Question

Imagine the market for Good X has a demand function of QDX = 100 – 2PX – 4PY + .05M + .1AX and a supply function of ...


Imagine the market for Good X has a demand function of QDX = 100 – 2PX – 4PY + .05M + .1AX and a supply function of QSX = 4PX – 10, where PX is the price of Good X, PY is the price of Good Y, M is the average consumer income and AX is the amount spent to advertise Good X. If PY is $3, M is $24,000, AX is $500, find the equilibrium quantity of Good X.

Answer

To find the equilibrium quantity of good X we have to equate the supply and demand of good X because the equilibrium quantity is determined where demand equals the supply of a good.

QDX=1002PX4PY+.05M+.1AXQSX=4PX10PY=$3M=$24,000AX=$500Put QSX=QDX4PX10=1002PX4PY+.05M+.1AX4PX10=1002PX(4×3)+(0.05×24,000)+(0.1×500)4PX10=1002PX12+1,200+504PX+2PX=10012+1,200+50+106PX=88+1,200+50+106PX=1,288+50+106PX=1,338+106PX=1,348PX=1,3486PX=224.67Put PX=224.67 in supply equation to find equilibrium quantity.QSX=4PX10QSX=4×224.6710QSX=898.6810QSX=888.68The equilibrium quantity of good X=888.68

Therefore, the equilibrium quantity of good X is 888.68 units.

Recent Questions