📘 microeconomics

1. **State the problem:** We have a duopoly with market demand $P=100-0.5Q$ where $Q=Q_1+Q_2$, and cost functions $C_1=5Q_1$ and $C_2=0.5Q_2^2$. We want to find the Cournot equilib

1. **Problem statement:** Given the demand function for a monopolist $Q = 150 - 4P$, find expressions for Total Revenue (TR), Marginal Revenue (MR), and Average Revenue (AR). Then

1. **Problem Statement:** A company produces widgets with production function $$Q = \alpha L^{0.5} K^{0.5}$$ where $L$ is labor and $K$ is capital. The market price per widget is 1

1. **Problem Statement:** A two-product firm faces the demand functions:

1. **Problem statement:** Two firms produce quantities $q_1$ and $q_2$ facing a market demand $P = 100 - 1.5Q$ where $Q = q_1 + q_2$. Their cost functions are $C_1 = 100q_1$ and $C

1. **Problem Statement:** Determine Big Top's profit-maximizing price, output, and economic profit when charging a single price for all tickets.

1. **Problem statement:** En konsument har nyttefunksjonen $$U(x,y) = x^\alpha y^\beta$$ og ønsker å maksimere denne gitt budsjettbetingelsen $$5x + 5y = 100$$.

1. **بيان المسألة:** لدينا دالة المنفعة $$u = x^{\frac{1}{4}} y^{\frac{3}{4}}$$.

1. **Problem Statement:** Find the Marshallian demand functions given a consumer's utility maximization problem with a budget constraint. 2. **General Setup:** The Marshallian dema

1. **Stating the problem:** We have a demand function for good X: $$X = 20 + MPx^{-2}$$ where $M$ is income, $P_x$ is the price of good X, and $X$ is quantity demanded.

1. **Nyatakan masalah:** Diberikan fungsi biaya rata-rata (AC) dan pendapatan rata-rata (AR) sebagai berikut: $$AC = 15 + \frac{8000}{Q}$$

1. **Stating the problem:** Given a budget constraint $p_x x + p_y y = M$ and a set of indifference curves $K_1, K_2, K_3$, find the maximum consumer satisfaction (utility) represe

1. **Problem Statement:** Given two figures showing Sam's consumption bundles of herbal tea and pancakes, and his preferences, determine which bundles Sam strictly prefers to bundl

1. **State the problem:** Avery has $30 to spend on cheeseburgers and seltzer. The budget constraint shows all combinations of cheeseburgers and seltzer he can buy. 2. **Identify p

1. **Problem Statement:** Determine the output level and price at which the firm maximizes profit given the curves MC (Marginal Cost), ATC (Average Total Cost), MR (Marginal Revenu

1. **Problem Statement:** We are given a perfectly competitive firm producing terrible towels with the following curves: Average Total Cost (ATC), Marginal Cost (MC), Average Varia

1. **Problem Statement:** We have a utility function $$U(x,y) = x^y$$ with prices $$p_x = 3$$ and $$p_y = 4$$, and income $$I = 72$$.

1. **Problem statement:** Find the values of $x$ and $y$ that maximize the utility function $$U(x,y) = x^y$$ subject to the budget constraint $$3x + 4y = 72$$ using the Lagrange mu

1. **Problem Statement:** Find the values of $x$ and $y$ that maximize the utility function $U(x,y) = x^y$ subject to the budget constraint $3x + 4y = 72$ using the Lagrange multip

1. **Problem Statement:** We have a firm's production function given by $$q = a k^\alpha l^\beta$$ where $a>0$, $0<\alpha<1$, and $0<\beta<1$. The input prices are $w$ for labor ($

1. **Problem statement:** We have a firm's production function given by $$Q = A k^\alpha l^\beta$$ where $0 < \alpha < 1$ and $0 < \beta < 1$. The input prices are $w$ for labour (