Answer to Question #168872 in Microeconomics for n2222

Question

epresented by the equation 𝑃^D= 20 − 𝑄 , where 𝑃^D is the price paid by the consumer and Q is quantity. Also, suppose the supply schedule can be represented by the equation

𝑃^s = Q, where 𝑃^s is the price received by the producer. Based on this information, answer questions A- E

A.Calculate the equilibrium price and quantity in this market. Draw the graph showing the equilibrium quantities and the intercepts.

C.Calculate the producer surplus, consumer surplus and total surplus at equilibrium.

D.Calculate the producer surplus, consumer surplus, deadweight loss and total surplus at P=$12.

E.What will be the price elasticity of demand and price elasticity of supply if P increases from $10 to $11? (Use mid-point formula). 

Answer 1

A. Market equilibrium occurs when $P_d=P_s$:

$$20-Q_E=Q_E,$$ $$20=2Q_E,$$ $$Q_E=10.$$

Then we can find equilibrium price:

$$P_E=20-10=\$10.$$

Let's draw the graph showing the equilibrium quantities:

C. Let's calculate producer surplus, consumer surplus and total surplus:

$$PS=\dfrac{1}{2}\cdot(\$10-0)\cdot10=\$50,$$ $$CS=\dfrac{1}{2}\cdot(\$20-10)\cdot10=\$50,$$ $$TS=PS+CS=\$50+\$50=\$100.$$

D. Let's calculate the producer surplus, consumer surplus, deadweight loss and total surplus at P=$12:

$$PS=\dfrac{1}{2}\cdot(\$12-2)\cdot8=\$40,$$ $$CS=\dfrac{1}{2}\cdot(\$20-12)\cdot8=\$32,$$ $$DWL=\dfrac{1}{2}\cdot(\$12-\$10)\cdot(10-8)=\$2,$$ $$TS=PS+CS=\$40+\$32=\$72.$$

D. If price increases from $10 to $11, the quantity demanded decreases from 10 to 9 units. Let's calculate the price elasticity of demand using midpoint formula:

$$E_d=\dfrac{\dfrac{Q_2-Q_1}{(Q_2+Q_1)0.5}}{\dfrac{P_2-P_1}{(P_2+P_1)0.5}}=\dfrac{\dfrac{9-10}{(9+10)\cdot0.5}}{\dfrac{\$11-\$10}{(\$11+\$10)\cdot0.5}}=-1.1.$$ $$E_s=\dfrac{\dfrac{Q_2-Q_1}{(Q_2+Q_1)0.5}}{\dfrac{P_2-P_1}{(P_2+P_1)0.5}}=\dfrac{\dfrac{9-10}{(9+10)\cdot0.5}}{\dfrac{\$11-\$10}{(\$11+\$10)\cdot0.5}}=-1.1.$$