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The consumer’s indirect utility is generally:

With permit trading in the environment described in the previous question with two firms, the equilibrium price will be:

Consider the following economy: A representative consumer allocates a fixed 24‐hour time endowment between labor and leisure. Leisure provides direct utility, while labor earns income used for consumption. A single firm hires labor to produce output, but production emits pollution, generating an external cost. A benevolent planner internalizes this cost when choosing labor. This exercise explores private versus social optima, the role of taxation, and comparative statics when preferences or technology change.  Consumer:

In the two firm environment described above,  after trading, firm 2 will 

If investors are risk‐neutral, what is the effective yield on the corporate bond they would expect, assuming they were only concerned about the risk of heatwaves?

In the two firm environment described above, after trading, firm 1 will 

At

Imposing

The difference in the planner’s FOC and the consumer’s FOC can be explained by:

Which algebraic expression is the consumer’s FOC, assuming no income taxes?