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# Consider a region where the self-sufficient wage is constant at $4. Suppose the payoff from innovation in a city with population n (measured in thousands) is a. Suppose a group of 1 (thousand) workers form a city. Will other workers have an incentive to join the cluster? b. Suppose a group of 9 (thousand) workers form a city. Will other workers have an incentive to join the cluster? c. Compute the (stable) equilibrium size of the innovation city.

**Chapter 2, Problem 12**

(choose chapter or problem)

**QUESTION:**

Consider a region where the self-sufficient wage is constant at $4. Suppose the payoff from innovation in a city with population n (measured in thousands) is \(\pi \left( n \right) = 2 + {n^{1/2}} - \left( {n/10} \right)\).

a. Suppose a group of 1 (thousand) workers form a city. Will other workers have an incentive to join the cluster?

b. Suppose a group of 9 (thousand) workers form a city. Will other workers have an incentive to join the cluster?

c. Compute the (stable) equilibrium size of the innovation city.

### Questions & Answers

**QUESTION:**

Consider a region where the self-sufficient wage is constant at $4. Suppose the payoff from innovation in a city with population n (measured in thousands) is \(\pi \left( n \right) = 2 + {n^{1/2}} - \left( {n/10} \right)\).

a. Suppose a group of 1 (thousand) workers form a city. Will other workers have an incentive to join the cluster?

b. Suppose a group of 9 (thousand) workers form a city. Will other workers have an incentive to join the cluster?

c. Compute the (stable) equilibrium size of the innovation city.

**ANSWER:**

Step 1 of 4

Given data:

Consider a region where the self-sufficient wage is constant at 4. Suppose the payoff from innovation in a city with population n (measured in thousands) is \(\pi \left( n \right) = 2 + {n^{1/2}} - \left( {n/10} \right)\).