Question

Consider a competitive market with aggregate demand

D(p) = { 0 if p≥20
200−10p if p<20
​and aggregate supply
S(p) = { 0 if p≤5
20p−100 if p>5
​ Suppose the market is efficient, i.e. inverse demand accurately reflects marginal social value and inverse supply accurately reflects marginal social cost.
1. Find the equilibrium price p∗ and the quantity traded in equilibrium Q∗
. The government introduces a per-unit tax of t=$1 per unit traded. Hence, the price paid by consumers, pD , is no longer the same as the price received by producers, pS . The two prices differ by the amount of the tax and consumers pay a higher price (including the tax) than producers receive (net of the tax), pD − pS = t.



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Answer 1

The equilibrium price is $10 and the quantity traded in equilibrium is 100. The equilibrium price and quantity in a competitive market are determined by setting the aggregate demand equal to aggregate supply.

Step-by-step explanation:

To find the equilibrium price, we need to equate the quantity demanded and quantity supplied. In this case, the equilibrium price is the price at which the aggregate demand (D) equals aggregate supply (S). First, we set D(p) = S(p):

200 - 10p = 20p - 100.

Solving this equation for p, we get p = 10. Substituting this back into the demand function, we find that Q∗ = 200 - 10(10) = 100. Therefore, the equilibrium price is p∗ = $10 and the quantity traded in equilibrium is Q∗ = 100.

The equilibrium price and quantity in a competitive market are determined by setting the aggregate demand equal to aggregate supply. With the introduction of a $1 tax per unit, the supply curve shifts, creating different prices for consumers and producers, leading to a new equilibrium with a reduced quantity traded compared to the pre-tax situation.

The equilibrium price and quantity traded in a competitive market are found by equating aggregate demand to aggregate supply: D(p) = S(p). Initially, setting 200 - 10p = 20p - 100, we solve for p, which yields the equilibrium price p* = 10. Subsequently, the equilibrium quantity, Q*, is found by substituting p* into either the demand or supply equation, giving Q* = 100.

Introducing a tax of $1 per unit, the supply curve shifts left, increasing the cost for producers. This creates two prices: the price paid by consumers, Pc, and the price received by producers, Pp. The new equilibrium is found where S(p + t) = D(p), reflecting the new supply curve and the willingness of consumers to pay the price including tax.

Using these equations and conditions, we solve for the new equilibrium prices and quantities, now taking into account the tax imposed on the market. The new equilibrium will reflect the burden of the tax on both consumers and producers and will result in a reduced quantity traded compared to the previous tax-free scenario.