There are 10 identical consumers whose demand is D: p = 20 - 10q. There are 10 identical firms, each firm's marginal cost is MC(q)= 5 + 5q. The market is competitive.

a) derive the market demand function
b) derive the market supply function
c) what is the market equilibrium quantity and price?

An excise tax of $3 per unit is imposed on firms (you may introduce Pc and Pf where consumers face the price Pc and firms face the price Pf)

d) analyze the tax incidence. That is, how is the $3 excise tax divided between the firm and the consumers?

for part a) would I just multiple the demand function given D: p=20 -10q by 10?

thanks in advance for your help.

ewrewre

a) To derive the market demand function, you need to sum up the individual demand of all consumers. Since there are 10 identical consumers, you can simply multiply the individual demand function by the number of consumers:

Market demand function (Qd): Qd = 10(20 - 10q)

b) The market supply function is derived by summing up the individual supply of all firms. Since there are 10 identical firms, you can multiply the individual supply function by the number of firms:
Market supply function (Qs): Qs = 10q

c) To find the market equilibrium quantity and price, you need to set the market demand equal to the market supply and solve for quantity (Q) and price (P).
Equating Qd and Qs: 10(20 - 10q) = 10q
Simplifying: 200 - 100q = 10q
Combining like terms: 110q = 200
Solving for q: q = 200/110 = 1.82 (rounded to two decimal places)

Substituting q back into either the market demand or supply equation to find the equilibrium price:
P = 20 - 10q
P = 20 - 10(1.82)
P ≈ 20 - 18.2
P ≈ 1.80 (rounded to two decimal places)

Therefore, the market equilibrium quantity is approximately 1.82 and the market equilibrium price is approximately 1.80.

d) To determine the tax incidence, we need to analyze how the $3 excise tax is divided between the firms and the consumers. The incidence of the tax refers to who ultimately bears the burden of the tax.

In this case, the excise tax is imposed on firms, so the firms are responsible for remitting the tax to the government. However, the burden of the tax can be shared between firms and consumers, depending on the price elasticity of demand and supply.

Since there is no information given about the price elasticity, we cannot determine the exact division of the tax burden. Generally, the incidence of the tax can be determined by analyzing the relative price elasticities of demand and supply. If demand is more elastic than supply, consumers will bear a larger share of the tax burden. Conversely, if supply is more elastic than demand, firms will bear a larger share of the tax burden.

Without further information, it is not possible to determine the specific division of the $3 excise tax between the firms and consumers.