Unconstrained Optimization
1. Assume that you can sell widgets at $25 per widgets, for as many
widgets as you can make. Assume that the marginal cost of producing
each widget increases with the number of widgets that are produced. The
formula is MC(Y) = Y2. For example, the marginal cost of producing the
second widget is 4.
a) Using Excel or similar spreadsheet program, calculate the revenues
for producing 1, 2, 3, … , 10 widgets. Calculate the marginal costs
of producing the 1, 2, 3, …, 10 widgets. Calculate the total cost to
produce 1, 2, 3, … , 10 widgets. Determine your profits for producing
1, 2, 3, …, 10 widgets. What level of production maximizes your
profits?
b) Remember from micro economics that in a perfectly competitive market,
a producer will produce the number of products such that MC = Price. Is
this the case here? Verify it.
Business Homework Solutions
#2749
Unconstrained Optimization
Unconstrained Optimization
1. Assume that you can sell widgets at $25 per widgets, for as many widgets as you can make. Assume that the marginal cost of producing each widget increases with the number of widgets that are produced. The formula is MC(Y) = Y2. For example, the marginal cost of producing the second widget is 4.
a) Using Excel or similar spreadsheet program, calculate the revenues for producing 1, 2, 3, … , 10 widgets. Calculate the marginal costs of producing the 1, 2, 3, …, 10 widgets. Calculate the total cost to produce 1, 2, 3, … , 10 widgets. Determine your profits for producing 1, 2, 3, …, 10 widgets. What level of production maximizes your profits?
b) Remember from micro economics that in a perfectly competitive market, a producer will produce the number of products such that MC = Price. Is this the case here? Verify it.
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