There are three types of dance studios in a competitive market in Des Moines, Iowa. Due to the peculiarities of zoning in Des Moines, commercial space can be rented in only three sizes: 1000 square feet, 2000 square feet, and 3000 square feet. For each of the three sizes of dance studios, the information below shows the number of dance lessons that can be given by your full-time dance instructors. Iowa labor law requires you to hire people full-time or not at all. For every 1000 square feet of space you rent, the monthly rent is $5,000 and you must sign a one-year lease. The monthly wage for a full time dance instructor is $2,000. These represent all economic costs including the normal profit.

1000 sq. ft.		2000 sq. ft.		3000 sq. ft.
Number of Instructors	Lessons		Number of Instructors	Lessons		Number of Instructors	Lessons
0	0		0	0		0	0
1	100		1	123		1	139
2	152		2	187		2	193
3	193		3	237		3	263
4	215		4	263		4	319
5	233		5	286		5	366
6	249		6	306		6	407
7	263		7	323		7	430

Read the lecture notes for week three on returns to scale and remember the definition of a marginal product of an input is the change in output divided by the change in the input, holding other factors constant.

1. Given the wage and rental information above, for each level of studio size what is the short-run average total cost of producing 263 dance lessons? What is the long-run average total cost of producing 263 dance lessons? [Hint:Remember that the short run average total cost is equal to the average fixed cost plus average variable cost at that level of output. For long run average total cost look at the section on Economies of Scale in the notes and remember that you are looking for the long run average total cost at a specific quantity.] Explain in words why you chose each answer. (4 points)

Short run average total cost of 263 with 1000 sq. ft? __________________.

Short run average total cost of 263 with 2000 sq. ft? __________________.

Short run average total cost of 263 with 3000 sq. ft? __________________.

Long run average total cost of 263 units? _______________

Explanation for why you chose this Long run average total cost:

1. For firms with each studio size at each number of instructors, determine variable cost, total cost, average variable cost per lesson, average total cost per lesson, and the marginal cost of an additional lesson. (8 points)

Insert tables from Excel:

1. Due to differences in the periods of the leases that the various dance studios have signed, all three types of dance studios shops are currently in the market. If the price of a dance lesson is $70, and you seek to maximize profits, what is the optimal number of instructors to hire for each level of capital? What profits are earned in the dance studios for each type of capital? Explain why you made each choice in words. (6 points)

Optimal number of instructors for 1000 square feet: _______________________.

Optimal number of instructors for 2000 square feet: _______________________.

Optimal number of instructors for 3000 square feet: _______________________.

Maximum profit for 1000 square feet: _______________________.

Maximum Profit for 2000 square feet: _______________________.

Maximum Profit for 3000 square feet: _______________________.

Explanation for choices:

1. Consider the long run situation in the market where there will be strong price competition, dance studios can change their size, and dance studios easily enter and exit the market. What do you anticipate will be the price of a dance lesson in the long run? Based on that price, what will be the profit maximizing studio size and number of instructors? Explain why you come to these conclusions. (2 points)

Price in Long Run equilibrium _______________.

Profit maximizing square footage in Long run equilibrium ________________.

Profit maximizing number of workers in long run equilibrium _____________.

Explanation for your choices.