# Questions tagged [consumer-theory]

the study of consumer choice and its fundamental underpinnings in preferences and constraints.

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### Optimal consumption for infinite number of periods and exogenous income

I have the following optimization problem: $\max_{\{c_t, s_{t+1}\}} \Pi_{t=0}^\infty c_t^{\beta^t}$ $\text{subject to } \space c_t + s_{t+1} = y_t + (1 + r) s_t \text{ and } s_0 = 0$ How do I find ...
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### Calculate income and sustitution effect from utility funcion

Utility function $U(x_1 , x_2) = x_1 + 4 * x_2$ $p_1 = 3, p_2 = 8, m =120$ $p_2$ changes from $8$ to $10$ How can I calculate the income and substitution effect. I first thought about calculating ...
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### Pigouvian tax with general utility function

Suppose person a's consumption of good $y$ imposes a negative externality on person b. Person a's utility maximisation problem is $$\max_{x_a,y_a} \ u_a(x_a,y_a),$$ subject to $$p_x x_a+p_y y_a=e_a.$$ ...