Answer to Question #217551 in Macroeconomics for EMY

Question

6 A monopolist has demand and cost curves given by: (5 marks) QD = 10,000 - 20P TC = 1,000 + 10Q + .05Q2 

Answer 1

Given

$QD = 10,000 - 20P$

$TC = 1,000 + 10Q + .05Q^2$

$Q= 10,000 - 20P\\20P=10,000-Q\\P=\frac{10,000}{20}-\frac{Q}{20}$

$P=500-\frac{Q}{20}$

$TR=P\times Q\\$

$TR=(500-\frac{Q}{20})Q=500Q-\frac{Q^2}{20}$

$MR=500-\frac{Q}{10}$

$TC = 1,000 + 10Q + .05Q^2 \\MC=10+0.1Q$

$MR=MC\\500-\frac{Q}{10}=10+0.1Q\\500-10=0.1Q+\frac{Q}{10}\\490=\frac{Q}{5}\\Q=490\times5=2450$

$Q = 10,000 - 20P\\2450=10,000 - 20P\\20P=10,000-2450\\20P=7550\\P=377.5$