Exercise
1. What is a perfectly competitive market? What features or assumptions do these industries have?
2. What is the difference between the short run and the long run? In the long run, how much profits do all firms in a perfectly competitive market earn?
3. How do we find the average total cost, average fixed cost, marginal cost, and marginal revenue? What do each of these mean?
4. What is the point at which producing is no longer profitable? What is the shutdown point for a firm? What should a firm do if it is not profitable, but not at the shutdown point? Why?
5. The table below describes a partial demand function. Estimate marginal revenue for the third unit.
|
Quantity Demanded
|
Price
|
|
1
|
30
|
|
2
|
28
|
|
3
|
24
|
|
4
|
12
|
6. Production Under Perfect Competition
Consider the problem faced by Alice, the owner of a small restaurant in Stockbridge, Massachusetts. In the short run (this week), her scale of production is fixed with respect to all factors except labor: she can hire as many hours of help as she wants at $10 per hour. Her fixed costs (all of which are unavoidable) total $10000 per week.
Alice's production of meals this week is described by the function
Y = 100√L
where Y is meals served per week and L is hours of labor hired.
Graph the production function above (for 0 to 900 hours of labor input). Explain what is meant by "diminishing marginal returns" to a factor of production and illustrate using this production function.
Calculate Alice's total cost of producing 200, 300, and 400 meals per week. Does this production function result in "increasing marginal costs"?
Now suppose that there are a large number of restaurants in Stockbridge, all of them too small to affect the price of meals, and that meals are a homogeneous good. Assuming that the market clears at $10 per meal, so that Alice can sell as many meals as she wants at $10 each, what is Alice's total revenue and profit at 200, 300, and 400 meals per week? Graph Alice's total revenue and total cost.
How many meals will Alice choose to produce this week? What is her profit (or loss) at this level of production? Suppose instead that Alice must pay $20 per hour to hire labor. How will this change Alice's production decision and profit?
Hint: TC = 10000 + Q2/10000, MC = Q/500, P=MR=10, TR = 10Q