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# Theory of the Firm Question watch

1. Barbara’s Bats (BB) sells cricket bats around the world. The firm faces a demand curve given
by
Q = 10 - 0.4P
where Q is measured in the thousands of bats and P is the £ price per bat. BB has a
marginal cost curve given by
MC = 5Q
i. Solve for BB’s profit maximising level of output. Show this profit maximising decision
graphically.
ii. What price will BB charge to maximise profits?
iii. Calculate the deadweight loss at the profit-maximising level of output.
2. i. Profit maximising level of output will be where MR = MC. You can get MR by differentiating TR with respect to Q. You start with Q = 10 - 0.4 P. Rearrange in terms of P and then multiply by Q, so you get an expression for TR (as TR is PQ) and then differentiate to get MR. Then you can set MR = MC. You will also have to sketch the MR and MC curves and show where MR and MC cross, and go up from this point to the demand curve to find P.

ii. You will have a value for Q where MR = MC, this is the profit maximising level of output. Then just put that back in to the demand function to get P at that level.

iii. Where you have drawn the curves you have to compare the profit maximising point of output with the socially optimal level of output (which is where it would be if P=MC rather than MR=MC. When you have gone up to the demand curve from the point at which MR=MC you will see a triangle between that and the point where P=MC. Find the area of this triangle.
3. Is it possible if you could show the workings swell or if you could upload a photo of the workings. It would be much appreciated.

Thanks

(Original post by MagicNMedicine)
i. Profit maximising level of output will be where MR = MC. You can get MR by differentiating TR with respect to Q. You start with Q = 10 - 0.4 P. Rearrange in terms of P and then multiply by Q, so you get an expression for TR (as TR is PQ) and then differentiate to get MR. Then you can set MR = MC. You will also have to sketch the MR and MC curves and show where MR and MC cross, and go up from this point to the demand curve to find P.

ii. You will have a value for Q where MR = MC, this is the profit maximising level of output. Then just put that back in to the demand function to get P at that level.

iii. Where you have drawn the curves you have to compare the profit maximising point of output with the socially optimal level of output (which is where it would be if P=MC rather than MR=MC. When you have gone up to the demand curve from the point at which MR=MC you will see a triangle between that and the point where P=MC. Find the area of this triangle.
4. What did you get for the deadweight loss?

(Original post by LeroySmith)
Barbara’s Bats (BB) sells cricket bats around the world. The firm faces a demand curve given
by
Q = 10 - 0.4P
where Q is measured in the thousands of bats and P is the £ price per bat. BB has a
marginal cost curve given by
MC = 5Q
i. Solve for BB’s profit maximising level of output. Show this profit maximising decision
graphically.
ii. What price will BB charge to maximise profits?
iii. Calculate the deadweight loss at the profit-maximising level of output.
5. What is the answer to this, really struggling to understand this!?

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Updated: November 19, 2015
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