Answer to Question #298287 in Economics of Enterprise for ashwini

Question

the demand curve faced by a Monopolist is p= 120-3Q.the marginal cost curve in factory 1and factory 2 are respectively as follows MC1=10+20Q1 MC2=60+5Q2 what is the equilibrium price

Answer 1

Equilibrium Price

$P=120-3Q$

$MC1=10+20Q1$

$MC2=60+5Q2$

To get the firms quantity at equilibrium from the two factories Marginal Cost we get the total Marginal Cost$(MC_T)$ . Equating $MC_T=MR_T$ gives the quantity of the firm. $(MR_T)$ is equal to the firms AV with similar intercept but double the slope.

$MC_T=Q=Q1+Q2$

$=10+\frac{MC1}{20}+60+\frac{MC2}{5}$

$=70+\frac{5}{20}MC_T=\frac{20}{5}Q+70=4Q+70$

$MR_T=AR\ with\ double\ the\ slope$

$AR=P=120-3Q$

$MR_T=120-6Q$

$MC_T=MR_T;$

$4Q+70=120-6Q$

$10Q=50$

$Q=5$

Replacing the quantity amount in the demand function we get the equilibrium price as;

$P=120-3(5)$

$\bold{P=105}$