Question: Suppose that Jill (Ted's sister), also gets excited about farming so she decides to plant something in the (huge) land she inherited. She decides to produce strawberries. There, she needs to use tractors (T) and farmers (F) who are willing to pick up the strawberries. The technology she has access to can be summarized by a Cobb-Douglas production function, where Qstrawberries \((\mathrm{T}, \mathrm{F})=10(\mathrm{TF})^{1 / 2}\)

When she starts operations, there are 10 tractors for rent in the local market and she rented them all in advance. The rental rate is $1 per day and she needs to keep them for at least 3 months. Agricultural wages are $7.50 per hour.

1. Given that the number of tractors is fixed, would you say that she faces increasing, diminishing or constant returns to labor? This is, doubling the amount of labor more than doubles, less than doubles or exactly doubles the number of strawberries produced?
2. How many workers is she going to hire if she wants to produce \(Q\) pounds of strawberries?
3. What is Jill's cost function?
4. What is her average cost function? And her marginal cost function?
5. If she chooses to produce \(Q=50\), what's her total cost, marginal cost and average cost? What if \(\mathrm{Q}=100 ? \mathrm{Q}=200\) ?
6. Graph the AC curve and the MC curve.
7. Now assume that the number of tractors is still fixed, but you just know that it is fixed at some level L What is the cost function now if you know that w=7.5, r=1 and we want to produce Q pounds of strawberries?
8. From all the possible numbers of tractors that she could have faced (I), which one would have produced the lowest short run cost? Here you need to find what value of I minimizes the expression you found in (g).
9. Substituting the value of I you just found into the cost function, what does it look like? (j) Now assume that after the three months she can reallocate her budget to produce more efficiently. Show that she faces constant returns to scale.

(k) What is Jill’s long run cost function?

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