium price and above the new supply curve, compared to the original equilibrium.
The change in total short-run profits in the snuffbox industry due to taxation can be calculated by finding the difference between the total short-run profits before and after the tax. This can be calculated by subtracting the new total costs (including the tax) from the original total costs. Fixed costs do not enter into the computation of the change in short-run producer surplus because they remain the same regardless of the tax.