A firm sells two goods (X and Y) that are related in consumption. The estimated demand...
A firm sells two goods (X and Y) that are related in consumption. The estimated demand and cost conditions are:
PX = 20 – 0.1QX – 0.005QY
PY = 70 – 0.3QY – 0.1QX
MCX = 1 + 0.1QX
MCY = 2 + 0.25QY
What are the profit-maximizing levels of output for the two goods?
QX = 20, QY = 10
QX = 41, QY = 24
QX = 56, QY = 24
QX = 51, QY = 74
none of the above
Homework Answers
Rx = Px.Qx = 20Qx - 0.1Qx2 - 0.005QyQx
Ry = Py.Qy = 70Qy - 0.3Qy2 - 0.1QyQx
MRx = dRx/dQx = 20 - 0.2Qx - 0.005Qy
MRy = dRy/dQy = 70 - 0.6Qy - 0.1Qx
Profit is maximized where MRx = MCx and MRy = MCy
19 = 0.3Qx + 0.005Qy
68 = 0.85Qy + 0.1Qx
Qx = 62, Qy = 73 (none of the above)
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