Optimality condition for consumer: the marginal utility per dollar spent on each good is equal when the consumer consumes optimally, \(\frac{MU_x}{P_x} = \frac{MU_y}{P_y}\).Marginal rate of substitution: the rate at which a consumer is willing to substitute between the two goods, shown by the slope of the indifference curve, \( - \frac{MU_x}{MU_y}\). Equal to the price ratio at optimality. Price elasticity of demand: the proportional change in the quantity demanded of a good resulting from a proportional change in its price, \(\epsilon _{x} = \frac{\frac{\Delta x}{x}}{\frac{\Delta P_x}{P_x}} = \frac{\partial x}{\partial P_x} \cdot \frac{P_x}{x}\).Income elasticity: the proportional change in the quantity demanded of a good resulting from a proportional change in the consumer's income, \(\epsilon _{I} = \frac{\frac{\Delta x}{x}}{\frac{\Delta I}{I}} = \frac{\partial x}{\partial I} \cdot \frac{I}{x}\).Cross-price elasticity: the proportional change in the demand of one good resulting from the proportional change in the price of another good, \(\epsilon _{xy} = \frac{\frac{\Delta x}{x}}{\frac{\Delta P_y}{P_y}} = \frac{\partial x}{\partial P_y} \cdot \frac{P_y}{x}\).Monopolist and elasticity: a monopolist will never choose to operate where the demand curve is inelastic, \(MR = p[1 + \frac{1}{ \epsilon}]\) where p is price and elasticity is negative (naturally). This is because the marginal revenue is less than the marginal cost at this point. Factor exhaustion theorem: factors of production are paid their marginal revenue product, \(h_a = mrp_a\). To derive: \(MC \equiv \frac{h_a}{mp_a}\). Dividing both sides by marginal revenue: \(\frac{MC}{MR} = \frac{h_a}{mp_a \cdot MR}\). We know that the marginal revenue product is equal to the marginal product (quantity) times the marginal revenue it generates (dollars): \(mp_a \cdot MR = mrp_a\). \(\frac{MC}{MR} = \frac{h_a}{mrp_a}\). Since the firm's equality condition for profit-maximization in the product market is MR = MC, it must also be that at the same output quantity, \(h_a = mrp_a\). Cost/product reciprocals: \(MC = \frac{dTC}{dQ} = \frac{dTC}{dL} \cdot \frac{dL}{dQ} = P_L \cdot \frac{1}{\frac{dQ}{dL}} = P_L \cdot \frac{1}{MP_L}\).Insurance: if the expected utility function takes the form, \(E(u) = p(w_g^n)\), then the optimal amount of insurance to maximized utility will be found by, \(\max p(w_g -pxi)^{n} + (1 - p)(w_b - pxi + i)^{n}\).Returns to a factor of production: in Cobb-Douglas form, given by the exponents, \(Q = K^\alpha L^\beta \Longrightarrow \alpha, \beta\). Increasing if positive. Returns to scale: in Cobb-Douglas form, given by the sum of the exponents, \(k^{\alpha + \beta}(Q) = kK^\alpha kL^\beta \).Coefficient of absolute risk aversion: a way to quantify risk-aversion of an agent, \(CARA = - \frac{u''}{u'}\). The larger the coefficient, the greater the risk-aversion. Marginal revenue product: the marginal effect on revenue (MR) due to the marginal increase in the output (MP), \(MRP_x = MR_y \cdot MP_x = p(y) \cdot (1 + \frac{1}{\epsilon}) MP_x\). Equal to the value of the marginal product in competition since marginal revenue is equal to price, \(pMP_x\). Sum of infinite series: \(\sum \limits ^\infty _{t = 0} \beta ^t= \frac{\beta}{1 - \beta}\) or \(\sum \limits ^\infty _{t = 0} \beta ^t X = \frac{X}{1 - \beta}\).Mixed strategy NE: setting probabilities to your play such that the payoffs for each of your opponent's choices are equal, \(p(A) + (1 - p)(B) = p(C) + (1 - p)(D)\).