Question

An American producer of steel produces and sells his products on two geographic regions: at home (H) and abroad (F). Demand on those markets is different. Also production costs in those two regions are different. Demand function on the home market is: PH = 260 – 0,1QH , and on the foreign market is PF = 240 (illimited amount can be sold for the price 240 dollars). Cost function on the home market is: CH = 1000 + 0,4Q2 H , and on the foreign market: CF = 5000 + 0,25Q2 F .

a. The products can not be exported due to high custom duties . Calculate amount of production and prices on home and foreign market to maximise profit. What will be profit? b. The company can export without limits and transport costs are low. Answer now the question from point a. c. Now suppose that transport costs are 16 dol. per ton. Answer the question from point a.

Answer 1

P_H=260-0.1Q_H

C_H=1000+0.4Q_H²

P_F=240

C_F=5000+0.25Q_F²

A) $TR_H=260Q_H-0.1Q_H^2$

$MR_H=260-0.2Q_H$

$MC_H=0.8Q_H$

$MR_H=MC_H$

$260-0.2Q_H=0.8Q_H$

${{Q_H}^*}=260$

$P_H=260-0.1(260)$

$P_H=\$234$

$\pi_H=TR_H-TC_H$

$\pi_H=260(260)-0.1(260)^2-(1000+0.4(260)^2)$

$\pi_H=\$32800$

$TR_F=240Q_F$

$MR_F=240$

$MC_F=0.5Q_F$

$MR_F=MC_F$

$240=0.5Q_F$

$Q_F=480$

$P_F=\$240$

$\pi_F=240(480)-(5000+0.4(480)^2)$

$\pi_F=\$18040$

B) $P=P_H+P_F$

$P=260-0.1Q+240$

$P=500-0.1Q$

$MR=500-0.2Q$

$C=C_H+C_F$

$C=1000+0.4Q^2+5000+0.25Q^2$

$C=6000+0.65Q^2$

$MC=1.3Q$

$MR=MC$

$500-0.2Q=1.3Q$

$Q=333$

$P=500-0.1(333)$

$P=\$466.7$

$\pi=500(333)-0.1(333)^2-(6000+0.65(333)^2)$

$\pi=\$77333.33$

C)if transportation costs are $16 per ton,

$P_H=260-0.1Q_H$

$Q_H=(2600-10P_H)-16=2584-10P_H$

$P_H=258.4-0.1Q_H$

$TR_H=258.4Q_H-0.1Q_H^2$

$MR_H=258.4-0.2Q_H$

$MC_H=0.8Q_H$

$258.4-0.1Q_H=0.8Q_H$

$Q_H^*=258.4$

$P^*_H=258.4-0.1(258.4)$

$P_H^*=\$232.56$

$\pi_H=258.4(258.4)-0.1(258.4)^2-(1000+0.4(258.4)^2)$

$\pi_H=\$32385.28$

$P_F=240-16=224$

$TR_F=224Q_F$

$MR_F=224$

$MC_F=0.5Q_F$

$224=0.5Q_F$

$Q_F^*=448$

$\pi_F=224(448)-(5000+0.4(448)^2)$

$\pi_F=\$15070.40$