Quantity Produced Total Cost 0 $15 1 $21 2 $33 3 $50 4 $72 5 $95 6 $120 1. Migue
ID: 1237032 • Letter: Q
Question
Quantity Produced Total Cost0 $15
1 $21
2 $33
3 $50
4 $72
5 $95
6 $120
1. Miguel is a farmer who produces oats. The oat market is a pure competition market. Miguel is now making choices in the short run. The going rate for oats is currently $24 per unit. The total cost function is as the table above shows. What is the profit-maximizing level of output? Explain your answer.
2. Miguel is now looking at the long run so that he can plan for the future.
a) Should Miguel expect a change in the number of firms in the industry, given the information from question 1? Explain your answer.
b) More time passes, such that the oat industry is in long run equilibrium with a constant cost industry. The government imposes a $1.50 tax per unit of oats. How will this affect the quantity of output in the long run for Miguel? Explain your answer.
Explanation / Answer
Quantity Produced Total Cost
0 $15
1 $21
2 $33
3 $50
4 $72
5 $95
6 $120
1. Miguel is a farmer who produces oats. The oat market is a pure competition market. Miguel is now making choices in the short run. The going rate for oats is currently $24 per unit. The total cost function is as the table above shows. What is the profit-maximizing level of output? Explain your answer.
Profit maximization is always achieved when Marginal Cost (MC) equals Marginal Revenue (MR). In other words, MC = MR.
Now, we have our total cost. Marginal cost is simply the derivative of the total cost function -- the slope of the function; the amount by which quantity x changed in cost when we moved to quantity (x + 1).
In a perfectly competitive market, the marginal revenue equals the price. Here, the price is given at $24. So, we want a MC = $24 (or as close to it as possible) to maximize our profit.
At which level of output does the total cost increase by $24?
Well, TC increases by $27 at the output 3 and $22 at the output 4.
Since $22 is closer to $24 than $27, we will produce an output of 4 because that is where MC is closest to MR -- where, by definition, we maximize profit.
Answer: 4
2. Miguel is now looking at the long run so that he can plan for the future.
a) Should Miguel expect a change in the number of firms in the industry, given the information from question 1? Explain your answer.
No; though firms in perfect competition are always entering and exiting the market, the number of firms tends to remain relatively constant.
b) More time passes, such that the oat industry is in long run equilibrium with a constant cost industry. The government imposes a $1.50 tax per unit of oats. How will this affect the quantity of output in the long run for Miguel? Explain your answer.
This will cause the price -- the MARGINAL REVENUE -- of each oats unit to increase from $24 to $25.50.
This means that we are now seeking a marginal cost as close as possible to $25.50, NOT $24. This means that we'll have to cut back output to 3, since at that output MC is $27, which is closer to $25.50 than the $22 MC at an output level of 4.
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