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Question

For the monopolist's problem, I got the answer by taking derivative of pi function through Q:

pi=(a0-a1Q+n+e)*Q-c0+c1Q^2

My question is:

Do I need to multiply q in pi function, cuz the pi function use c but cost function use capital C?

To find the variance Q, is Q function equal to a0+n+e/2(a1+c1) , which is the answer I got in question one.




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微信图片_20200211180028.png

Question 2 - Modelling demand in a structural setting Now instead assume that in addition to the measurement error, 6, there is a structural shock to demand, 1], Le. a random variable that shifts the
demand curve up and down: P*:ao—oqQ—l—q and we observe this P“ with the same error as before: PIClo—G1Q+T]+€ Let EM] : 0 and Vhfl : 0%. Now assume that the market for walnuts is a monopoly, and the monopolist faces costs: C(Q) : Co +le2 and chooses Q to maximize profit: «(62) : P* x Q , C(Ql- Solve the monopolist‘s problem (i.e. solve for Q). What do you notice about the relationship between Q and 7]? Use your answer to the above to make a prediction about whether your estimator, 651 from Question (1) will work. Calculate C(P, Q) and V[Q] in terms of the structural parameters of the model. Now, derive an expression for the estimator 5:1 in terms of the structural parameters. Use this to argue that in this new setting, the estimator
won’t in general be consistent. . Set co : 0, c1 : 0.1, and 0% : 0.1, and retain the other parameters from the previous question. Simulate 500 samples of size 500,
compute the estimator, and show its distribution. Does the simulation prove your point in part (5)? .U‘PPJN." cn

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