Daily exercise 1 for 9/9

Suppose that suppliers of a healthful product are currently selling 1000 units and receiving a seller price `P^s=$100`. The government would like to increase output to 1200 units by adopting a policy that would raise `P^s`. (You don't need to worry about the details of the policy but the usual way to do this would be a subsidy.) The government knows that the industry's supply elasticity `\eta_s=2`.

1. What would the new value of `P^s` need to be to achieve the output goal?
2. Please calculate the change in producer surplus that would result from the policy.

If you have more time, try doing the second piece of the policy design: figuring out what has to happen on the buyer side. Suppose the initial buyer price is `P^d=$100` , the initial quantity is 1000 (both same as the initial conditions for the the sellers), and the demand elasticity `eta=-1`.

3. What would the new value of `P^d` have to be in order to get buyers to purchase the target amount of the good?

When you're done, please scan your work and submit it.